Background of the Invention Currently, radiant tubing is installed under flooring surfaces by press fitting tubing into a parallel track of extruded aluminum or polymers. The tubing extends out of the straight track curved and then installed in the opposing directions leaving a fixed geometry for installers of tubing.

Accordingly, there is a continuing need in the art for a type of building structure that can provide arrays of curved and straight tubing; curved and straight conduit pattern in a hexagonal building block with offset tab retainers for tubing retention during installation of radiant tubing, fire sprinkler systems, and/or wiring desired in the construction of a floor, wall ceiling, and wall. A further objective is to offset retainer tabs that hold the tubing within the conduit, providing a convenient fast tubing installation by walking (stepping on the tubing) the tubing into the conduit in a zig-zag (sign wave)

around offset tabs that retain the tubing. Offset tabs provides a low stress drop in installation rather than a press fit in parallel tracks.

Currently, building lumber boards, layered insulated panel structures, and composite materials are engineered products that must be custom manufactured for every job, requiring manual cuts to achieve the geometry's desired in a building. It would be far superior to use a building structure that does not require customization in order to assemble the geometric shapes required to construct a building or other structure with radiant heating tubing inherent in the building structure. Further, many materials are either not easy to cut, or are unhealthy to fashion on the job. It would be highly desirable to have a building structure that can tolerate high stress loads and does not require numerous amounts of customization.

Accordingly, there is a continuing need in the art for a type of building structure that can be used to produce most geometry desired in the construction of a building or other structure. It is also desirable for a building structure to recyclable, allowing building occupants to be able to change a building's geometry in relatively short time without cutting any panels to achieve the new geometry. This is useful since in the field of building materials, many composite materials are very difficult to cut, and many concrete fiber-type materials produce carcinogens when cut.

It is desirable to have building blocks that provide curved and straight radiant heating tube or fire sprinkler conduit formation in building structures. Radiant heating tubes are flexible, but are composite tubes that can break down, bend, and close the fluid path of the tubes inner diameter when attempts are made to bend the tube in a tight radius. This invention teaches geometric arrays of curved and straight conduit formation in building structure, providing radiant heating or other tubing an array of conduit matched to the radial curves specified by the manufacturers.

This invention teaches tileable building system, tamper resistant fasteners, curved and straight conduit arrays, equilateral male/female fastening, hexsuperelement analysis process of hexagon assemblies. Hexablocks, for the purposes of this invention are; tileable"common"hexagon shapes with integrated fasteners and based on a hexsuperelement service (a superelement finite element method analysis). Any building

material can be sold and easily assembled into thousands of shapes by users in prior art.

This invention teaches how human imagination can be converted directly to"real life" hexsuperelement based structures that are safe, if assembled exactly as the hexsuperelement code suggests would be the most optimized final assembly.

Hexsuperelement Service: Hexagons are the most efficient near round shapes to foam and assemble building geometries from. Hexsuperelements answer how insulated a building is, analysis building stresses and thermal properties, defining how many people can live, work or apply a building. Many materials exist that are difficult and expensive to shape into useful buildings or stages and this invention teaches how to tile these different materials into optimized structures. This invention teaches customers a hexsuperelement service process. The name hexsuperelement was coined from a term used in the field of structural analysis called the Finite Element Method. In the finite element method, superelements are mathematical entities that capture the behavior of complex structural bodies using a relatively small number of equations. Hexagon structures are analyzed most efficiently with superelements, since a single instance of the hexagonal superelement (i. e. , hexsuperelement) can be replicated to form roughly 90% of the total structure. The remaining portions of the structure consist of additional superelements representing various edge details, all of which fit up together at common connection points. With the structural analysis cast in this format, highly detailed structural calculations are easily and automatically performed on virtually any floor plan, and this is the key ingredient of hexsuperelement service.

A further objective of this invention is to apply a brand new foaming process developed to uniformly add air to most polymers. Hexagons can be foamed from any polymer with air/gas densities from 1% to 97% (percent) with many minerals added.

A new science to foam hexagon building blocks for homes and other structures is taught in this invention. This invention teaches how managing gas pressure around the mold can provide uniform foam with micro-cellular foam. Natural hexagon shapes made from uniform foaming processes enable optimized engineering analysis; automated design, and building code verification, Internet application processes will allow the customer to design

hexablock structures using online libraries of material properties and floor plans, perform appropriate code checks, produce engineering drawings and bill of materials.

Tileable hexagon building block with tamper proof fastener, build and rebuild without damage to hexablocks, fasteners ratchet into place holding the structure together, hexablock wiring conduit is molded in for lighting and sound, any wall thickness or height can be built, floors can be wired for any application, sound proofing is provided by spaced layering of hexablocks, and time is reduced substantially by the ease of rebuilding. Hexagon building structure with curved and straight conduits, array when tiled and tubing can be inserted uniformly.

Hexsuperelement service provides detailed structural analysis quickly providing confidence that the engineering design data is near the real life performance.

Prior art provides engineering information about a buildings first design, without a process to provided for future recycling of the original materials. Hexsuperelement service applied to used hexablocks provides the same state-of-the-art structural analysis tools used to perform the original new material analysis. Hexablock and hexsuperelement teaches a process to apply used or new hexablocks for recycling many materials.

The most sophisticated analysis is useless without accurate structural material properties. Rigorous laboratory tests of the custom high-tech materials insure quality information for each hexablock construction. This is true for the hexablock mechanical compression fasteners as well, which are ratcheted to maintain the original specification throughout the life of the building.

Hexsuperlement building plans represent a"sustainable"building with optimized superelement engineering data that can be rebuilt into any other new design.

Superelement computer analysis of stress in a hexagon building occurs very quickly and uniform predictable foam makes such an analysis a match to real applications.

A further objective of this invention is to apply triangles on hexagons combining the geometry of hexagon and triangles and cutting a groove in the triangle, which provides mounting secure fastener geometry. Equilateral triangles are molded onto hexagons in such a way that one third of the hexagon layers on top of the triangle

offsetting with aligned dowel holes for optional fasteners. In a wall triangles mount to each other inside the wall and hexagons face the inside and outside of the wall.

In still a further embodiment of the present invention, three equilateral triangles are molded onto a single hexagon in an alternating male/female array three female and three male. The male-triangle has a groove around its three base edges with a depth approximately one half of the height of the male-triangle, providing clearance for future assembly. The extension past the edge of the hexagon portion is approximately equal to the groove depth providing geometries that can be assembled and locked into place. In this 3-triangle hexagon monolith the extension (tongue) and groove on the male three male-triangles forces the hexagon into alignment preventing slipping along the plane.

Summary of the Invention In brief, this invention is directed to a building block that does not need to be cut to assemble geometric shapes required to build a building or other structure. For the purpose of this invention tessellation will mean any shape that can be tiled together along the edges. For the purpose of this invention curved conduit will mean straight and curved conduit that form when hexagons are assembled. Building structures can provide arrays of curved and straight tubing; curved and straight conduit pattern in a hexagonal building block with offset tab retainers for tubing retention during installation of radiant tubing, fire sprinkler systems, and/or wiring desired in the construction of a floor, wall ceiling, and wall. Offset retainer tabs will hold the tubing within the conduit, providing a convenient fast tubing installation by walking (stepping on the tubing) the tubing into the conduit in a zig-zag (sign wave) around offset tabs that retain the tubing. Offset tabs provides a low stress drop in installation rather than a press fit in parallel tracks.

Hexagonal conduit patterns are male and female alternating in an array around the center point of the hexagon, providing a tile that can be a single layer retaining tubing or a second like hexagon can be assembled in a point to center offset layer providing an interlocking surface retaining and protecting hexagon within the sandwich hexagon layers.

The curved radius of the retainer tabs are such that; a wide range of tube diameters can be retained in the radius of the tab retainer. Materials can be selected for building blocks

automatically by a superelement formula that are not easy to cut or healthy to cut on the job, but are good environmental material like concrete fiber sheeting. The skill level needed to produce or design a building is reduced by allowing the computer to process the common shapes in a superelement formula analysis. Structures are recyclable to other like buildings in the normal course of remodeling and can be retrieved for new buildings, after natural disasters like tornado, hurricane, flooding, earthquakes, and tidal waves randomly scatter building parts. The present invention is recyclable directly to another building using the same dimension of hexagon, or a hexagon twice the size and half the size.

Hexagons can be clustered providing construction of smaller hexagons with larger hexagons. In one embodiment of the present invention, the apparatus is a hexagon panel assembly, which includes geometric derivatives of hexagons and a header for door and window openings to assemble single or double hexagon panel walls including a pitched roof. A floor base plate is designed to mount to the floor and establish the wall locations.

Steel wire can make the independent hexagon components all one strong assembly.

Contractors could pick the building off the ground as one unit.

In still a further embodiment of the present invention, equilateral triangles are molded onto hexagons in such a way that one third of the hexagon layers on top of the triangle offsetting with aligned dowel holes for optional fasteners. Triangles on hexagons combine the geometry of hexagon and triangles tiles, which provides a groove in the triangle for mounting secure triangles and hexagons together by mounting the triangle to the triangles attached to the hexagon geometry. In a wall triangles mount to each other inside the wall and hexagons face the inside and outside of the wall.

In still a further embodiment of the present invention, three equilateral triangles are molded onto a single hexagon in an alternating male/female array three female and three male. Hexagon geometry is six equilateral triangles arrayed around a center point and this embodiment of three equally spaced male-triangles uses the maximum surface area of the six arrayed triangles that form a hexagon. The male-triangle has a groove around its three base edges with a depth approximately one half of the height of the male-triangle, providing clearance for future assembly. The extension past the edge of the hexagon portion is approximately equal to the groove depth providing geometries

that can be assembled and locked into place. In this invention the groove is a radius, but could be square or any shape. The three male-triangles are larger than the female-triangles and extend past the edge of the hexagon it is mounted to providing an extension (tongue) and groove locking building block when assembled. Male-triangles insert into the female- triangles by geometry fit; facing the male-triangle faces toward each opposing male- triangle relative to the hexagon center-point, rotate one of the two hexagons 60-degrees where male-triangle are aligned with female-triangles, maintaining the parallel alignment of opposing hexagon side edges, move that same hexagon a distance greater than the sum of the hexagon center-to-point distance and groove-depth distance, move that same hexagon toward the opposing hexagon along the center axis perpendicular to the faces a distance equal to the grove depth, and move the male-triangle of the same hexagon into the female- triangle of the opposing hexagon until point-to-center contact is made. Hexagon male/female triangles are arrayed around the center of the hexagon they are molded to and dowel holes (fastener means) are centered in the middle of the face of each equilateral triangle providing alignment of fasteners when assembled. Layering and tiling hexagon by offsetting hexagon point-to-center aligns dowel holes for a wide range of optional fasteners. Round holes, triangle holes (oriented points in alignment with hexagon larger triangle), or hexagonal dowel holes (orienting three equally spaced hexagon faces parallel to the three equilateral triangle edges it is centered in) align to the six large hexagon triangles when rotated for assembly. Three triangles on hexagons combine the geometry of hexagon and triangles tiles, which provides a groove in the three male-triangle for mounting triangles and hexagons together by inserting the male-triangle into the grooves of three triangle hexagon monolith geometry. In a wall, triangles mount to each other hidden inside the wall, and hexagons are visible on the face of the wall. When three hexagons are assembled to one opposing hexagon three of the single hexagon points aligned to the mating edges of the three opposing hexagons exposing a point air gap. It is desirable to overlap material to cover that air gap. The points can be cut into (e. g. slots, dowel hole, radial cut for disk insertion into three joining hexagon) for insertion of compressible material that extends past the point providing a seal, simple adhesive backed foam seals or in a composite compressible material can be molded in the point as part of

the chemical/pressure/thermal process. Hexagon point air gap can be closed by offsetting the geometry of the points slightly into a tongue and groove male/female structure. These point grooves in the hexagon triangle monolith points only have three possible assembly points. Male points are 120-degrees apart, providing three alternating female points with any offset shape. Conduit can be integrated in parallel to the triangle-groove pattern, which forms during assembly. Triangle extensions (tongue) can be molded with a cavity to form conduit; a smaller groove in the surface will form a continuous conduit in an assembly. Triangle extensions (tongue) can be molded or machined with a hole smaller than the extension radius and centered along the radial axis of the extension providing a conduit tube continuously through an assembly. A rod or tube could be inserted into this conduit hole providing a fastener, in addition to, or as a replacement to, the fastener in the center of each equilateral triangle. The grove surface could be cut into to form conduit.

Hexagons will be split along opposing points and opposing flats and hinged along the cut to provide wall corners, floor to wall, and wall to ceiling connections. Extra material could be added to the symmetrical dividing cut to form hinge structure of exterior hexagons in a two or more layered wall. The male-triangle female triangle hexagon monolith could be molded into a one piece rounded corner or other angles. In a further embodiment, the three male-triangles can be molded on both opposing faces of the hexagon monolith providing any wall thickness by the number of layers tiled. 360-degrees of rotational alignment, relative to the central point axis, of these double sided hexagon/triangle faces can be any angle of rotation providing a number of relative angles.

The potential for two double sided options exist : male-triangles aligned on both faces of a single hexagon or male-triangles rotated 60-degrees aligning with female-triangles of the opposing face. Triangle surfaces carry (transfer) the load in addition to the six edges of the hexagon. Thermal-set or thermal-plastic composite polymers can be the materials applied.

In still a further embodiment of the present invention, square-shaped panel assemblies and their derivatives are utilized for the offset layering building structures.

Square shapes, however, do not assemble into 30 degree pitched roofs, circular geometry, or provide the maximum equally spaced fasteners per square foot of buildings. Stresses

are lower in hexagons than in squares. Concrete squares layered, provides a high performance foundation floor. Walls made from squares and square derivatives in the shape of rectangles and triangles form walls and 45° pitch roofs. Window and door openings can also be assembled from square tessellations and their derivatives. Square and hexagon tessellation walls and floors, or other structures can be assembled into one structure. Other types of tessellation panel assemblies are also contemplated, and can be utilized without departing from the scope of the present invention.

In still a further embodiment of the invention a hexagon tessellation frame is provided to replace dimensional lumber for the construction of ceilings, roofs, wall and other structure. These tessellation frames also can be a variety of shapes, but hexagons are a preferred embodiment for offset layering and common fastening points.

In still a further embodiment of the invention, closed cell spheres are cast into foam from aluminum, ceramic, glass, polymers, polyimides, and other materials as spheres or closed cell materials become available. Further these closed cell foam spheres can have the gases or air replaced with fluids like perilites that are phase change materials or gases like helium. Some spheres are coatings providing spheres within spheres.

Utilizing the present invention, a structurally sound building can be assembled in harsh climatic regions. The building can be assembled on snow, ice fields, desert sand, and flood plains. When panels contain foam materials the building will float on water and will rise from the ground during flooding of the grounds around the building.

This building could be used as a houseboat.

Brief Description of the Drawings The foregoing aspects and many of the attendant advantages of this invention will become more readily appreciated as the same become better understood by reference to the following detailed description, when taken in conjunction with the accompanying drawings, wherein: FIGURE 1 illustrates a perspective view of the hexagon and peg; FIGURE 2 illustrates a perspective view of the peg dowel; FIGURE 3 illustrates a perspective view of two hexagons assembled; FIGURE 4 illustrates a perspective view of three hexagons assembled;

FIGURE 5 illustrates a perspective view of four hexagons assembled; FIGURE 6 illustrates a perspective view of the opposite side of FIGURE 5; FIGURE 7 illustrates a perspective view of the FIGURE 6 showing foam tubes; FIGURE 8 illustrates a sectional view of the center of a hexagon assembly showing the detail of the peg dowel system; FIGURE 9 illustrates an exploded view of the hexagon panel assembly; FIGURE 10 illustrates a perspective view of the foam hexagon core; FIGURE 11 illustrates a plan view of the six shapes used to build geometric patterns from hexagons; FIGURE 12 illustrates a perspective view of the hexagon split on points; FIGURE 13 illustrates a perspective view of the hexagon split across flats ; FIGURE 14 illustrates a perspective view of the hexagon cut long across points; FIGURE 15 illustrates a perspective view of FIGURE 14 split left; FIGURE 16 illustrates a perspective view of FIGURE 14 split right ; FIGURE 17 illustrates a perspective view of door and window header; FIGURE 18 illustrates a plan view of hexagon wall sections; FIGURE 19 illustrates a plan view of hexagon wall sections assembled into a wall; FIGURE 19A illustrates a cross-sectional view of the hexagon wall section of FIGURE 19; FIGURE 20 illustrates a perspective view of building walls, door and window openings, and floor double hexagon panel wall assembly; FIGURE 21 illustrates a sectional view of hexagon assemblies showing how mechanical fasteners penetrate the full layer of hexagons; FIGURE 22 illustrates a perspective top view of a substantially round hexagon assembly;

FIGURE 23 illustrates a perspective bottom view of the substantially round hexagon assembly in FIGURE 22; FIGURE 24 illustrates a perspective inside wall view of hexagons partially assembled around a door; FIGURE 25 illustrates a perspective view of a home assembly of one-meter wide hexagons; FIGURE 26 illustrates a plan view of all the shapes in FIGURE 25 ; FIGURE 27 illustrates a perspective view of the door and window header; FIGURE 27A illustrates a side view of the door and window header; FIGURE 28 illustrates sectional view A-A of FIGURE 27A; FIGURE 29 illustrates sectional view B-B of FIGURE 27A; FIGURE 30 illustrates a perspective view of the top and bottom plate of a wall or floor; FIGURE 31 illustrates a side view of the top and bottom plate assembly in FIGURE 30; FIGURE 32 illustrates a sectional view A-A of FIGURE 31 ; FIGURE 33 illustrates a perspective view of a hexagon frame; FIGURE 34 illustrates a side view of the hexagon frame of FIGURE 33; FIGURE 35 illustrates an end view of the hexagon frame of FIGURE 33; FIGURE 36 illustrates a perspective view of a hexagon frame split on the flats ; FIGURE 37 illustrates a side view of the split hexagon frame of FIGURE 36; FIGURE 38 illustrates an end view of the split hexagon frame of FIGURE 36; FIGURE 39 illustrates a perspective view of a hexagon frame split on points ; FIGURE 40 illustrates a side view of the split hexagon frame of FIGURE 39;

FIGURE 41 illustrates an end view of the split hexagon frame of FIGURE 39; FIGURE 42 illustrates a side view of a partial wall assembly of the hexagon frames of FIGURE 33,36, and 39; FIGURE 43 illustrates an end view of hexagon frame assembly of FIGURE 42; FIGURE 44 illustrates a perspective view of the six common fastening holes between four hexagons; FIGURE 45 illustrates the top view of the six common points displayed in FIGURE 44; FIGURE 45A illustrates a sectional view C-C of FIGURE 45; FIGURE 46 illustrates a perspective view of"A"frame building end walls; FIGURE 47 illustrates an end view of the"A"frame building end walls of FIGURE 46 showing the hidden lines of the hexagons offset in the second layer; FIGURE 48 illustrates a perspective view of square layered offset tessellations showing the common fastener locations; FIGURE 49 illustrates a front perspective view of a layered offset square tessellation-building wall with a 45-degree roof pitch and square derivatives; FIGURE 49A illustrates a rear perspective view of the layered offset square tessellation building wall of FIGURE 49; FIGURE 50 illustrates a front perspective view of a layered offset square tessellation building wall with 45-degree roof pitch and square derivatives forming doors openings; FIGURE 50A illustrates a rear perspective view of the layered offset square tessellation-building wall of FIGURE 50; FIGURE 50B illustrates an end view of the building wall of FIGURE 50 showing the hidden lines of offset squares and derivatives of squares point-to-center locations; FIGURE 51 illustrates a perspective view of a square tessellation panel;

FIGURE 52 illustrates a perspective view of a rectangle derivative that is one half of the square panel of FIGURE 51 split along flats ; FIGURE 53 illustrates a perspective view of a triangle derivative that is one half of the square panel of FIGURE 51 split along points; FIGURE 54 illustrates a perspective view of a trapezoid derivative of the square panel of FIGURE 51 ; FIGURE 55 illustrates a perspective view of a triangle derivative of the square panel of FIGURE 51 ; FIGURE 56 illustrates a side view of a TV screen; FIGURE 57 illustrates a perspective view of a tessellation TV screen cathode/backplate circuits and faceplates aligned by point-to-center offset layering; FIGURE 58 illustrates a perspective view of an optically transparent multi- color film for TV screen or large optical projectors; FIGURE 59 illustrates a perspective view of a hexagon carbon foam heat exchanger assembly formed from offset hexagons integrated and held together by tubes; FIGURE 60 illustrates a perspective view of a hexagon carbon foam heat exchanger assembly formed from closely tiled hexagons and tubes; FIGURE 61 illustrates a side view of a hexagon bridge assembly; and FIGURE 62 illustrates a top view of the hexagon bridge assembly of FIGURE 61; FIGURE 63 illustrates a hexagonal shaft fastener with a threaded ratchet head; FIGURE 64 illustrates a seat for the assembly of fastener FIGURE 63; FIGURE 65 illustrates a perspective close exploded view of a hexagon with the hexagonal shaft fastener of FIGURE 63 aligned with the hexagonal molded hole of FIGURE 64; FIGURE 66 illustrates a perspective view of all six hexagonal ratchet fastener seat, FIGURE 67 illustrates an alternate tamper resistant bouquet fastener ;

FIGURE 68 illustrates a fastener that provides a male press fit fastener; FIGURE 69 illustrates a hexagon the fastener in FIGURE 68 mates to; FIGURE 70 is a side view of a preferred fastening means when walls are spaced and filled with straw bales or cast with concrete; FIGURE 71 is a section view of a fastener head with an insert for wall coverings.

Detailed Description of the Preferred Embodiment FIGURE 72 illustrates a perspective view of a preferred hexagon conduit pattern.

FIGURE 73 illustrates a perspective view of an assembly of preferred hexagon conduit pattern in FIGURE 72 and FIGURES 63,64, 66, and 67.

FIGURE 74 illustrates a cross sectional view of fasteners configured for multiple layers.

FIGURE 75 illustrates a set of hexagon panels glued to hexagon assemblies to make a single structurally insulated panel.

FIGURE 76 illustrates the process of analyzing by superelement formulas.

FIGURE 77 illustrates an end view of alternative fastener comprising a rod or conduit insertion into a matching plurality of protrusions up off the plane surface of hexagons illustrated in FIGURE 72 and 73.

FIGURES 78 illustrates a cross sectional side view of an alternative fastener comprising a rod or conduit insertion into the common matching plurality of protrusion up off the plane surface of hexagons illustrated in FIGURE 72 and 73.

FIGURE 79 provides flexible rod extensions out of hexagon assemblies in FIGURE 77 and 78 for roof tarps.

FIGURE 80 is a rotated illustration of hexagon building blocks injection molded with carbon nanotube polymers in an equilateral triangle attachment arrangement.

FIGURE 81 is a rotated illustration of hexagon building blocks in FIGURE 80 injection molded with carbon nanotube polymers in an equilateral triangle attachment arrangement.

FIGURE 82 illustrates hexagon panels providing curved conduits which align for tubing when assembled.

FIGURE 83 illustrates three hexagon panels tiled providing curved conduits which align for tubing when assembled.

FIGURE 84 illustrates two hexagon panels layered providing curved conduits which align for tubing when assembled FIGURE 85 illustrates side view of two hexagon panels in FIGURE 84 providing curved conduits which align for tubing when assembled.

FIGURE 86 illustrates isometric view of three hexagons rotated offset and layered onto three hexagon panels in FIGURE 83 providing curved conduits which align for tubing.

FIGURE 87 illustrates an equilateral triangle molded into a hexagon centrally providing three equally spaced points of six hexagon points, which assemble onto hexagons when rotated.

FIGURE 88 illustrates a side view of a hexagon, triangle, and hexagon stacked.

FIGURE 89 illustrates a single triangle.

FIGURE 90 illustrates an isometric view of a hexagon with male/female pegs, which replace equilateral triangles assembled exactly like FIGURE 80 and 81.

FIGURE 91 illustrates the outside top face of the hexagon triangle block.

FIGURE 92 illustrates an end view of block in FIGURE 91.

FIGURE 93 illustrates an isometric inside bottom view of hexagon triangle in FIGURE 91-99.

FIGURE 94 illustrates bottom view of FIGURE 91-95 with sectional line orientation.

FIGURE 95 illustrates an isometric view of FIGURE 94.

FIGURE 96 illustrates a sectional side view of sectional line in FIGURE 94 and 95.

FIGURE 97 illustrates an isometric view of two hexagon triangle blocks assembled with sectional line.

FIGURE 98 illustrates a sectional side view of sectional line in FIGURE 97.

FIGURE 99 illustrates top view of two hexagon triangle block assemblies in FIGURES 97 and 98.

FIGURE 100 illustrates an elevated inside face of a hexagon 3-triangle monolith.

FIGURE 101 is a bottom view of hexagon 3-triangle monolith in FIGURE 100.

FIGURE 102 illustrates an end view of face edge of hexagon in FIGURE 100,102, 103, and 104.

FIGURE 103 illustrates an elevated view of hexagon 3-triangle monolith top in FIGURE 100,102, 103, and 104.

FIGURE 104 illustrates a top face view of hexagon 3-triangle monolith in FIGURE 100,102, 103, and 104.

FIGURE 105 illustrates an isometric view of one-half hexagon 3-triangle monolith in FIGURE 100,102, 103, and 104 cut along the points.

FIGURE 106 illustrates a view of one-half hexagon 3-triangle monolith in FIGURE 100,102, 103, and 104 cut along the points.

FIGURE 107 illustrates a close view of triangle groove and extension.

FIGURE 108 illustrates bottom elevated view of two assembled halves FIGURES 105 and 106 of hexagon 3-triangle monolith in FIGURE 100 cut along the points.

FIGURE 109 illustrates top elevated view of two assembled halves FIGURES 105 and 106 of hexagon 3-triangle monolith FIGURE 100 cut along the points.

FIGURE 110 illustrates an isometric view of two hexagon 3-triangle monolith assembled with sectional line peg (dowel) holes.

FIGURE 111 illustrates a bottom view of hexagon 3-triangle monolith FIGURES 100-104 cut in one half along the flat opposing edges.

FIGURE 112 illustrates elevated view assembly of hexagon 3-triangle monolith in FIGURE 106, 111, and 100.

FIGURE 113 illustrates an elevated view assembly of hexagon 3-triangle monolith in FIGURE 106,111, and 100 FIGURE 114 illustrates an elevated view assembly of hexagon 3-triangle monolith in FIGURE 106,111, and 100.

FIGURE 115 illustrates a rotate elevated view of hexagon 3-triangle monolith in FIGURES 100-104.

FIGURE 116 is a sectional view of dowel holes and alignment grooves of hexagon 3-triangle monolith in FIGURE 100-119.

FIGURE 117 illustrates a sectional side view of hexagon FIGURES 111, 115,116, and 117.

FIGURE 118 illustrates a rotated elevated view of assembly in FIGURE 113.

FIGURE 119 illustrates two hexagon 3-triangle monoliths mounted to each.

FIGURE 120 illustrates conduit in a cross sectional view of two hexagon 3-triangle monoliths assembled.

FIGURE 121 is an isometric view illustrating a curved and straight conduit pattern in a hexagonal building block with offset tab retainers for tubing retention.

FIGURE 122 is a side view of FIGURE 121 illustrating a axial view of the straight conduit pattern within a hexagonal building block.

FIGURE 123 is a trimetric view illustrating three tiled hexagonal building blocks of FIGURE 121.

FIGURE 124 is a sectional view of FIGURE 122 illustrating a tube held within offset conduit retention tabs.

FIGURE 125 is an elevated view illustrating offset conduit retention tabs in FIGURE 123.

FIGURE 126 is an elevated view illustrating the same curved and straight conduit pattern in FIGURE 121 in a larger hexagonal building block.

FIGURE 127 is an elevated view illustrating triangle array along a straight curve.

FIGURE 128 is an isometric view illustrating a rectangle hinged corner with triangle patterns matching FIGURE 127.

FIGURE 129 illustrates an elevated inside face of a hexagon 3-triangle monolith with conduit in triangle edges.

FIGURE 130 illustrates a top face view of hexagon 3-triangle monolith in FIGURE 130.

FIGURE 131 illustrates an elevated view of one-half hexagon 3-triangle monolith in FIGURE 129 and 130 cut along the points into a female/male/female hexagon derivative half.

FIGURE 132 illustrates an elevated view of one-half hexagon 3-triangle monolith in FIGURE 129 and 130 cut along the points into a male/female/male triangle hexagon derivative half.

FIGURE 133 illustrates an elevated view of triangle faces of one-half hexagon 3-triangle monolith in FIGURE 131 and 132 hinged together at 180-degree angle.

FIGURE 134 illustrates an elevated view of hexagon faces of one-half hexagon 3-triangle monolith in FIGURE 131 and 132 hinged together at 90-degree angle with triangles facing each other.

FIGURE 135 illustrates an elevated view of triangle faces of one-half hexagon 3-triangle monolith in FIGURE 131 and FIGURE 132 hinged together at 90- degree angle with triangles facing each other inserted into the same components hinged together at 90-degrees with hexagon halves facing each other.

FIGURE 136 illustrates an elevated view of two sets of triangle faces of one-half hexagon 3-triangle monolith in FIGURE 131 and 132 hinged together at 90- degree angle and each set rotated 90-degress relative to the other set forming a corner.

FIGURE 137 illustrates an elevated rotated back view of FIGURE 136.

FIGURE 138 illustrates an elevated view of two sets of triangle faces of one-half hexagon 3-triangle monolith in FIGURE 137 hinged together at 90-degree angle and each set rotated 90-degress relative to the hinge and 90-degress relative to FIGURE 137.

FIGURE 139 illustrates a close-up view of 138 viewing hinge detail.

FIGURE 140 illustrates an elevated view of a pair of hinges made of six tubes assembled around a central tube of equal diameter and rotated offset pins.

FIGURE 141 illustrates an elevated view of a pair of the gear hinges made of six tubes assembled around a central tube of equal diameter, in FIGURE 140, each mounted to a common centrally pinned bracket.

FIGURE 142 illustrates the back side view of FIGURE 141.

FIGURE 143 illustrates an elevated view of two sets of triangle faces of one-half hexagon 3-triangle monolith in FIGURE 133 hinged together at 180-degree angle and each set rotated 90-degress relative to the other set for joining sets of hexagons into a cross.

FIGURE 144 illustrates FIGURE 143 for a view of hidden structure.

FIGURE 145 illustrates a face view of hexagon derivative halves cut along the flat sides with hinge structure and complete wall thickness structure forming a bottom wall plate.

FIGURE 146 illustrates a back elevated view FIGURE 145 with male/female S-Grove structure.

FIGURE illustrates a face view of hexagon derivative halves cut along the flat sides with hinge structure and complete wall thickness structure forming a top wall plate.

FIGURE 148 illustrates a back elevated view FIGURE 147 with female/male S-Grove structure.

FIGURE 149 illustrates a corner view of corner subassembly in FIGURES 135-142 and bottom and top plates in FIURES 145-148.

FIGURE 150 one-fifth pentagon section in view and one-third hexagon section inserted into a full hexagon-triangle elevated view of three assembled components: one-third of FIGURE 129 one-fifth of a pentagon, and filler edge to array into a sphere or dome.

FIGURE 151 illustrates a top elevated view FIGURE 150 with an arrayed tube pentagon connector.

FIGURE 152 illustrates a top elevated view FIGURE 151 with an arrayed tube pentagon connector inserted.

FIGURE 153 illustrates a top elevated view FIGURE 150 one-fifth pentagon section in view and one-third hexagon section inserted into a full hexagon- triangle.

FIGURE 154 illustrates a top elevated view FIGURES 150-152 arrayed around tube pentagon connector and center-point of a pentagon.

FIGURE 155 illustrates an outside elevated view of FIGURE 154 arrayed around tube pentagon connector and center-point of a pentagon.

FIGURE 156 illustrates an outside side view of FIGURE 155 arrayed around a tube pentagon connector and center-point of a pentagon with assembly in FIGURE 153 a full hexagon inserted.

FIGURE 157 illustrates an inside rotated elevated view of FIGURE 156 arrayed around tube pentagon connector and center-point of a pentagon.

FIGURE 158 illustrates an inside rotated elevated view of FIGURE 151 with five full hexagons of FIGURE 153 arrayed around center-point of a pentagon and inserted into the one-third hexagon connected to the one-fifth pentagon section.

FIGURE 159 illustrates a side elevated outside view of FIGURE 158 viewing the full hexagons inserted into the one-third hexagons connected to one-fifth a pentagon arrayed around the center-point of the pentagon.

FIGURE 160 illustrates a partially assembled inside view of a sphere comprised of the components in FIGURES 150-159.

FIGURE 160 illustrates a partially assembled inside view of a sphere comprised of the components in FIGURES 150-159.

FIGURE 162 illustrates an outside view of a fully assembled sphere comprised of the one-half sphere components in FIGURES 160 mirrored and faces assembled to each other.

FIGURE 163 illustrates an outside and inside view one-half sphere components positioned in 25-percent offset 180-degrees apart and comprised of the sphere in FIGURES 150-163 in offset.

FIGURE 164 illustrates a top elevated view FIGURE 1163.

FIGURE 165 illustrates a simplified schematic view of the hexagon- pentagon sphere in FIGURE 164.

FIGURE 166 illustrates a simplified schematic view of the hexagon- pentagon sphere in FIGURE 163.

FIGURE 167 illustrates a simplified schematic view of the hexagon- pentagon sphere in FIGURE 165 with the two spheres aligned forming a wind resistant sphere.

FIGURE 168 illustrates a simplified schematic view of the hexagon- pentagon one-half sphere in FIGURE 167 with the two spheres offset 100-percent and aligned forming a wind blade sphere.

FIGURE 169 illustrates a simplified schematic view of the hexagon- pentagon one-half sphere in FIGURE 168 with the two spheres offset 150-percent and aligned to form a wind-power blade sphere.

FIGURE 170 illustrates an elevated inside face of a hexagon 3-triangle monolith with conduit in triangle edges in FIGURE 129 and in addition conduit structure is provided along the face of the hexagon edges.

FIGURE 171a illustrates a top face view and sectional of one-sixth hexagon 3-triangle monolith structure within FIGURE 170 hexagon's six points.

FIGURE 171b illustrates a top face view of hexagon one-sixth 3-triangle monolith in FIGURE 170 and 171a.

FIGURE 172 illustrates an elevated exploded side view of FIGURES 171 a and 171b.

FIGURE 173 illustrates an elevated exploded central view of FIGURES 171a and 171b.

FIGURE 174 illustrates an elevated exploded hexagon-point end view of FIGURES 171a and 171b.

FIGURE 175 illustrates an elevated close-up view of only the rib structure profile within FIGURES 171a and 171b.

FIGURE 176 illustrates an elevated close-up view of the rib structure profile within FIGURES 171a and 171b.

. FIGURE 177 illustrates an elevated close-up view of tube edges, ribs, dowels, and dowel skirts within FIGURES 171a and 171b.

FIGURE 178 illustrates an elevated close-up view of simple flat ribs and round dowels without profiled skirts replacing ribs and skirts within FIGURES 171a and 171b.

FIGURE 179 illustrates a side view of a fastener inserted into a retention ring and the same fastener alone for insertion into hexagons in FIGURES 129-201.

FIGURES 180 illustrates an elevated close-up sectional view of slotted fastener in FIGURES 171a, 171b 179 and 181.

FIGURE 181 illustrates an elevated close-up sectional view of the slotted fastener end and retention ring in FIGURES 171a, 171b 179 and 180.

FIGURES 182 illustrates an elevated close-up sectional view of the slotted fastener end and retention ring profile in FIGURES 171a, 171b 179-181.

FIGURE 183 illustrates a tilted elevated view of one full hexagon 3- triangle monolith in FIGURE 170 for viewing hexagon tube structure.

FIGURE 184 illustrates bottom elevated view of two assembled hexagon 3-triangle monolith in FIGURE 183 assembled face to face male triangles inserted into female triangles.

FIGURE 185 illustrates top elevated inside face view of two full hexagons aligned showing the pattern of S-Groves and triangles and a third full hexagon partially assembled from hexagons of FIGURES 183.

FIGURE 186 illustrates top elevated inside face view of four full hexagons aligned showing the pattern of S-Grooves and triangles and the forth hexagon assembled face to face on the other three hexagon of FIGURES 183.

FIGURE 187 illustrates top elevated inside face view of one full hexagon with alternate circular S-Groves rather than equilateral triangle S-grooves with a radiant fluid tube extending from the parameter of the hexagon.

FIGURE 188 illustrates top elevated inside face view of two full hexagon with alternate circular S-Groves mating the faces in alignment and assembled.

FIGURE 189 illustrates an exploded side view of the components of one full hexagon with alternate circular S-Groves assembled including the ribs and dowels of FIGURES 178.

FIGURE 190 illustrates an elevated isometric view one tube bundle hinge with alternating tube structure configured to mate to the hexagon tube structures in FIGURES 192-204.

FIGURE 191 illustrates a rotated view of FIGURE 190.

FIGURE 192 illustrates a seal partially removed form the face of a pair of hexagons derivative halves cut along the points of the hexagon of FIGURE 129-130.

FIGURE 193 illustrates a rotated view of FIGURE 192 showing the locking tube inserts n the edge tubes of FIGURE 192-204.

FIGURE 194 illustrates a view of FIGURE 192 exploded open and the 2- triangle half is rotated 90-degrees to show the edge tube detail that locks together when rod inserts are inserted into the alternating matching tubes segments for FIGURE 192- 204.

FIGURE 195 illustrates a view of FIGURE 192 exploded open and the 2- triangle half is rotated 180-degrees to show the edge tube detail and mating alignment that locks together when rod inserts are inserted into the alternating matching tube segments for FIGURE 192-204.

FIGURE 196 illustrates a close up view of hinge in FIGURE 190 and 191 assembled to a hexagons in FIGURES 193-204.

FIGURE 197 is FIGURE 196.

FIGURE 198 illustrates a view of FIGURE 192 exploded open and the 2- triangle half is rotated 180-degrees and separated to for hinge assembly on hexagon edge tube alternating segments by rod insertion into the alternating matching tube segments in FIGURE 192-204.

FIGURE 199 illustrates a finished corner that overlaps the finished face of the hexagon and locks into the space between hinges forming 90-degree angles.

FIGURE 200 illustrates a rotated outside view of the finishing corner in FIGURE 199.

FIGURE 201 illustrates a rotated inside view of the finishing corner in FIGURE 199 and 200 with a void space between hinge matching tube bundles for insertion in the void spaces in a subassembly of corners in FIGURES 134-139 and FIGURE 149 assembled corner.

FIGURE 202 illustrates an inside top view of one-half hexagon 3-triangle monolith in FIGURE 190-198 cut along the points into hexagon derivative half with hexagon edge tube segments aligned at an angle by FIGURE 140 offset rods which form a curve when half a meter hexagons are hinged and arrayed around the central point 22- times providing 3501-milimeter (mm) radius.

FIGURE 203 illustrates a rotated close-up edge view of FIGURE 202.

FIGURE 204 is the same as FIGURE 202.

FIGURE 205 illustrates outside view of a tube assembled from two layers of hexagons tapered into the center relative to the tube axis providing a tube assembly from an inside hexagon smaller and tapered toward the center of tube relative to the outside larger hexagon scaled larger relative to the one circumferential dimension.

FIGURE 206 illustrates one-half of FIGURE 205.

FIGURE 207 illustrates the taper of the hexagons relative to the circumferential dimension the axial dimension related to a 1-meter hexagon (measured flat to flat edge) remains the same.

FIGURE 208 illustrates a view of a hexagonal taper geometry before a bullion cut is made by a surface to make hexagon blocks in FIGURE 207 curved.

FIGURE 209 illustrates tubes for bullion cutting fastener holes in the hexagon of FIGURE 207.

FIGURE 210 illustrates tube arrays for alternative hexagon structure that can easily be curved around the centerlines of the tubes providing an infinite curve with end tube segments aligned for mating to assemblies of hexagons.

FIGURE 210 illustrates the mating edges of the hexagons when two hexagon are assembled and tube edge segments inserted to male/female edge tube.

Detailed Description of Preferred Embodiment FIGURE 1 illustrates a preferred embodiment hexagon building structure 7 and peg retainer 5 constructed in accordance with the present invention. Preferably, six alignments fastening holes 4 are equidistantly spaced and located on interior panels 1 and 2. The panels 1 and 2 are adhered to a foam core 3. Preferably, the hexagon building structure 7 includes radial cutouts 6 for assembly to another peg retainer (not shown).

Preferably, the holes 4 are the primary fastener location for screwing or bolting through the layers of the hexagon. The holes 4 align with an offset layer of hexagons when assembled in the axial direction (as shown in the assembly of FIGURE 3). In one preferred embodiment of the present invention, the set of six holes 4 are the only fastening technique necessary for joining an offset layering assembly of hexagon building structures 7. Conduit holes 12 are selectively located depending on the fastening technique selected.

A preferred embodiment of the present invention includes a hexagon building structure 7 system for constructing buildings and other structures, including but not limited to, complex geometries such as door openings, window openings, roof pitches, and curved archways. Tessellations are seamless tileable patterns created from a basic geometric grid. Variations of tessellations can be formed from squares, triangles, stars shapes, hexagons, and curved shapes. Hexagons in particular, are easy to produce, and

provide the benefits of forming desirable geometric shapes, lowering stresses, and increasing leverage when the hexagons are used in an offset layering configuration. The hexagon building structure 7 is symmetrical and provides seven fastening points (at the six corner points and the center point) when layered and offset equally against three other hexagon-building structures 7 of the same size. When offset equally, the center point of a first six corner points aligns with a corner point three other hexagon building structures 7, in a corner point-to-center alignment. Thus, three hexagon-building structures 7 assemble symmetrically in the same plane and connect centrally to one offset hexagon building structure 7 in another plane.

In order to layer and offset a tessellation into a composite structure that is useful, symmetrical equal fastening points are desirable for calculating and predicting structural stress. An additional structural benefit of hexagon building structures 7 is the alignment of six additional common alignment points (alignments fastening holes 4 in this preferred embodiment) that result when hexagon building structures 7 are stacked or layered in the axial direction at an equal symmetrical offset distance. The six alignments fastening holes 4 are located between the six flat edges and center. These six alignments fastening holes 4 are found by drawing lines between each corner-point and the two closest non-adjacent, corner-points (forming two equilateral triangles). The intersecting points of these lines define the location of the alignments fastening holes 4, which are equally spaced. This additional set of six fastening points provides the most substantial fastening points for maximum strength. These six alignments fastening holes 4 align in stacked offset layers of hexagons to provide common predictable fastening locations.

In a preferred embodiment of the present invention, thirteen common fastening points (the six alignments fastening holes 4, six corner points, and one center point) align in stacked offset hexagons. Other common fastening points can also be derived without departing from the scope of the present invention. Bolt, wire, or other suitable fasteners penetrate through the panels 1 and 2 to mechanically compress the panels at the fastener points. In some embodiments, the walls at right angles are compressed together for building integrity. This is desirable over panel systems dependent on adhesives.

In another aspect of the present invention, adhesives or caulking sealant are added between the panels during assembly. A void or a full sheet of insulation can also be sandwiched between the hexagon building structures 7 depending upon the particular application. Further, in some embodiments an adhesive closed cell tape seal, similar to automotive weather stripping, is wrapped around the hexagon building structures 7 prior to assembly for additional compression sealing. Preferably, joint fasteners with flat heads fasten hexagon-building structures 7 together. Screws can either partially or fully penetrate through the full set of layered hexagon building structures 7 and are also adaptable.

In other embodiments of the present invention, the peg retainer 5 is replaced with a small bolt (not shown), depending upon the strength of the materials utilized. Fasteners can be inserted through the alignments fastening holes 4 either manually or by CNC automation. The number of fasteners applied is an issue typically specified by the builder. In some embodiments, steel cables (not shown) are threaded through the wiring holes 12. The steel cable can be configured to run in all directions, as required by the builder. Further, in high wind and/or flood areas, the steel cables and wiring holes 12 can be used as a cabling system in order to anchor a building to the ground.

As further illustrated in FIGURE 2, the peg retainer 5 includes a peg portion 5a and a retainer portion 5b (see also FIGURE 9). The peg portion 5a and the retaining portion 5b fasten the panels 1 and 2, and the core 3, together during the manufacturing of the hexagon building structures 7. Further, the retaining portion 5b provides dowel panel assembly registration during the manufacturing of the hexagon building structures 7. FIGURE 2 shows the peg portion 5a and the retainer portion 5b joined together, while FIGURE 9 shows the peg portion 5a and the retainer portion 5b separated apart. In one preferred embodiment, a polyvinyl chloride adhesive is utilized to adhere the peg portion 5a to the retainer portion 5b.

Referring now to FIGURE 3, two hexagon-building structures 7 can be correspondingly configured to assemble around a peg retainer 5. Similarly, three hexagon-building structures 7,8, and 9 can also be correspondingly configured to

assemble around peg retainer 5, as shown in FIGURE 4. The panels of the hexagon building structures 8 and 9 act to conceal the peg retainer 5. This concealment feature is of intrinsic cosmetic value to many builders. The peg retainer can penetrate though the panel and be slanted on its face as well as on the points of the hexagons. The central peg hole can be much larger than the point slants providing a full peg with two slanted ends.

This slanted peg would be easy to install and aid in building a building. However, for other builders, other embodiments of the present invention employ bolts fasteners that penetrate completely through the panels, mechanically compressing and fixing the panels in location.

Standard metal stamped cleats or metal earthquake straps can also be inserted between the hexagon building structures during assembly. These earthquake type straps can be sandwiched between hexagons and fastened to fasteners 4, extending out of the hexagon to be a corner fastener strap or an insertion into a concrete foundation. This has value when using superelement stress analysis, which is designed to use common fastening points and symmetry.

When four hexagon building structures 7,8, 9, and 10, are assembled together, as shown in FIGURE 5, the peg retainer 5 cannot be seen. Alternatively, a joint fastener, barbed press fit plastic fastener, screw or metal cleats is placed in the center of hexagon building structure 7 and the joining points of hexagon building structures 8,9, and 10 (instead of a peg retainer 5). Referring now to FIGURE 6, the alignments fastening holes 4 and 11 of hexagon building structure 7 align with the alignments fastening holes of hexagon building structures 8,9, and 10.

As shown in FIGURE 7, foam tubes align to form wiring and plumbing conduit holes 12. Referring now to FIGURE 19, conduit holes 25,26, and 27 can be seen. Wire cable conduit hole 25 provides a connection path from corner 28 to base plate 19 at location 19a. Conduit holes 26 and 27 provide a steel wire hole to compress the wall together from one end to the other. The steel wire cable 29 and 30 can be extended through the adjoining wall forming corners 31 (shown in FIGURE 20). These steel wire cables or ropes can be used to anchor the building to the ground. Cable can also be connected across the interior of the walls through common hole 4. These cables will be exposed when applied in buildings for food storage of grains, fluids, and other biomass.

These interior cables strength additions can easily be calculated with accuracy, because of the superelement modeling.

Referring again to FIGURE 7, graphite rod 32 and rod flange 33 are inserted into conduit holes 12. The rod 32 is centered and fixed in location by the rod flange 33. Rod 32 can be constructed of tubing, wood or other materials, without departing from the scope of the present invention. In one embodiment, rods are placed in multiple locations between every hexagon building structure 7, in order to connect the hexagon building structure 7 during assembly. Preferably, one side of the rod is attached to a hexagon building structure 7 prior to assembly. In low stress construction designs, rods 32 are sized in length and diameter to replace the need for offset double walls. In some climates and wind conditions, conduit holes 12 are not produced. This is particularly true when higher strength structures are required, or when replacing concrete block buildings where wiring and plumbing is run in an external conduit as a standard practice.

Although conduit holes 12 are convenient, the holes do result in some weakening of the panel. Wiring, water plumbing, toilet pea-traps, alarm systems, fans, sensors, refrigeration components, heat exchangers, heating sources, and air-ducting systems can be packaged into hexagons. In some embodiments, the conduit holes 12 have hoses inserted for radiated liquid heating or liquid circulation for absorption cooling. Any amount of foam can be removed and replaced by thermal storage and/or release materials.

These materials change phase forming liquid when heated and solidifying releasing stored heat when cooled. Hexagon panels provide a building structure for packaging these types of phase change materials and containing them within a building environment for safety.

Referring now to FIGURE 8, a peg retainer 5 is shown in the center of an offset layering hexagon building structure assembly. In one embodiment of the present invention, a peg retainer 5 is constructed from an assembly of PVC pipes adhered together with glue. Injection molding is one suitable technique for this purpose. Conduit holes 12 are formed in the foam core 3.

As shown in FIGURE 9, the peg portion 5a and the retainer portion 5b can be separated. The retainer portion 5b provides the dowel function during glue assembly

of exterior panel 7b and interior panel 7a. The peg portion 5a is inserted and glued into the retainer portion 5b. The hexagon foam core 3 and conduit holes 12 are shown in greater detail in FIGURE 10.

Referring now to FIGURE 11, a hexagon building structure 7 and five- hexagon derivative building structures 13,14, 15,16, and 17 are shown. These six structures are assembled into the geometric shapes that make walls, floors, window, and door openings. Hexagon derivative building structure 13 is a hexagon split on points, and is shown in FIGURE 12. Hexagon derivative building structure 14 is a hexagon split on flats, and is shown in FIGURE 13. Hexagon derivative building structure 15 is a hexagon cut long across points, and is shown in FIGURE 14. Hexagon derivative building structure 16 is a hexagon cut long across points and split left, and is shown in FIGURE 15. Hexagon derivative building structure 17 is a hexagon cut long across points and split right 17, and is shown in FIGURE 16. Finally, hexagon derivative building structure 18 is a hexagon door and window header 18, and is shown in FIGURE 17.

Referring now to FIGURE 18, hexagon wall sections door 20, window 21, and the finished ends assemble into corners of a building. Hexagon wall sections can be computer numeric control (CNC) machined out of a single solid panel. All of the above- described hexagon and hexagon derivative building structures are utilized in this embodiment. In this embodiment of the present invention, partial hexagons extend out of the wall sections. Corner sections can also be prefabricated as a single part. Accordingly, corner sections are prefabricated out of a single part or by joining smaller corner sections in order to strengthen the corners of the structures. These prefabricated corner sections can be applied on the interior or exterior of the house to join the main walls to a room wall or partitions wall. Prefabricated hexagons can take the form of a cross with extensions off the front and back of the hexagons for locations where the interior and exterior walls are on the same locations, and a top cross sectional view would form a cross. A corner is also a monolith and can represent a stepped portion of hexagons, where other full hexagons fasten and become a full surface without steps. These corners have the appearance of missing a hexagon when first put up, because they are stepped and integrate

to the wall. The preferred corner is a molded corner that can be flipped upside down and fit onto a like corner providing an infinite height potential.

Builders can use these hexagon computer aided design sections to rapidly build wall sections. Super-elements are computer models that the computer processes stress calculations around. Hexagons make desirable super-elements that process as one math node in the computer. This reduces computer time dramatically to optimize building designs. Super-elements are possible from common symmetrical shapes, which is why hexagons, hexagon derivatives, or tessellation shapes are useful in building design. One of the advantages of tessellation symmetrical shapes, and specifically hexagons, is that accurate optimized designs are produced when calculating super-elements computer design assemblies. Prior art buildings structures have proved to be near impossible to use in calculating stress. Current dimensional lumber homes have random fastener locations and random tetrahedral element meshes resulting in billions of nodes to calculate to obtain the same accuracy of several hundred-hexagon nodes. Online World Wide Web Internet services can be provided to builders, because results can be obtained in minutes. Even the most unskilled builder will have data on the building structure using superelement efficiencies across networks. FIGURE 76 is a drawing of the superelement analysis of tessellating structures that have common fasteners. Customers enter a design environment, process 1, which would appear to the customer as a finished rendered wall or the hexagons patterns would show up on the computer display. After a geometry is selected the x, y, and z coordinates are sent to the superelement process 502, which is the a formula of the superelement providing uniform symmetrical hexagons or other tessellations. The superelement formula in process 502 provides very fast analysis of the design for stress, thermal behavior, and other common structural engineering questions.

Process 502 is very fast because of the symmetrical common shapes and common fasteners. A variety of materials are in the materials library and the superelement formula optimizes the design by selecting various materials and thickness, as well as special composites of shapes to meet engineering requirements. Process 503 is the post results, which can be viewed in the analysis program as"raw"data, only most professional engineers would understand or the customer can view their data in the rendering program

they started in. Process 504 is the bill of materials providing the list of parts needed to build a building or other structure. Process 504 includes the different materials that the analysis automatically selects when optimizing the Process 501 image.

Referring now to FIGURE 19, hexagon wall sections are assembled into a wall. Cable locations are provided by conduit holes 25,26, 27,27a. Cables 29,30, and 30a are inserted in a preferred embodiment of the present invention. It is to be understood that any one of the many conduits holes can be used in the wire cable compression.

In further embodiment of the invention, shown in FIGURE 19A, the hexagon building structures 7 and 37 are spaced apart by beam 35 in a spaced apart, double wall assembly. Location dowel fasteners 38 and 39 are placed along the beam 35 to join the hexagon building structures together. Preferably, the beam 35 is substantial vertical and is arrayed along the building for increased strength. In another embodiment the beam 35 runs horizontally as well, is divided into segments providing a fluid path for concrete or cast in place foams, or at other angles. Hexagon frame building structures 70, 71, and 72 (shown in FIGURE 33,36, and 39, and described in further detail below) are used between solid panels in order to make the panels on the outside and inside walls symmetrical. These panels can be cut for the wiring, water or plumbing pipes, or other building requirements.

As shown in FIGURE 20, hexagon building structures 7 and their hexagon derivative building structures 13,14, 15,16, and 17 are used to simply and efficiently build walls, door openings, window openings, and a floor double hexagon panel wall assembly. A header 18, hexagon building structures 7 (50-centimeter structures in this preferred embodiment), and hexagon panel derivatives 13,14, 15,16, and 17, assemble into a double wall system. Preferably, a hexagon beam 50 is utilized as a crossbeam, which has a foam core 3, along with air ducts and wiring, integrated into the beam. In one embodiment of the present invention, the wall hexagons are 50-centimeter flat to flat, and the floor hexagons are 1-meter flat to flat.

Hexagon building structures 7 of different sizes can be assembled into a single building. Referring to FIGURE 20, one-meter hexagon building structures 7c, and hexagon derivative building structures 13c, 14c, 15c, 16c, and 17c, assemble into a double

floor system. One-meter hexagon building structures 7c exhibit substantial strength, and thus, are preferable for many floor applications. Conduit holes 12 in these floor panels are large enough to use as heating and air-conditioning air ducts. One-meter hexagon building structures 7c are also a good selection for roof cover. Using smaller hexagon building structures 7c (such as 50-centimeter hexagons) allows an increased amount of possibilities for changes. The roofline on the preferred embodiment hexagon building of <BR> <BR> FIGURE 20 is 30 degrees. In another embodiment, "A"frame steep roof alpine building is produced when the hexagon building structures are rotated 90 degrees and assembled.

The thickness of the hexagon building structures can be adjusted to meet climate conditions. Any size hexagon can be made. Other tessellation made from squares and square derivatives have a 45 degree pitched roofline. These multiple tessellation can be combined for a desired shape.

In some embodiments of the present invention, mechanical fasteners penetrate the full layer of hexagon building structures 7, as shown in FIGURE 21. A larger number of layers of hexagon building structures 7 can also be layered in this alternating offset layering structure, without departing from the scope of the present invention. The hexagon building structure center hole and alignments fastening holes 4 align with the bolt 63 and holes 60 and 61, respectively. Preferably, T-NUTs are utilized for fastening the bolts.

Substantially round hexagon assemblies 34 are also produced using hexagon building structures 7 and hexagon derivative building structures 13 and 15, as shown in FIGURES 22 and 23. These substantially round hexagon assemblies 34 are assembled without requiring cutting or other customization of hexagon building structures 7. These shapes can form substantially round hexagon assemblies 34, or circular openings for windows, door arches, and other builder-specified needs. For regional specific designs, such as in Japan and China, these round hexagon assemblies 34 can be assembled to poles in multiple floor levels to make religious or cultural buildings similar to those of ancient construction. It is to be understood that hexagons can be stacked as high as necessary in order to make big beams. Tessellation can also be curved on the surfaces and

assemble around the circular shape. Hexagons can be uniformly curved on the plain surfaces and assemble into a tube.

Further, in some embodiments, long graphite poles are inserted into high stacks of offset layered hexagon building structures 7. For example, a 20-foot beam could be assembled from 20 hexagons a foot thick and assembled in the substantially round hexagon assembly 34 configuration. The hexagon building structures 7 can be joined together by inserting rods into the set of six alignments fastening holes 4. Alternatively, tubes can be used instead of rods. In another embodiment of the present invention, these type of multiple stack arrangements form complex shapes like boat hauls and airplane fuselage, or wings. Only the exterior hexagon building structures 7 need to be shaped to match a desired design. Preferably, the rods act to fasten the hexagon building structures 7 together. These types of three-dimensional shapes can be fiber-glassed on the surface, including fiber-resin winding of the whole structure. Other surfaces can also be used without departing from the scope of the present invention.

Referring now to FIGURE 24, hexagon-building structures 7,8, 9, and 10 are partially assembled around a door. Specifically, the offset layering of the hexagon building structures 7,8, 9, and 10 is shown in this house wall assembly. A hexagon building structure home assembly is illustrated in FIGURE 25. This particular embodiment utilizes one-meter wide hexagons. When larger hexagon building structures 7 are utilized, fewer of the hexagons building structures 7 are needed. However, as shown in FIGURE 26, a larger number of hexagon derivative building structures are then required (items 4,5, 7,8, 9, and 10). These additional hexagon derivative building structures are constructed with optional plates 67a, and 68a.

One interesting hexagon derivative building structure is the door and window header 67, as shown in FIGURES 27 and 27A. Optional plates 67a, 67b, and 67c are integrated into the panel 67 for strengthening and providing a platform for bolting the wall to the floor and joining corners, as shown in FIGURES 28 and 29. Another interesting hexagon derivative building structure is the top and bottom plate for a wall or floor, as shown in FIGURES 30 and 31. Similarly, optional plates 68a, 68b, and 68c are integrated to the panel 68 for strengthening and providing a platform for bolting the wall

to the floor and joining corners, as shown in FIGURE 32, including any adjustment for the height of the wall, window, or door opening.

A hexagon frame building structure 70 is shown in FIGURES 33,34, and 35. Hexagon frame building structure 70 can be constructed from any of a wide variety of materials, depending upon the particular application. A wide variety of fabrication methods can also be utilized, including but not limited to extruding, molding, casting, etc.

In a preferred embodiment of the present invention, the hexagon frame building structures 70 are extruded recycled plastic composites (70 percent oak wood fiber and 30 percent plastic in a more preferred embodiment). Preferably, channels and stamped metal are applied during the fabrication process. Channels are provided to slide and lock the edges of the hexagons together. Further, adhering a solid board to each side of this frame can provide full hollow panels.

The hexagon frame building structures 70 of the present invention also allow reinforced materials and spacers to be inserted between the hexagon frame building structures 70, due to the open configuration of the structures 70. Further, concrete can be poured between the hexagon frame building structure 70 system to form a permanent structure like a wall, floor, road bed, bridge (see FIGURES 60 and 61) and other possible structure.

In one embodiment of the present invention, the hexagon frame building structures 70 contain six cavities. A vacuum is pulled in these cavities to provide the capability for insulation cavities. Insulation or other substances with a thermal storage and release function can be added to this cavity. The preferred insulative material to be inserted into the frame cavities is a bladder full of phase change materials (PCM's) (which can be obtained from Oak Ridge National Lab, Oak Ridge Tennessee U. S. A.).

Additionally attic insulation materials, called RCR, that absorbs heat during the day and release heat at night, are a preferred insulative material. This phase change material is insulation that consists of perlite embedded with hydrogenated calcium chloride. The phase change material changes from a solid to liquid at 82°F, absorbing heat (from a hot attic for instance) during the day, before the heat can penetrate a home. When attic

temperatures cool at night, the phase change material solidifies and releases the heat back into the attic, moderating outdoor temperatures.

A preferred board for use when applying phase change thermal materials is Concrete Hardie Board. If a hexagon frame building structures 70 is glued to a sheet of hexagon building structure panels, half of a panel is produced. In one embodiment, these panels are provided with gypsum board for the finished wall. Other embodiments employ Concrete Hardie Board to finish the floor.

A hexagon frame building structure that is split along flats 71 is shown in FIGURES 36,37, and 38. A hexagon frame building structure that is split along points 72 is shown in FIGURES 39,40, and 41. A partial wall assembly of the hexagon frame building structures 70 and the partial hexagon frame building structures 71 and 72, of FIGURES 33,36, and 39, is shown in FIGURES 42 and 43. The full and partial hexagon frame building structures 70, 71, and 72 are assembled into a wall (preferably 3.5 inches in thickness). The six alignments fastening holes 4 of each hexagon frame building structures 70 are equally spaced and are located as described in detail above.

Referring again to hexagon building structures in FIGURES 44,45, and 45A, the alignment of the fastening holes 4 of the hexagon building structure 7 with the fastening holes 4 of the hexagon building structures 8,9, and 10, is clearly shown. The hexagon building structures form a central structure 100 for increased load bearing capability. These six alignments fastening holes 4 are found by drawing lines between each corner-point and the two closest non-adjacent, corner-points (forming two equilateral triangles). The intersecting points of these lines define the location of the alignments fastening holes 4, which are equally spaced. The size of the alignments fastening holes 4 can be varied in order to fit a particular fastening system (or in the case of carbon foam heat exchangers, as described below in further detail, the conduit location).

"A"frame building end walls 101 and 102, are shown in FIGURE 46.

When the walls are assembled with hexagon flat ends on the floor, the roof 103 has a pitch of 60 degrees. Depending upon the type of window and door configurations selected, new hexagon derivative building structures 104 may be produced. Alternatively, full

hexagon building structures 7 are used, which results in the window size being reduced.

The hidden lines 105 produced by the offset layering of the hexagon building structures 7 and hexagon derivative building structures in the second layer, are shown in FIGURE 47.

Panel materials are selected based upon many different criteria, including but not limited to, climate and bug resistance requirements. In one preferred embodiment, the panels 1, and 2 are manufactured from wood chipboard. Some other suitable materials include foam, aluminum, steel, fiberglass, concrete, aluminum foam, create, plastics, composites, and the natural fibers native to the home can be selected as building material.

The thickness of foam or boards can also be changed to meet the specific builder requirements. In a preferred embodiment, the present invention primarily uses 7/16-inch Weyerhaeuser chipboard and 2-inch foam, however any metal wood, plastic, concrete fiber, or other material can also be combined. Screws, bolts, and other fasteners are selected by the builders to fit their existing tools and engineering needs. Carpets, hardwood floors, tile, gypsum board, finish wood paneling, and any other suitable finishing materials can be pre-assembled on hexagons.

As previously mentioned, in another preferred embodiment of the present invention the offset layered tessellations take the shape of square building structures 106, as shown in FIGURE 48. In this embodiment, four alignment-fastening holes 107 are utilized to produce the common point-to-center fastener locations. Additional alignments fastening holes can be added for specific applications, however, the holes 107 are the preferred number and are positioned in the preferred locations.

Referring now to FIGURES 49 and 49A, the front 111 and back 112 of two layered offset square building walls are shown. The square building walls have a 45 degree pitched roof 120. Further, the construction of the square building walls preferably also utilizes square derivative rectangle building structures 113 (shown in FIGURE 52), triangle building structures 114 (shown in FIGURE 53), trapezoid building structures 115 (shown in FIGURE 54), and triangle quarter-section building structures 116 (shown in FIGURE 55), in addition to the square building structures 106.

Referring now to FIGURES 50 and 50A, the front 121 and back 122 of another set of two offset layered square building walls are shown. In this embodiment the

square building walls also have a 45 degree pitched roof. Once again, the construction of the square building walls preferably also utilizes square derivative rectangle building structures 113, triangle building structures 114, trapezoid building structures 115, and triangle quarter-section building structures 116, in order to form doors openings. The hidden lines 118 produced by the offset layering of the square building structures 106 and square derivative building structures (rectangle building structures 113, triangle building structures 114, trapezoid building structures 115, and triangle quarter-section building structures 116) in the second layer, are shown in FIGURE 50B, as well as corresponding point-to-center locations.

A square tessellation panel 106 is shown in FIGURE 51. Common fastening points 107 are located in the center of each of the four-quarter sections.

Preferably, the insulation foam core 108 has oriented strand boards (OSB) 109 and 110 adhered to the core 108. Due to the difficulty in cutting concrete, square tessellation panel 106 are a preferred configuration when James Hardie concrete fiberboard is utilized as a building material. Further, square tessellation panels 106 make effective floors and roofs, because concrete can easily be cut and applied to a square shape, and floor covering (i. e. tongue and groove flooring) can come adhered to the concrete fiberboard. Marble, granite, glass, and other difficult to cut materials are better in square form.

Referring now to FIGURES 56-58, in one embodiment of the present invention, the hexagon building structures are fabricated from a glowing layered plastic developed by Cambridge Display Technology (CDT) of Cambridge, England. In accordance with the present invention, computer and television displays are made from these light-emitting polymers (LEP's). Preferably, these computer and television displays are only approximately 2-millimeters thick.

Other miniature display technologies are field emission devices, which essentially rely on miniaturized versions of electron guns used in cathode ray tubes. These new emerging flat technologies are also compatible with the offset layering hexagon building structure technique of the present invention. To make polymer light-emitting diodes (LED), very thin layers of fluorescent polymer are sandwich between two electrodes. The tooling of these displays to all the needed sizes of is very expensive.

Each application requires a new display size. The tessellation offset layering of the present invention is well suited for efficiently constructing flat display technology in order to meet customer's requirements.

Display technologies constructed in accordance with present invention integrate display electrical connections from one offset tessellation layer to one or more other offset tessellation layers, thus, producing a light enhancing screen that projects an even display of light. In light-emitting polymers, this"macro"offset layering can be the poly (p-phenylene vinylene), or PPV layer offset from the CN-PPV layer, including the offset of the protective transparent substrate. These joining lines can be angled to further provide an even display of light where one circuit joins the other. A dramatic advantage of utilizing the present invention for this type of structure, is that to the customer the display appears substantially as one large screen, while to the display manufacturer the screen component sizes are common tessellations and small enough to produce a wide range of sizes, thus reducing costs.

In a preferred embodiment of the present invention that incorporates the offset layering of light-emitting polymer tessellations, hexagon tessellations are employed on one layer, while another layer employs another shaped tessellation, such as square tessellations. (This alternative technique can also be used with the offset layering of hexagon or square building structures). Due to factors such as crystal lattice structure, different materials are prone to effectively produce different types of tessellations. Thus, preferably a material and tessellation matched for optimal configuration parameters.

The offset layering of hexagon building members in accordance with the present invention, is particularly effective when utilized in conjunction with display technologies, because the human eye does not readily distinguish hexagon angles in a scan. Further, the fabrication of display technologies with hexagon building members is complete without the requirement of any hexagon derivative shapes, because the display can be optically turned on or off to make light emit from only half of the hexagon split at the points or flats of the hexagon. Thus, a completely square display can be produced from offset layered hexagon building members. Additionally, uneven edges of the

hexagon display assembly can be covered with an opaque frame. In some embodiments of the present invention, more than two layers of tessellations are employed.

The screen technology of a cathode ray tube desktop monitor, or CRT can be combined with a low-power cold cathode to produce a display module less than eight millimeters thick. This technology is known as ThinCRTTM (produced by Candescent Technologies Corporation, 6320 San Ignacio Ave. San Jose, CA 95119) and has been developed with the demands of portable multimedia in mind--to deliver bright true color fidelity, brighter video-rate images with no motion smearing, wider viewing angles and lower power consumption than prior art. The offset layering of hexagon building members in accordance with the present invention is ideally compatible with ThinCRT technology for flat panel displays.

Unlike semiconductor devices, where costs typically decline over time as consumer demands push reducing the size of these devices, the opposite effect is true for displays. Display screens continue to grow larger, and thus, the need for these displays screens to be manufactured with a scaleable technology, such as the hexagon building member offset layering technology of the present invention, continues to increase. By utilizing the present invention, larger sizes of displays screens can be manufactured with little increase of effort, due to an efficient offset layering tessellation architecture of the present invention. Further, fewer tools and processes are needed than that required by the prior art.

Referring again to FIGURE 56, a preferred embodiment of the present invention incorporates a cathode/backplate 130 is a matrix of row and column traces.

Each crossover lays the foundation for an addressable field of microscopic cathode emitters. Each crossover has up to 5000 emitters, 150 billionths-of-a-meter in diameter.

This emitter density assures a high quality image through manufacturing redundancy, and long-life through low operational stress. Emitters generate electrons when a small voltage is applied to both row (base layer) 131 and column (top layer) 132. This method of emission is known as"cold cathode"and is very power efficient because the devices do not have to be heated. Faceplate picture elements (pixels) are formed by depositing and patterning a black matrix, standard red, green, and blue TV phosphors 134 and a thin

aluminum layer 133 to reflect colored light forward to the viewer. A focusing grid is layered on the cathode, collimating electrons to strike the corresponding subpixel, ensuring color purity and power efficiency.

FIGURES 57 and 58 illustrates ThinCRT display utilizing the offset layering hexagonal building member architecture of the present invention. The cathode/backplate circuits 130 and faceplates 137 are aligned by point-to-center offset layering (as described in detail above), and are sealed with the driver electronics attached.

Total display thickness is less than 8 millimeters. Each pixel is illuminated by thousands of tiny electron emitters providing an even display of light through seamless tileable tessellation patterns (preferably hexagons) formed from pixel layers and cathode layers created from a basic geometric hexagon grid. Emmitters produced from carbon nano- tubes need to be circuited and this tessellation offset layering provides a uniform base.

Alternatively, other tessellations can be applied to form the seamless grid, like squares, triangles, or complex shapes.

Beneficially, hexagon grid seams can be at right angles to the surface plane or slightly angled in order to provide an overlapping seam for phosphors application on that angle or a stepped fit ledge. This phosphors placement eliminates the visible seam, thus, further illustrating the ideal computability of the use of the offset layering hexagonal building member architecture of the present invention with CRT technologies.

Additionally, different CRT technologies can be layered in between different functioning structures of the present invention.

Retroreflective sheeting is based on transparent microprism films (manufactured by Reflexite Corporation 120 Darling Drive Avon, Connecticut 06001).

Microprism retroreflective sheets are produced in a variety of colors and reflect color back to the source of light. These sheets can be cut or cast in hexagon tessellation forms for offset layering in accordance with the present invention, thereby producing images with multiple colors in the same plane. Referring again to FIGURE 8, in a CRT display of the present invention, the red 140, blue 141, and green 142 colored hexagons are selected and joined such that at least one of the six hexagon points 143,144, 145,146, 147, and 148, is

touching all three different colors. This allows light projecting through the hexagon from a back light source 149 to be angled such as to allow most desired colors to be produced.

Multiple layers of colors can be applied to achieve the color desired and the color film can be pure transparent colored filin or reflective opaque backed film. In one embodiment of the present invention, this type of apparatus is manufactured on a microscopic level. Top electrodes and transparent electrodes are positioned in each of the six hexagon corner locations. Microscopic hexagon sheeting can be manufactured by Frenel Optics 1300 Mount Read Blvd, Rochester New York 14606. Alternatively, grid patterns of other tessellation are utilized in this offset layering architecture of the present invention, since curved tessellations can be easier to shape. However, hexagon is the preferred shape for this optical color grid. In accordance with the present invention, projected or reflective observable colors are also modified by moving a light source large enough to cover several of the colors around the intersecting points of the hexagon- building members. The movement of the light relative to the intersecting points creates the resultant color mix.

In yet another embodiment of the present invention, the hexagon building structure is constructed from materials that include carbon foam, reticulated aluminum foam, copper foam, sintered metals, cast foams, and molded natural pumice, allowing the hexagon members to act as heat exchangers (see FIGURES 59 and 60). Fluid heat exchanger tubes fabricated from materials such as copper or graphite are inserted into the alignments fastening holes 4 (shown in FIGURE 1) and stacked in the substantially round hexagon assembly 34 in (shown FIGURES 22 and 23). In another preferred embodiment, the heat exchanger tubes are inserted into the conduit holes 12 located in the plane of the hexagon building structures 7. Hexagon heat exchangers also have tubes positioned axially through the plane. A heat exchanger constructed in accordance with the present invention integrates directly into a building for passive solar heating (or if on the ground, in the floor for ground based cooling). The carbon foam integrates very effectively with a heat exchanger of the present invention since carbon foam has substantially more thermal capability than copper.

Referring again to FIGURE 59, hexagon carbon foam members 200 are clearly shown. The hexagon carbon foam members 200 are the same shape throughout the heat exchanger assembly 201. The heat exchanger assembly 201 is formed from offsetting hexagon carbon foam members 200 in alternating layers (in the same offset layering manner as previously described above with respect to other aspects of the present invention). Heat exchanger tubes 202 are inserted through alignments fastening holes 4 in order to hold the hexagon carbon foam members 200 together, as well as to integrate the thermal conductivity of the carbon foam. Tubes 202 represent the plumbing fluids that are passed during the functioning of a heat exchanger.

Heat exchangers typically require fluid transfer. The assembly of heat exchanger tubes 202 adapt to normal round tubes inherent in heat exchanger design. <BR> <BR> <P>Thermalgraph foam (manufactured by Amoco in Atlanta Georgia, U. S. A. ) is a sheet of carbon that conducts in the direction of its plane. In one preferred heat exchanger embodiment of the present invention, Thermalgraph foam is integrated as a layer within ORNL carbon foam (which conducts in every direction). Alternatively, ThermalgraphfS) foam is used as a complete replacement for ORNL carbon foam members 200.

Thermagraph conducts in the hole where it is cut so it works very well as hexagon 200.

In other preferred embodiments of the present invention solid carbon foam, solid metals, ceramics, carbons, polymers, glasses, or other materials make up heat exchanger materials. These tubes can be inserted along the plane as shown in the above-mentioned hexagon assembly 201 of FIGURE 59.

In another preferred embodiment of the present invention, a hexagon carbon foam heat exchanger assembly 203 is formed from closely tiled hexagons 200 and tubes 202, as shown in FIGURE 60. The assemblies 203 are close fitting tiled hexagons that are not offset when layered. In this embodiment, the tubes do not hold the hexagons together as in assembly 201. This is an advantageous configuration in an embodiment where the tube bundles need to be pulled apart or spaced for fluid flow. This configuration is also beneficial in an embodiment where a slightly larger offset hexagon assembly 201 is positioned to fix a non-offset hexagon assembly 203 in a controlled space.

In some embodiments, spacers are placed on the hexagons 200 in order to hold the

hexagons 200 in a desired space and provide a path for fluid flow between the hexagons 200. (See new drawing with spacers).

FIGURE 63-66 illustrates the preferred hexagonal shaft joint fastener 300 with a threaded ratchet head 302 mating to a hexagon fastener ratchet seat 308 and 309.

FIGURE 64 illustrates a perspective close exploded view of a hexagon 311 with the male hexagonal shaft fastener 300 of FIGURE 63 aligned with the hexagonal molded hole 307 of FIGURE 64. FIGURE 66 illustrates a perspective view of all six hexagonal ratchet fastener seats 308. Male hexagonal shaft joint fasteners 303 are inserted through hexagonal molded holes 307 until head 301 is seated on seat 308. Female threaded head 302 is rotated freely on threads 304, until ratchet 305 contact mating ratchet 309. A spanner wrench is inserted into holes 306 to rotated the head down ratcheting 305 and 309 together, until head 302 seats with 308 on hexagon 311, mechanically compressing layers of two or more hexagons. Ratchet surfaces 305 and 309 prevent the fastener from rotating due to structural vibration, securing the building for the live of building. Ratchet surfaces compress and expand, as they are being forced together or withdrawn by force rotating the head 302. Male fasteners 303 are inserted from the outside, which is the long shaft 303, and cannot rotate out, because of the hexagonal shaft 303 and mating hexagonal hole 307 prevents rotation. Hexagonal shaft 303 has a raised bump 303a to hold the fastener in the hexagon making assembly easier. These raised bumps can be put in numerous locations to pressure hold the hexagonal shaft in the hexagon during assembly.

This is a tamper proof fastener that cannot be rotated. People can feel secure within the wall side facing head 302 fasteners.

FIGURE 67 is an alternate tamper resistant fastener head 312. The bouquet type fastener 313 flares out on bevel 314 preventing rotation. This is less favorable, because the threads are much smaller to provide the bevel 314. This fastener does not have a need for ratchet 309 in the hexagon, because the bouquet 313 frictions against 314 resists reverse rotation.

FIGURE 68 and 69 is another alternative fastener that provides a male press fit fastener 315 and'/4-turn fastener 316 that insert into female dowel retainer 317.

Dowel retainer 317 has two female fastener fixtures 318 that are identical and yet provide

two separate means of fastener retention press fit flange 319 and'/4-turn slot 320.

Hexagon dowel plate 321 fits into six hexagon holes 322. Hexagon holes 322 mates to the dowel retainer and fasteners.

In FIGURE 63-69 this invention teaches how a shaped hole can be applied to layer, offset, and layer tessellations like hexagon. Square, triangle, rectangle, polygons, and other infinitely variable curved tileable shapes also have an unmet need to apply a shaped shaft to secure the fastener from one side and compress the building together mechanically in a friction fitting or mechanically locked fastener. These wholes can be slotted so the hexagon pressure is on the side of the hexagons and not on the fastener system. Fastener holes can be rotated as long as all the"shaped fasteners are rotated at the same angle relative to a flat corresponding flat edge. Three holes could be placed around the single fastener to increase strength. Vibration will not rotate the heads off and people outside can not dismantle the building. Shaped fastener shafts will not rotate in a matting hole. The preferred arrangement in this invention is a hexagonal shaft where each of the small hexagon holes are oriented pointing one of the points to each of the six flat sides of the hexagon. This hexagon shaped orientation provides registered holes for offset layering of hexagons. A shaped hexagonal hole is disclosed, but it is understood that other shaft and hole shapes can be applied, if all oriented the same way for symmetrical assembly.

FIGURE 70 is a side view of a preferred fastening means when walls are spaced and filled with straw bales or cast with concrete.

FIGURE 71 is a section view of a fastener head 333 with an insert 334.

These inserts can be cast in or pushed into a barbed molded hole 335. These have mounting value when placing finish sheathing like sheetrock"plasterboard, or decorative paneling. Sheetrock insert 334 would be protruding out past the sheetrock thickness or preferable just below the sheetrock thickness. Sheetrock can be hung on these barbed insets 334 without breaking through the surface of the sheetrock. This does not work on ceiling hung sheetrock and so inset 334 has to penetrate through the sheetrock to locate it and then a washer type fastener is pounded on the barbed insert. Sheetrock is a building

code firewall and this building fastener provides the means of hanging sheetrock to the plastic.

FIGURE 72 illustrates a perspective view of a preferred hexagon conduit pattern. A star 400 is formed where the points of the star are located at the mid-point 401 of each flat edge of the hexagon. A rhombus 402 forms at each point 403 of the hexagon.

An inner hexagon 404 forms in the center of the hexagon and is oriented the same as the hexagon perimeter. An equilateral triangle forms between the inner hexagon 404 and mid- point 401. Applying this preferred pattern eliminates conduits that are not matched to others in an assembly. All conduits mate up and form full conduit throughout an assembly. Where hexagons are layers and offset in this invention.

FIGURE 73 illustrates a perspective view of a corner assembly of preferred hexagon conduit pattern in FIGURE 72 and fastener in FIGURES 63,64, 66, and 67.

Applying this pattern is not limited to the fasteners in this invention. FIGURE 73 provides a conduit system 405 that mates and forms full conduit when hexagons 406 are layered in a point to center arrangement with conduit facing the conduit of opposing hexagons 407.

FIGURE 74 illustrates a cross sectional side view of fasteners configured for multiple layers. Fastener 408 can only mechanically lock four other hexagons in this illustration. This invention teaches how any number of layers of hexagons can be fastened together by offsetting the fasteners perpendicular to the face of the hexagons. Each fastener 408 is inserted in the same pair of hexagons 409 and alternately inserted in two different pairs of hexagons 410 and 411 locking six hexagon layers together. This stepped pattern can continue any number of layers building a locked together wall. Fastener 412 is for the outside or inside wall to finish off the fastener system.

FIGURE 75 illustrates how sheathing panels can be glued to hexagon assemblies to make single structurally insulated panels. Hexagons edges 413 protrude outside the sheathing edge and will assemble into another panel by inserting and overlapping the hexagons in the panel. Glue or fasteners can be inserted through the overlapping hexagons from each full panel locking the panels together.

Curved hexagons can be injected or molded. GE Plastics makes a brand name Norolide and it is the preferred material where users want to meet water fire sprinkler building codes. These GE polymers are ideas to place fill materials in.

Bentonite is a natural mined mineral that has an adsorption of water 100 layers thick on its surface. This mineral is used in paper form and paint form to seal The present invention allows common tessellations to be integrated with tube bundles in order to make heat exchangers in a larger number of geometries, ranging from flat radiator-like devices to flat plane-type heat exchangers. The tubes can be extruded shapes like squares, triangles, hexagons, polygons or other shapes, without departing from the scope of the present invention. Tubes groves can be cut along the plane of these hexagons to make flat plane oriented heat exchangers for floors, walls, working surfaces, and other industrial cooling systems like refrigeration beds. These tube groves in FIGURE 72 and 73 increase structural stability by preventing hexagons from shifting in the plane direction. Some heat exchanger materials like reticulated aluminum foam can be compressed onto the surface of a tube insertions, which may have corrugated surfaces holding the tube and hexagon in rigid location. In another embodiment of the present invention, FIGURE 59 and 60 also illustrate how helium hexagons are assembled to make aircraft fuselages (as will be described in further detail below).

FIGURE 77 and 78 illustrates an alternative fastener comprising a rod or conduit 415 insertion into the common matching plurality of protrusions 431 and 432 up off the plane surface 430 of the hexagons conduits 400 in FIGURES 72 and 73. FIGURE 78 is a cross sectional side view of alternate conduit 400 which provides a plurality of protrusions 431 and 432 up off the plane surface 430 of the hexagons. These protrusions 431 and 432 have holes 416 and 417, which line up for rod 415 insertion when hexagons are assembled in layers onto each other according to FIGURE 72 and 73. This invention teaches a novel fastener along the conduits, which matches all conduits and fasteners along any conduit formed when two hexagons are assembled as referenced in FIGURES 72 and 73. FIGURE 77 end view 425 of FIGURE 78 425b. FIGURE 78 has a partially assembled cross sectional side view 427 of hexagon 418 and 419 spaced apart by air gap 420, and cross sectional side view 428 with the closure of air gap 420 and insertion of

conduit (or rod) 415 into holes 416 and 417 locking hexagon 418 and 419 together. These fasteners provide a long fastener 415 along the length of the hexagon, which can float (relative to the plane of the hexagons), move within holes 416 and 417, due to thermal growth of hexagon or fastener materials. In this preferred embodiment, the hexagon can settle into place and grow and shrink thermally without added stresses to fasteners or materials. Gross movement can occur without the loss of the fastener performance. The weight of the hexagons and the loads placed upon them will compress or pull just hexagons six edges not through fixed fasteners represented in prior art. It is understood that not all hexagons will be a molded plastic; and alternative materials will be applied where metal plates (or composites) 435 and 436 with holes 416 and 417 could insert in, or replace the protrusions 431 and 432 in the hexagons 418 and 419 conduit 400 receiving insertion of rod 415 (conduit). Optional metal plates 435b and 436b provide a punched tab 437 that snaps and locks the two plates 435b and 436b together eliminating the need for conduit rod 415 insertion.

Figure 79 provides flexible rod extensions 440 out of hexagon assemblies in FIGURE 77 and 78 for roof tarps 441, sports net attachments, wide rain collection, and extensions for cable attachment or insertion into conduits. These roof tarps can be layered for insulation functions and clear for plant green house food growth buildings or sun rooms. Flexible solar voltaic films are also available to attach to rods. Reflective polymers are available in a wide range of plastics, however polyimide materials are preferred clear or reflected polyimide films from SRS Technologies 1800 Quail Street, Suite 101 Newport Beach, California 92660. SRS's films are the only available polyimide thin films that are clear/colorless. They also have higher UV resistance, are more transparent, and have greater long-term storage capacities than competing films. Furthermore other potential commercial applications for SRC CP1 and CP2 include integration of electric circuits in a flexible film, inflatable structure for reducing fiom vibration and increasing insulation quality with air or other gases like argon and helium. Inflatable SRC polyimides can also have phase change pyrolytic salts for chemical change brought about by the action of heat. Liquid, gases, and solids can be combines to build inflatable structures that attach to the hexagon structure. SRS's films polyimide thin filins that are clear/colorless

can enclose adsorbent composites like carbon foam coated with montmorillinites or zeolites to adsorb and desorb adsorbates. Carbon nanotubes can be grown onto a wide range of adsorbents like montmorillinites or zeolites to lower the temperature of desorption of adsorbates like water, nitrogen, carbon dioxide, volatile organic compounds.

Lower temperature passive solar heat can desorb adsorbates from adsorbent composites provided within SRC film envelopes where prior zeolites alone could not desorb.

A super critical fluid MuCell microcellular process is the preferred foam for tessellation building material, because it can be foamed out of virtually any polymer at any density, and filled with a voluminous number of fillers like carbon fibers, glass fibers, ground glass, wood fibers, and other minerals.

A microcellular thermoplastic foam technology was invented at Massachusetts Institute of Technology is being commercialized by Trexel of Wobern, Massachusetts. The innovative new process uses high-cell nucleation rates within the foaming material to create foams with small, evenly distributed and uniformly sized cells (generally 5-50 micron in diameter). Trexel claims have been validated that the foam materials produced by this process, called MuCell2), have properties and uniformity superior to conventionally foamed products. MuCell uses Super Critical Fluids (SFCs) of atmospheric gases to create evenly distributed and uniformly sized microscopic cells throughout the polymer. It's suitable for structural-foam molding, as well as other injection-molding applications, blow molding, and extrusion, and does not require chemical blowing agents, hydrocarbon-based physical blowing agents, nucleating agents, or reactive components.

MuCell process enables molders to foam materials that cannot be foamed successfully with conventional technologies, such as high-temperature sulftones, polyertherimides, liquid-crystal polymers, and thermoplastic elastomers such as high- temperature elastomers such as Kraton@ and Santoprene, and realize a 20-50% weight reduction and a reduction in Shore A hardness@. Some polymers can reduced in weight by 93% and others 9%. There is a wide range of materials that will seal in the small molecule of helium into closed MuCell cells of a polymer.

MuCell microcellular foam process follows four basic steps:

1. GAS DISSOLUTION: A supercritical fluid (SCF) of an atmospheric gas is injected into the polymer through the barrel to form a single-phase solution. The super critical fluid delivery system, screw, and injectors design for the MuCell process allow for the rapid dissolution rate required. This invention teaches a helium gas to produce a buoyant material. 2. NUCLEATION : A large number of nucleation sites are formed (orders of magnitude more than with conventional foaming processes) where controlled cell growth occurs. A large and rapid pressure drop is necessary to create the large number of uniform sites. 3. CELL GROWTH: Cells are expanded by diffusion of gas into bubbles. This invention teaches helium gas diffusion. Processing conditions provide the pressure and temperature necessary to control cell growth 4. SHAPING: Any shaped mold design controls part shape. This invention teaches using polymers that will trap helium permanently. For example, a choice is polycarbonate and combinations of the above-mentioned polymers as well as others. Hydrogen gas can be injected into the foam, but will ignite and this has function where it is desirable to destroy high altitude weather balloons for example. Phosphors can also be introduces into the cells in a controlled manor to provide extruded flat panels TV's or monitors. Mineral fills can be applied to this invention. Minerals like bentonite can be used as fill in this material. This invention teaches a bentonite component montmorillonite, where the mineral is modified to integrate to the polymer and later adsorb moisture in some application as well as just act as a very uniform filler. This invention teaches montmorillinite is the preferred material because it naturally forms a"T"bond from its high negative and positive charge, cat ion sites. The very flat mineral is a best"modified"custom mineral, because it has such a high exposed surface area to modify to bond to the polymer in a very uniform or surface coating. This invention teaches a modification of montmorillinite where the montmorillinite forms on the wall of the mold in one case and uniformly integrated within MuCell in the other case.

Minerals and other metals will combine with montmorillinite. Moisture is the biggest layer on montmorillinite and when injecting polymers with water-saturated montmorillinite (bentonite family of minerals) under the MuCell process the water steams through the polymer structurally reticulating the foam. This produces reticulated foam.

Montmorillinite can be viewed as the carrier mineral of a range of other"agents"into the

MuCell process. This invention teaches that polymer binders of zeolite molecular sieves can be produced under MuCell's process providing foamed zeolites with increased surface area multiples more than current pellets provide much larger monoliths can be"foamed" with the same effective surface area as thousands of pellets. This type of foam can be cst into hexagons and used for"transpiration"cooling of a building, where the moisture draws the heated molecules out of the building keeping the building cool or frozen, which is dependent on the rate. MuCell's process is ideal for hexagons injected centrally, because a very high energy release occurs during MuCell injection, which naturally wants to form a circle. Hexagons only have six points to fill in not far from the edges of the circular force being stopped by the flat edges of the hexagon.

After hexagons are formed a coating of infrared paint is applied to the hexagon surface reflecting heat away from the hexagons and retaining heat within the hexagon. This paint is similar to Army tank coating used to reduce infrared signature of men within the tanks.

Referring again to FIGURE 1, the foam 3 can be manufactured from many different substances, including but not limited to neoprene, hypalon, vinyl nitrile, nitrile, (NBR), epichlorohydrin, or urethane foam. Closed cell foam is manufactured in several densities. The more air or gas pressure applied during the foaming process, the more or less dense the foam becomes as a final product. Nitrogen gas is typically applied to the gas to make closed cell foam, because trapping nitrogen in the closed cell foam rather than air reduces oxidation. In a preferred embodiment of the present invention, the nitrogen is replaced with helium, producing a new neoprene closed cell helium material. In the present invention helium gas (or another suitable lightweight gas or gas mixture) is used to form closed cell foam, trapping the lightweight gas in the closed cells.

The present invention advantageously traps helium in the closed cells to produce foam that will float in the air. The foam density is determined by the pressure of gas volume applied to the foaming process and can be very dense or of very low density (to the point of being extremely fragile). The mole weight of helium is 0.004. In one atmosphere, one-cubic foot of helium will lift approximately 0.0646 pounds off the

ground. Each engineering project utilizing this invention will determine the requisite helium foam density based on strength and lift requirements. Applications designed to encounter only low levels of stress (such as telecommunications or high atmospheric satellite broadcast and transmission systems) use very low-density fragile foam, because the equipment is installed only once, and with very minimal handling or need of impact resistance. In contrast, a personal airplane will be higher density foam for strength, because of landing impact and frequent human handling.

Helium closed cell foam can be shaped into a hexagon building structures 7, as shown in FIGURE 1. The closed multi-cell material can form many small shapes, including but not limited to tubes, squares, triangle polygons, hexagons, honeycombs, and other shapes, without departing from the scope of the present invention. Further, in some embodiments of the present invention, loose beads filled with helium are packed in the cavities (like existing aircraft voids) or in hexagon building structures that are specifically engineered to have cavities to hold these beads or relatively small bladders. Multiple balloons are contemplated as well.

Referring now to FIGURE 9, in one embodiment of the present invention, carbon fiber composite sheathing 7a and 7b are applied to the hexagon building structures 7 making them substantial structural panels by adding strength to the helium hexagon foam panel. Long rods, preferable graphite carbon fiber rods (or tubes) are inserted in the alignments fastening holes 4 (shown in FIGURE 1) or another desired location. In yet another embodiment, substantially round hexagon assemblies 34 (shown in FIGURES 22 and 23) are stacked forming the fuselage of a plane or a boat haul. In the embodiment of the present invention shown in FIGURE 44, alignments fastening holes 4 are sized and configured for rod fastener insertion to connect hexagon building structure 7 to hexagon building structures 8,9, 10, as well as any number of other layers and shapes.

In still other embodiments of the present invention, flat wings and shaped wings are derived using the assembly methodology of present invention. Graphite rods, cable, rope, plastic, carbon fiber, tapes, adhesives, or any other fastener can also be used to build desired shapes. Once a shape is constructed, skin can be wrapped around it. The skin is applied using a variety of methods, including but not limited to fiber glassing,

carbon fiber spinning, painting, plastic vinyl wrapping, dipping, and shrink-wrapping. Any cavities in the hexagons can be filled with a foaming agent or other material. Hexagons can be built into personal aircraft or industrial aircraft, toys or any other floating application where floating is desired.

Any shape helium foam parts can be tooled by molding, machining, extruding, hot knife, wire cutting, saw, and water jet cutting techniques. Future shaping by extrusion, ultrasonic, dielectric, microwave, and lithography, chemical or laser is also possible. Some embodiments of the present invention utilize helium closed cell foams for buoyant aircraft. Many base materials will foam other than neoprene and are applied in alternate embodiments of the present invention. Aluminum foam is a good candidate for aircraft. Indeed, many metals can be foam manufactured in accordance with the present invention, such as titanium. Flexible foams are also available and are considered good species of foam for helium.

Honeycomb cores are used in the fabrication of lightweight structures typically used in the aerospace and commercial markets and are employed as the material for hexagon building structure 7 in some embodiments of the present invention. The core material is typically"sandwiched"between skins of aluminum or other high strength composite material. A bonding adhesive is used to attach the"skin"material to the honeycomb core while the in the presents of a helium gas trapping the helium in the honeycomb. The resultant honeycomb panel offers one of the highest strength to weight constructions available. Aircraft engine nacelles, flaps, overhead bins, floor panels, and galleys all are constructed from honeycomb core. Honeycombs can be cut into hexagon shapes, or other tessellations, with fasteners referenced for use in embodiments of the present invention.

Helium gas can be used as the fill gas for the bubbles packaging (such as SealedAir Bubble packaging manufactured by Sealed Air, Park 80 East, Saddle Brook, NJ 07663) making the packaging float in air. This bubble helium packaging can be engineered geometrically to match and be sealed into the honeycomb materials referenced above, by sealing the bubbles packaging in additional skin for strength. The plastic can be selected for adhesive bonding, dielectric, or ultrasonic sealing. This sealed helium

packaging is used as filler in many parts of aircraft or other structures in accordance with the present invention.

Applications of this technology range from air floating to water floating structures or devices. Space structures are also possible and would aid earth-launching weight. Toys, signs, planes, bridges, boats, trains, barges, cargo, underwater systems, air or watercraft, manned or unmanned systems are possible. Homes and furniture could be built to float in air. An untrained aviator farmer could apply agriculture chemical or biological agents from air. Any air, water, land, space transport, or fixed floating type device could be assembled from this invention. Extremely lightweight planes can be produced that have an actual weight (without helium) that is substantially larger. Carbon foam and other heat adsorbent material can be employed to heat the helium obtaining extra lift. These materials are covered and uncovered to control heat. Phase change heat storage systems are also applied to the present invention to keep the system in high elevation at night by heat recovery.

Prior art in helium systems consist of bladder or balloon type containment.

None of this prior art could be accelerated in the air without distorting the shape or destruction. A hole in the bladder type configuration generally loses all the gas in that section. A hole of the same size in the present invention does not significantly impact this helium foam because the present invention teaches a closed cell helium foam that compartmentalizes the gas in millions of individual chambers (in the case of large systems). Thus, this structure can float in the air, be cut without dramatically reducing buoyancy, and has structural strength so building structures can be shaped, coated, and assembled into a variety of configurations. Reticulated foams are open cell, and can still be used as a helium vessel of the present invention, if a coating is placed completely around the foam to seal the helium in the foam.

In still another aspect of the present invention, aircraft related systems are being directed through the air by thin layer composite unimorph ferroelectric driver <BR> <BR> "wafer" (U. S. Patent No. 5,632, 841 Hellbaum et al. ). Motion occurs when high frequency voltage is applied to the wafer driver directing airflow to move the whole

aircraft related systems. Hexagon wafers can effectively morph the whole surface of a craft. This technique can be applied to water equipment as well.

Polyimide foam can be foamed in place for installation and repair, resulting in dramatic labor and material cost savings. This low-density foam can be processed into neat or syntactic foams, foam-filled honeycomb or other shapes, and micro spheres. Small glass micro sphere have iron tunnels that cause them to leak helium gas. These same iron tunnels allow glass spheres to be filled with helium, which can then be sealed shut by polyimide thin films or metalizing the iron tunnels shut. These products offer excellent thermal and acoustic insulation, and high-performance structural support, as well as other benefits. Polyimide foam meets aerospace industry demands for high-performance structural foam with increased stiffness but without large weight increases.

The process for this foam begins with a monomeric solution with salt-like properties to yield a homogeneous polyimide precursor solid residuum. The resulting precursor can be processed into polyimide neat or syntactic foams, foam-filled honeycomb or other shapes, and microspheres, all of which produce useful articles through normal foaming techniques. These spheres can be opened vacuumed clean of gas and moisture filled with helium and reclosed. These helium filled foam spheres are ideal for containing the helium, which is a very small molecule that escapes most polymer or latex bladders.

These polyimide foams can be coated around other helium filled foam structures like urethane foam structures or reticulated foam filled with helium to form gas tight monolith helium filled foam. Any composite, such as carbon graphite materials, carbon foams, metal aluminum foam, paper, paper fiber products, cloth, and fiberglass can be coated with these foams to seal in helium. Very low-density materials can also be coated with polyimide foam to seal in helium.

This process can produce foam and microsphere materials by reacting a derivative of a dianhydride (e. g. , ODPA, BTDA, PMDA) with a diamine (e. g. , ODA, PDA, DDS). A mixture of two or more polyimides can be combined or used separately to make a variety of polyimide foams with varying properties. Foams and microspheres can be fabricated to specific densities from approximately 0.5 to over 20 pounds per cubic foot.

A preferred method of the present invention converts the above-mentioned low-density stable polyimide foam into a low-density stable carbon foam or fiber composite by applying microwave energy. In some methodologies of the present invention, pressure is applied during heating the polyimide resin as an added control of density. The resultant carbon foam is very thermally conductive. Aluminum molds are preferred for this process because they do not require a mold release agent. In some alternate embodiments, other molds are selected because they will bond to the carbon end product and become the final integrated net shape products. Carbon foam, carbon fiber, and graphite composites, are all products that can be produced by microwaving a cast or molded shape of polyimide foam. The foam can be cast, molded, and formed on a variety of materials. This foam is transparent and can be backlit illuminating a building. This foam can me easily molded into curved shapes and dome tessellation components.

The unique quality this stable foam has is its integration to other materials and then conversion to carbon materials by microwave or other heat energy. A preferred embodiment of the present invention microwaves polyimide foams to achieve control of polyimide density. This invention teaches converting carbon materials and controlling density to produce reticulated carbon foam having near original polyimide foam density.

By controlling the density and form of the foam prior to carbonizing the foam, new levels of material density and material integration can occur.

Microwaving is a radiant energy source so when converting polyimide foam to carbon materials only a portion of the foam needs to be converted based on the power and direction the microwaves are directed. Metals like magnetic materials can be added to the foam prior to microwaving the materials into carbon materials. These metals can be positioned to reflect the microwaves into a pattern that localizes the carbon conversion of the polyimide. Insulators and conductive carbons result from this process.

These processes can be stopped at any point during conversion to get carbon, graphite, or other composites of the polyimide foam. No other process provides the localization of producing insulation and conductive materials as an integrated product. Carbon fibers (chopped, or long fibers), fiberglass, metals, or other fibers can me molded into this

composite system. Paper molds can be cast onto and then removed to form complex shapes.

In a preferred embodiment of the present invention, aluminum foam material is utilized to construct foam panels, hexagon building structures 7, and other tessellation shapes. Additionally, aluminum foam can be applied to obtain a final net shape on the outer structure of a hexagon assembly. Hard aluminum foam cores can have complex exact shapes on the outside. The final outer skin hexagonal composite can also be a unimorph ferroelectric driver"wafer"that provides electronic control of the surface shape. These wafers can be seeded with materials carbon nanotubes (referenced in this invention) can be grown on under a vapor deposition process. High or low density carbon nanotubes will grow on the surface based on the density of the seeded materials. This invention teaches that growing carbon nanotubes on these wafers will enhance the thermal absorption into the wafer. These wafers are made in a variety of shapes and sizes providing a wide range of density requirements to optimize thermal absorption needed to increase the thermal absorption into the wafer and to radiate heat back to the surrounding environment. Carbon nanotubes can be deposited in a straight, curved, zigzagged, and combinations of each shape. Each carbon nanotube is"individually, bonded to the wafer substantially perpindicular to the wafers surface, providing the wafer a wide vibration bending range with no stress to the nanotube. Fluid flow across the carbon nanotubes connected to the wafer can be dipped in fluid, exposed to air or gas, and integrated into other materials the wafer might be mounted to. Adhesives could be applied to nanotube ends. Zigzagged carbon nanotubes would provide the wafer a predictable spring surface to lay the wafer onto during its operation. Wafers will generate voltage when a thermal absorption process is applied across the wafers surface ; carbon nanotubes increase the efficiency of this process by substantially increasing the surface area. More nanotubes can be provided to one side of the wafer absorbing heat unevenly relative to each wafer surface driving the wafer frequency generating more voltage. Different types of nanotubes can be provided to each wafer side and mixtures of carbon nanotubes types and lengths can be grown on the surfaces to match the thermal source. These wafers can be the hexablock in this invention, where hexsuperelements service processes are applied to

optimize the placement of carbon nanotubes to generate the greatest voltage from the selected heat-source. Heat sources can be solar, gas fires, waste heat, or other sources like ice sources. These voltage generating wafers can be mounted between a hot (heat rejection side) and cold side (heat absorption side) of a heat pump system. This invention teaches that the most optimized application of this wafer/carbon nanotube wafer is in the heat pump thermal battery system described in PCT/US01/12369, U. S. Patent Application No. 09/898,758, and United States Patent number 5,813, 248, where a temperature difference is generated and the potential to store the energy is an unlimited time. These wafers are ceramic layers of materials bonded by co-polyimide providing high temperature surfaces for carbon nanotube applications.

Silica carbonate aluminum foam exhibits a combination of qualities not found in other low-density materials including sufficient strength to serve as structural members, good thermal qualities for insulation, resistance to fire and immunity to electromagnetic fields. Aluminum foam is strong enough to build panels without sheathing bonded to each side of the panel, just aluminum foam is needed. Sheathing panels can be bonded into a sandwich arrangement if extra strength is desired in application where thickness and strength need to be at the highest density. Aluminum foam can be heated in shaping the hexagon building structures 7 into curved shapes in order to form a macro-sphere, large tube, aerospace component, boat hull, auto body, or frame components. Final net shape surfaces can be polyimide foams as described above.

During the gas injection stage of aluminum foam production, helium gas can be substituted for air. (Other gases and/or liquids can also be substituted for air and combined with the aluminum foam.) The combination of low aluminum alloy weight and helium gas is ideal for making strong air buoyant structures. Heat should be applied along with any other coating to seal the helium into the aluminum foam. Copolymides polyimides, or other suitable materials can be added to the aluminum foam to form a gas tight seal for helium gas. Carbon fiber, carbon foam, ceramic spheres, copper foam, glass, and other structural material can be cast while the foam is in the liquid state. Paper and burnable cores can also be cast forming complex shapes.

Aluminum foam can be cast around a carbon foam or carbon fiber monolith to produce gas tubes. In the case of the carbon fiber, an insulated structural vessel will form around the carbon fiber. A copolymide coating can be applied to the outside of the carbon fiber to form a gas tight seal between the carbon fiber and aluminum foam. The closed cell foam of the aluminum has small fractures that require closure to produce a gas tight seal. This aluminum foam can produce simple structural insulated foam around a pressure vessel. Carbon fiber reduces gas pressure by adsorbing the gas. Natural gas stores at 3000 pounds per square inch (psi) in a typical pressure vessel, but when stored on carbon fiber gas pressure is reduced to 500 psi. The aluminum foam as a structural and insulating material further reduces the possible rupture of a gas pressure or vacuum vessel.

Thus, fuel vessels can be inserted into hexagon building structures to store fuels. ORNL carbon foam referred to above is porous foam and aluminum does not stick to it when it is molded to its surface shape. The porous carbon foam can have air passed through it to foam the silica carbonate aluminum foam materials. The crucible containing the aluminum just prior to foaming would be totally or partially made from carbon foam. This carbon foam will not provide an opening for aluminum to flow through, but does provide an air path for blowing air into the aluminum foam replacing mechanical stirring and air insertion rods that do not make uniform aluminum.

Reticulated aluminum foam can be manufactured by placing the silica carbonate aluminum in a carbon foam closed tube. In one embodiment the mold can be a hexagon mold with the walls of the hexagon a graphite closed surface and two of the opposing flat ends of the hexagon would be porous carbon foam, one to rest the molten aluminum materials on and the other to pull a vacuum. When a vacuum is pulled, the aluminum will foam into a reticulated porous aluminum in the form of a hexagon.

Hexagon molds are used in this example, but any shape will work where there is a carbon foam surface to rest the molten aluminum on and a vacuum surface to pull gas through the aluminum reticulating it.

FIGURE 80 is a rotated illustration of hexagon building blocks injection molded with carbon nanotube polymers in an equilateral triangle attachment arrangement.

FIGURE 81 is an illustration of hexagon building blocks 1000 injection molded with equilateral triangle male patterns 1001 and female equilateral triangle pattern 1002. Hexagons measure 1-meter (m) flat-to-flat and when two hexagons are assembled the thickness is 150-millimeters (mm). It is understood that any size can be made with any material. Every other equilateral triangle pattern on hexagon 1000 has pattern 1001 and pattern 1002, three each for each hexagon. 50-centimeter (cm) diameter tube 1003 is inserted into hole 1004 after hexagons are assembled onto each other. In FIGURE 80 triangle pattern 1001 and 1002 are assembled onto each other male to female patterns providing an aligned hole 1004 for tube 1003 insertion. Alignment hole 1004 is also an equilateral triangle formed by the three triangle coordinate points aligned on the midpoints of each flat edge of the hexagon. Two triangles are formed and rotated; offset one flat edge forming six tubes all in the same plane and coordinate points relative to rotating the hexagon around six equal times. These holes 1004 align to assembled hexagons and form straight hexagon conduit throughout a wall hexagon assembly. Hexagons can be molded (or cut) along the points or flat edges dividing the hexagon in half that when assembled form flat wall edges. These hexagons can have thermal materials, water maker adsorbents, inserted in-between the wall or in the conduits. The polymers of the hexagon can be made of zeolites or other adsorbents, including any fill materials. NASA/Langley polyirnides can be foamed and when burned convert to C02 and H20 meeting any fire code. These same polyimides can provide the base material for a wide range of fill materials, PZT Pezos- electric (magnetic field shielding), microscopic reflective particles suspended in an infrared transparent matrix binder, and a wide range of gases can be inserted into the foam, like argon, helium, nitrogen. NASA invented RP46 and 50 polyimides make aluminum foaming possible and provide the base material to substitute the air used to foam with pyrolytic phase change salts to fill the closed cells with a thermal management material.

The heat pump in FIGURE 9 and FIGURE 28 are tooled to insert into these hexagon for climate control.

Water makers are formed from these hexagon assemblies when the optional adsorbent materials are applied in the hexagon wall. Nighttime air moisture is adsorbed by the adsorbents and the daytime heat desorbs the adsorbent (water) from the wall.

FIGURE 81 is a rotated illustration of hexagon building blocks in FIGURE 80 injection molded with carbon nanotube polymers in an equilateral triangle attachment arrangement. Optional double sided hexagon patterns can be provided on hexagons so any number of wall layers can be assembled. It is preferred that he last hexagon be a flat surface in the case where a finish wall is provided. Conduit hole 1004 can also be assembled around a frame structure of tubing connected. Tubing 1003 is connected to tubing to form corners, roofs, floors, and wall structure. The tubing frame alone would provide the outline of the final wall assemble. Liquids can be passed from the grounds to through this tubing to cool or heat the assemble of tubes and hexagons. Magnetic material insertions can be placed into the hexagons to make a magnetic levitation train track invented by Magna Force of Port Angeles Washington. Magna Force proprietary magnetic field can be inserted into hexagon tubes 1004 or mounted onto the hexagon for a ready made track surface. Sensors, electric switching and general wiring can be inserted into the hole 1004. Flexible cables can be inserted into hole 1004 to make suspended walls, floors, roof, bridges, and climbing walls for athletic facilities. FIGURE 80 is an illustration of hexagon building blocks injection molded with carbon nanotube polymers in an equilateral triangle attachment arrangement.

FIGURE 82 illustrates hexagon panels providing curved conduits 1000 and 1002, and 1003 which align when assembled 1004. Radiant fluid heating and cooling tubes applied in flooring, walls, and ceilings for sprinkler systems can not be over curved or they will crack and leak. Hexagon 999 conduits can be curved in a wide range of radius to accommodate any tubing requirement. A layer of radiant infrared coatings are applied to the surfaces to manage heat radiating the heat into the room rather than floor. Offset layering, placing hexagon conduit face over opposing conduit lines up radius tolerance.

Curved hexagons can be injected or molded. GE Plastics makes a brand name Norolide (trademarked Noryl@) and it is the preferred material where users want to

meet water fire sprinkler building codes. These GE polymers are ideas to place fill materials in.

FIGURE 82 illustrates hexagon panels providing curved conduits which align for tubing 1101 when assembled.

FIGURE 83 illustrates three hexagon panels 1100 tiled providing curved conduits which align for tubing 1101 when assembled. This illustrates how FIGURE 84 illustrates two hexagon panels layered providing curved conduits 1100 which align for tubing when assembled FIGURE 85 illustrates side view of two hexagon panels in FIGURE 84 providing curved conduits which align for tubing when assembled.

FIGURE 86 illustrates isometric view of three hexagons rotated offset and layered onto three hexagon panels in FIGURE 83 providing curved conduits which align for tubing.

FIGURE 87 illustrates an equilateral triangle molded into a hexagon centrally providing three equally spaced points of six hexagon points, which assemble onto hexagons when rotated.

FIGURE 88 illustrates a side view of a hexagon 1200, triangle 1201, and hexagon 1200 stacked into hexagon-triangle-hexagon assembly 1202. an isosceles slot is formed This assembly can be molded into one part. In this invention the parts are bonded with adhesive. Triangle 1201 inserts between the hexagon stack and is also loose as an optional method of assembly.

FIGURE 89 illustrates a single loose triangle 1206 for insertion into hexagon-triangle-hexagon assembly 1202. Assembly 1202 has three triangle voids 1205, which loose triangle 1206 inserts into when assembling a wall or structure. This method of assembly is not offset layering, because the hexagon has three voids 1205 that receive triangle 1206. Holes 1207 are provided for added security when required. The change in the structure relates directly to materials used to make hexablocks. Many materials in the polymer family creep and thermally grow, while other metal materials or composites of carbon exhibit little growth.

FIGURE 90 illustrates an isometric view of a hexagon with male/female pegs, which replace equilateral triangles assembled exactly like FIGURE 80 and 81. The male peg 1210 and female hole 1211 for receiving male peg 1210 has advantages over equilateral triangles, when materials require thermal expansion clearance. Male peg in hole 1210 carries the weight of an assembly, while the hexagon edges provide clearance for said thermal material expansion.

HEXAGON TRIANGLE MONOLITH (one triangle): FIGURE 91 illustrates the outside top face of the hexagon triangle block 1111. Equilateral triangles 1112 are molded onto hexagons 1111. FIGURE 92 illustrates an end view of block in FIGURE 91 with a groove cut 1113 for offset triangle hexagon assembly FIGURE 96. FIGURE 93 illustrates an isometric inside bottom view of hexagon triangle 1111 in FIGURE 91-99. FIGURE 94 illustrates bottom view of FIGURE 91- 95 with sectional line orientation 1119. FIGURE 95 illustrates an isometric view of FIGURE 94 hexagon triangle 1111.

FIGURE 96 illustrates a sectional side view of sectional line in FIGURE 94 and 95.

FIGURE 97 illustrates an isometric view of two hexagon triangle blocks assembled with sectional line peg (dowel) holes 1118 and 1117 aligned when one third of the hexagon is offset-layered on top of the triangle. Triangles on hexagons combine the geometry of hexagon and triangles tiles 1111, which provides a groove 1113 in the triangle for securely mounting triangles and hexagons together by mounting the triangle 1112 to the triangles attached to other like hexagon geometry. In a wall triangles 1112 and 1112a mount to each other inside the wall and hexagons face the buildings inside and outdoors relative to the wall. Dowels 1120 can be inserted into dowel holes 1117 and 1118 for optional peg fasteners. FIGURE 98 illustrates a sectional side view of sectional line 1121 in FIGURE 97. FIGURE 99 illustrates top view of two hexagon triangle block assemblies 1111 and 111 la in FIGURES 97 and 98.

FIGURE 98 sectional view of section 1121 exposes the dowel hole alignment and grooves 1113 and 1113a. Groves 1113 in the triangle structure lock in the triangles 1112 and 1112a with the hexagon 1111 and 1111 a, which are molded to the

triangles as a monolithic structure (or bonded composite). Derivative blocks can be molded or cut from whole triangle hexagon building blocks 1111 to obtain geometries provided in previous disclosure of this invention.

HEXAGON 3-TRIANGLE MONOLITH (THREE TRIANGLES): FIGURES 100-118 illustrate a hexagon with three equally spaced extruded equilateral triangles 1141a (edges 1142 extending past face 145 equal to groove depth) forming monolithic building block 1135 and its hexagon 1135 derivative halves: cut symmetrically along two opposing flat sides 1138, and cut along two opposing points in hexagon derivatives 1136 and 1137. For the purposes of this invention the FIG 100-119 hexagon with three triangles mounted to it will be named: hexagon 3-triangle monolith or hexagon 1135. The triangles are molded with edge extension 1142 and groove 1143 cut equally around the three equilateral triangles 1141 a mounted to hexagon providing shape hexagon 3-triangle monolith 1135. The radius of groove depth and radial extension length is centered relative to face edge 1145 and are approximately equal with clearance for assembly ease. A triangle extension 1142 points are cut (molded) forming two faces 1144.

Faces 1144 provides geometric fit when triangles meet in the center of the hexagon 1135 or derivatives, if cut (molded) and assembled in less than a full hexagon. Dowel holes 1140 and 1141 always align with each other when any of the hexagon or derivatives illustrated in FIGURES 100-119 are assembled to each other. FIGURE 119 illustrates two hexagon 3-triangle monoliths 1135 mounted to each other by rotating 1135 180 degrees relative to the horizontal axis 1160, on the face exposed on 101, and passing through the center axis 1161 (where all the triangles meet) perpendicular to either face exposed in FIGURE 101 and 104. FIGURE 102 is the front end view of FIGURE 100 dropped to a horizontal level.

FIGURE 100 illustrates the inside face of the hexagon 3-triangle monolith 1135. Three equilateral triangles 1140 are molded onto hexagons 1135. FIGURE 102 illustrates an end view of face edge 145 of hexagon 1135 in FIGURE 100,102, 103, and 104 with a groove cut 1143 for offset triangle hexagon assembly FIGURE 110,112, 113, 114, and 118. FIGURE 116 illustrates an isometric inside bottom view of hexagon triangle 1135 in FIGURE 100-118. FIGURE 111 illustrates a bottom view of FIGURES

100-104 with sectional line orientation 1150. FIGURE 115 illustrates a rotate elevated view of hexagon 3-triangle monolith 1135 in FIGURES 100-1004.

FIGURE 117 illustrates a sectional side view of sectional line 1150 in FIGURES 111,115, 116, and 117. Dowel holes 1140 and 1141 are aligned for peg 1120 insertion. Other fasteners like compression bolts, screws, twist fasteners, and other commercial fasteners can be fit to this hole. Fasteners can be part of the molded hexagon 1135 providing a press fit peg hanging on a molded flexible hinge like material.

FIGURE 110 illustrates an isometric view of two hexagon triangle blocks assembled with sectional line peg (dowel) holes 1140 and 1141 aligned when one third of the hexagon is offset-layered on top of the triangle. Triangles on hexagons combine the geometry of hexagon and triangles 1140a and 1141 a, which provides a groove 1143 and extension 1142 in each of the three triangles for securely mounting triangles and hexagons together by mounting the triangle 1140a to the triangles 1141a attached to other like hexagon-triangle monolithic geometry. In a two layer wall male triangles 1141a and female triangles 1140a mount to each other inside the wall when rotated 60 degrees relative to the center of each hexagon and hexagons face the buildings inside and outdoors relative to the wall. Dowels 1120 can be inserted into dowel holes 1140a and 1141a for optional peg fasteners. FIGURE 117 illustrates a sectional side view of sectional line 1150 in FIGURE 116.

FIGURE 108 illustrates top view of two hexagon 3-triangle monoliths which are cut along the points 1136 and 1137 in FIGURES 105 and 106. Two different halves form, a two triangle half 1136 and a single triangle half providing the geometry needed to assemble to Hexagon 3-trinagle monolith 1135 illustrated in FIGURE 110.

FIGURE 116 and 117 sectional view of section 1150 exposes the dowel holes 1140 and 1141 alignment and grooves 1143. Groves 1143 in the triangle structure 1141a lock in the triangles 1141a with the hexagon 1135, which are molded to the triangles as a monolithic structure (or bonded composite). Derivative blocks can be molded or cut from whole hexagon 3-triangle monolith 1135 to obtain geometries, one half along points, one half along flats, provided in previous disclosure of this invention.

A. FIGURE 100 illustrates an elevated inside face of a hexagon 3-triangle monolith.

FIGURE 101 is a bottom view of hexagon 3-triangle monolith in FIGURE 100. FIGURE 102 illustrates an end view of face edge of hexagon in FIGURE 100,102, 103, and 104. FIGURE 103 illustrates an elevated view of hexagon 3-triangle monolith top in FIGURE 100,102, 103, and 104. FIGURE 104 illustrates a top face view of hexagon 3-triangle monolith in FIGURE 100,102, 103, and 104.

FIGURE 105 illustrates an isometric view of one-half hexagon 3-triangle monolith in FIGURE 100,102, 103, and 104 cut along the points. FIGURE 106 illustrates a view of one-half hexagon 3-triangle monolith in FIGURE 100,102, 103, and 104 cut along the points. FIGURE 107 illustrates a close view of triangle groove and extension.

FIGURE 108 illustrates bottom elevated view of two assembled halves FIGURES 105 and 106 of hexagon 3-triangle monolith in FIGURE 100 cut along the points. FIGURE 109 illustrates top elevated view of two assembled halves FIGURES 105 and 106 of hexagon 3-triangle monolith FIGURE 100 cut along the points.

FIGURE 110 illustrates an isometric view of two hexagon 3-triangle monolith assembled with sectional line peg (dowel) holes. FIGURE 111 illustrates a bottom view of hexagon 3-triangle monolith FIGURES 100-104 cut in one half along the flat opposing edges. FIGURE 112 illustrates elevated view assembly of hexagon 3- triangle monolith in FIGURE 106,111, and 100.

FIGURE 113 illustrates an elevated view assembly of hexagon 3-triangle monolith in FIGURE 106,111, and 100. FIGURE 114 illustrates an elevated view assembly of hexagon 3-triangle monolith in FIGURE 106,111, and 100. FIGURE 115 illustrates a rotate elevated view of hexagon 3-triangle monolith in FIGURES 100-104.

FIGURE 116 is a sectional view of dowel holes and alignment grooves of hexagon 3-triangle monolith in FIGURE 100-119. FIGURE 117 illustrates a sectional side view of hexagon FIGURES 111, 115, 116, and 117. FIGURE 118 illustrates a rotated elevated view of assembly in FIGURE 113.

FIGURE 119 illustrates two hexagon 1135 assembled. FIGURE 120 illustrates conduits 1164 and 1165 in a cross sectional view of two hexagons 1135 assembled. Tubes or rods can be inserted in conduit 1165 to fasten the hexagons.

FIGURE 127 is an elevated view illustrating triangle array along a straight curve. FIGURE 128 is an isometric view illustrating a rectangle hinged corner with triangle patterns matching FIGURE 127.

Hexagons can be straight as illustrated above, curved (molded to a curve) to form tubes, or concave to form a dome (requiring a pentagon in center of five adjoining hexagon 3-triangle monolith; applied as truck canopy, truck transportation containers, homes, floors for computer wiring, desks, furniture, water makers, ballistic shelters, water ditch walls, aerospace fuselage, auto body, climbing wall, hot-tub cover, and many other applications where sheathing of other types is applied.

FIGURE 121 is an isometric view illustrating a curved 1181 and straight 1182 conduit pattern in a hexagonal building block 1170 with offset tab retainers 1171 and opposing tabs 1171a for tubing retention. On the straight tubing retention tabs 1171 is molded (fastened to the hexagon as a secondary operation, welded or glued) and aligned to conduit groove 1173 and 1171a is molded to fit the curve of conduit groove 1173a. In the transition from straight to curved tubing; grooves 1176 provides curved tubing retention tabs 1172 molded (fastened to the hexagon as a secondary operation, welded or glued) and aligned to conduit groove 1176 molded to match the curve of conduit groove 1171 and 1173a. FIGURE 122 is a side view of FIGURE 121 illustrating an open axial view of the straight conduit groove formed from curves 1173 and 1173a within a hexagonal building block 1170, including retention tabs 1171 and 1171a within the surface of side 1186. FIGURE 123 is a trimetric view illustrating three tiled hexagonal building blocks 1170 of FIGURE 121, providing aligned straight grooves 1173 and 1173a and curved conduit grooves 1172. The hexagon 1170 is divided up into six equilateral triangles arrayed around the hexagons center, which provides a male triangle 1187 and female triangle section 1188. The conduit patterns in each of the six equilateral triangles are patterns arrayed around the polar central point 1189 of each equilateral triangle. A central equilateral triangle 1190 is oriented and sized (including the straight groove curves 1173 and 1173a on the three edges of the triangle) providing three point contact with each of the three sides of the larger triangles 1187 or 1188. Each of these three curves 1172 are joined to straight lines forming shape 1191, which is arrayed around triangle center point

1189. Curved conduit 1172 faces these three edges of the central triangle 1190. FIGURE 124 is a sectional view 1192 of hexagon 1170 of FIGURE 122 illustrating a tube 1180 held within offset conduit retention straight tabs 1171 and 1171 a, and curved tabs 1172.

FIGURE 125 is an elevated edge view 1193 illustrating offset conduit retention tabs 1171, 1171a, and 1172 pattern across multiple hexagons tiled together illustrated in FIGURE 123. FIGURE 126 is an elevated view illustrating the same curved and straight conduit pattern in FIGURE 121 in a larger hexagonal building block. Molded or inserted fasteners can be provided along any of the hexagon edges to more easily retain the tiled position and alignment in a single layer of hexagon. It is understood that the thickness of the hexagon is greater than the tubing outside diameter and that substantially all the paterns arrayed in the conduit face are pads to provide clearance for the tubing. This invention teaches that a pattern of straight and curved conduit patterns can include alternating male and female patterns providing single open face layers or two or more point to center hexagon layers assembled and fastened like above mentioned hexagons in FIGURE 1 through 1120. Magnetic materials can be inserted into the inside diameter of the tubing and moved with the fluids. These magnetic materials can pull, push, and suspend other materials that are excited by magnetism like"other permanent magnets, coper, copper iron backed material, and windings. A motor can be driven from the permanent magnets moving within the tubing, providing linier, rotational, or sinusoidal motion. This is a novel motor moving magnets through straight and curved fields by the path the tubing takes within the conduit.

FIGURE 129 illustrates an elevated inside face of a hexagon 3-triangle monolith 1400 with conduit opening 1405 in triangle edge conduit 1406. Inner conduits 1407 lock hexagon/triangle monoliths 1400 together without additional fasteners.

FIGURE 130 illustrates a top face view of hexagon 3-triangle monolith 1400, female apex-faster holes 1403, male apex-faster holes 1404, hexagon edge 1401, female triangle S-Groove opening 1405, and S-Groove 1406 of male triangle 1404 in FIGURE 130.

FIGURE 129 illustrates an inside bottom face 1401 and 1402 view of hexagon 3-triangle monolith 1400, female equilateral male triangles 1402 and female triangles 1401, female apex-faster (relative to each triangle 1401 and 1402) holes 1403, male apex-faster holes

1404, hexagon edge 1401, female triangle S-Groove 1407 with conduit opening 1405, and S-Groove 1406 of male triangle 1404 in FIGURE 130.

FIGURE 131 illustrates an elevated view of one-half hexagon 3-triangle monolith in FIGURE 129 and 130 cut along the points into a female/male/female hexagon derivative half 1412. FIGURE 132 illustrates an elevated view of one-half hexagon 3- triangle monolith in FIGURE 129 and 130 cut along the points into a male/female/male triangle hexagon derivative half 1411. FIGURE 133 illustrates an elevated view of triangle faces 1401 and 1402 of one-half hexagon 3-triangle monolith in FIGURE 131 and 132 hinged together with hinges 1410a, 1410b, 1410c, and 1410d at an 180-degree angle.

FIGURE 134 illustrates an elevated view of hexagon faces of one-half hexagon 3-triangle monolith in FIGURE 131 and 132 hinged together at 90-degree angle with triangles 1401 and 1402 of half 1411 and half 1412 facing each other. FIGURE 135 illustrates an elevated view of triangle faces of one-half hexagon 3-triangle monolith in FIGURE 131 and FIGURE 132 hinged together at 90-degree angle with triangles facing each other inserted into the same components hinged together at 90-degrees with hexagon halves facing each other. FIGURE 136 illustrates an elevated view of two sets of triangle faces of one-half hexagon 3-triangle monolith 1440 in FIGURE 131 and 132 hinged together at 90-degree angle and each set rotated 90-degress relative to the other set forming a corner.

FIGURE 137 illustrates an elevated rotated back view of FIGURE 136 corner derivative hexagon halves 1440. FIGURE 138 illustrates an elevated view of two sets of triangle faces of one-half hexagon 3-triangle monolith 1440 in FIGURE 137 hinged together at 90-degree angle and each set rotated 90-degress relative to the hinge and 90-degress relative to FIGURE 137. FIGURE 139 illustrates a close-up view of 138 viewing hinges 1410a, 1410b, 1410c, 1410d alignment detail providing 90-degree alignment of each pairl410b, 1410c and 1410a, 1410b. In each of the previous FIGURES131-138 the hinges are marked to see the hinge location as orientation changes. Figure 133-139 are all the same pair of half hexagons assembled at against themselves and rotated around the center pin of the hinge. This hinge can be locked in at six angles respective of the six tubes or infinitely rotated without pins. FIGURE 140 illustrates an elevated view of a pair of hinges 1410 a and 1410 d locked in by an offset pin set 1413 and 1414 made of six tubes

assembled around a central tube of equal diameter and rotated offset pins. Offset pin set 1413 and 1414 insert into hinge tube 1415 and 1416 respectively. FIGURE 141 and FIGURE 142 illustrates an elevated view of a pair of the gear hinges 1413 and 1414 made of six tubes assembled around a central tube of equal diameter, in FIGURE 140, each mounted to a common centrally pinned bracket 1417 pins 1417a and 1417b. Hinges can be rotated in direction 1419 and 1420. This is ideal for sealing a roof line of foundation under hinge pressure. FIGURE 142 illustrates the back side view of FIGURE 141.

FIGURE 143 illustrates an elevated view of two sets of triangle faces of one-half hexagon 3-triangle monolith 1440 in FIGURE 133 hinged together at 180-degree angle and each set rotated 90-degress relative to the other set for joining sets of hexagons into a cross.

Figure 143 and 144 are ideal for building several walls off a central hinge axis and can be integrated into the roof as a 90 degree integrated beam structure. FIGURE 144 illustrates FIGURE 143 for a view of hidden structure. FIGURE 145 and 146 illustrates a face view of hexagon derivative halve bottom plates cut along the flat sides with hinge structure 1425 and 1426 with wall thickness structure 1429 forming a bottom wall plate the width of two hexagon layers. FIGURE 146 illustrates a back elevated view FIGURE 145 with male/female S-Grove structure. FIGURE 147 illustrates a face view of hexagon derivative halves cut along the flat sides for top of the wall plate 1431 with hinge structure 1427 and 1428 with wall thickness structure 1429 forming a top wall plate in FIGURE 149.

FIGURE 148 illustrates a back elevated view FIGURE 147 with female/male S-Grove structure.

FIGURE 149 illustrates a corner view of corner subassembly 1440 assembled from 1411 and 1412 derivative halves. Bottom plates 1430 line the bottom wall and plate 1431 line the top of the wall. Plates 1431 and 1430 height can be adjusted to obtain exact wall height's FIGURES 135-142 and bottom and top plates in FIURES 145 - 148. Partial hinged corners are showing 1412 and 1411.

FIGURE 150 one-fifth pentagon section 1450 in view and one-third hexagon section 1449 inserted into a full hexagon-triangle elevated view of three assembled components: one-third of FIGURE 129 one-fifth of a pentagon, and filler edge structure 1451 to array into a sphere FIGURES 162 or dome fig. 161. FIGURE 151

illustrates a top elevated view FIGURE 150 with an arrayed tube pentagon connector 1466. FIGURE 152 illustrates a top elevated view FIGURE 151 with an arrayed tube pentagon connector 1466 with male pin 1465 inserted into female hole 1464. Point 1450a is an important feature, because all the structure of the dome is arrayed around this pentagon 1450 point 1450a. FIGURE 153 illustrates a top elevated view of FIGURE 150 one-fifth pentagon section 1450 in view and one-third hexagon section 1449 inserted into a full hexagon-triangle 1400. FIGURE 154 illustrates a top elevated view FIGURES 150- 152 arrayed around tube pentagon connector 1460 and center-point of a pentagon 1450a.

FIGURE 155 illustrates an outside elevated view of FIGURE 154 arrayed around tube pentagon connector 1460 and center-point of a pentagon 1450a. FIGURE 156 illustrates an outside side view of FIGURE 155 arrayed around a tube pentagon connector 1460 and center-point of a pentagon 1450a with assembly in FIGURE 153 a full hexagon 1400 inserted into 1/3d hexagon section 1449. FIGURE 157 illustrates an inside rotated elevated view of FIGURE 156 arrayed around tube pentagon connector 1460 and center- point of a pentagon 1450a. FIGURE 158 illustrates an inside rotated elevated view of FIGURE 151 with five full hexagons 1400 of FIGURE 153 arrayed around center-point 1450a of a pentagon 1450 and inserted into the one-third hexagon 1449 connected to the one-fifth pentagon section 1450. FIGURE 159 illustrates a side elevated outside view of FIGURE 158 viewing the full hexagons 1400 inserted into the one-third hexagons 1449 connected to one-fifth a pentagon 1450 arrayed around the center-point 1450a of the pentagon 1450. FIGURE 160 illustrates a partially assembled inside view of a sphere comprised of the components in FIGURES 150-159. FIGURE 160 illustrates a partially assembled inside view of a sphere comprised of the components in FIGURES 150-159.

FIGURE 162 illustrates an outside view of a fully assembled sphere comprised of the one- half sphere components assembled in FIGURES 160 mirrored providing faces assembled to each other. FIGURE 163 illustrates an outside and inside view one-half sphere components positioned in 25-percent offset 180-degrees apart and comprised of the sphere in FIGURES 150-163 in an offset. These half sphere offset can be rotated in the wind for wind power by providing a balanced central turn table to mount the two spheres.

These spheres can be moved relative to one another in alignment to close the sphere so

the wind will not rotate them or moved in opposite direction to increase the moment arm relative to a central rotating axis. FIGURE 164 illustrates a top elevated view FIGURE 1163. FIGURE 165 illustrates a simplified schematic view of the hexagon-pentagon sphere halves 1460 and 1461 providing an open face 1462 and 1463 in each sphere in FIGURES 165-169. FIGURE 166 illustrates a simplified schematic view of the hexagon- pentagon sphere in FIGURE 163 to clarify the opening and relative position.. FIGURE 167 illustrates a simplified schematic view of the hexagon-pentagon sphere in FIGURE 165 with the two spheres aligned forming a wind resistant sphere. FIGURE 168 illustrates a simplified schematic view of the hexagon-pentagon one-half sphere in FIGURE 167 with the two spheres offset 100-percent and aligned forming a wind blade sphere. FIGURE 169 illustrates a simplified schematic view of the hexagon-pentagon one-half sphere in FIGURE 168 with the two spheres offset 150-percent and aligned to form a wind-power blade sphere. These hexagon pentagon based sphere can be moved to a wind-power or water power site and assembled in remote locations. Any fluid will drive the sphere of FIGURE 160-169 because a sphere cancels out the forces moving around its 360-degree surface. The open face traps the air fluid movement and therefore the maximum forces are transferred. One half the sphere transfers the forces most efficiently and the back rounded half moves through the air most efficiently. Several sets of half spheres can be mounted on a common axis at different rotated angles to have a near constant moment of rotation force from the multiple stacked sphere wind power blades.

FIGURE 170 illustrates an elevated inside face of a hexagon 3-triangle monolith 1500 with conduit 1405, and 1407 in triangle edges 1407 and 1406 in FIGURE 129 and in addition conduit structure 1521 and 1520 is provided along the face of the hexagon edges providing a male conduit 1520 that mounts into S-Groove conduit 1521.

FIGURES 171a through 177 illustrates 1/6"a hexagon around one of 6-points outlined in FIGURE 170 by line 1502 and 1501. FIGURE 171a illustrates a top face 1490 view and sectional of one-sixth hexagon 3-triangle monolith structure within FIGURE 170 hexagon's six points section 1501 and 1502. In order to make a hexagon the componenets of FIGURE 171 a-1777 are mirrored around lines 1501 or 1502 forming 1/3ru of a hexagon 1500 and then arrayed three times to form hexagon 1500. Fastener 1470 is in

FIGURE 171a and 171. The fasteners in FIGURE 171 is inserted in a stack of two assemblies of FIGURE 171 a against themselves. FIGURE 171b illustrates a top face view of hexagon one-sixth 3-triangle monolith in FIGURE 170 and 171a. FIGURE 172 illustrates an elevated exploded side view of FIGURES 171a and 171b. FIGURE 173 illustrates an elevated exploded central view of FIGURES 171a and 171b. FIGURE 174 illustrates an elevated exploded hexagon-point end view of FIGURES 171a and 171b.

FIGURE 175 illustrates an elevated close-up view of only the rib structure profile within FIGURES 171a and 171b. FIGURE 176 illustrates an elevated close-up view of the rib structure profile within FIGURES 171a and 171b. FIGURE 177 illustrates an elevated close-up view of tube edges 1785, ribs 1481 and 1482, dowels 1483 and 1484with dowel skirts within FIGURES 171a and 171b. FIGURE 178 illustrates an elevated close-up view of simple flat ribs 1491 and 1492, and round dowels 1483 and 1484 without profiled skirts replacing ribs 1481,1482 and skirts 1483,1486 within FIGURES 171a and 171b.

FIGURE 179 illustrates a side view of a fastener 1470 with fastner head 1471, and slot 1472, fin 1474, taper 1475 of fin 1474 1476,1479 inserted into a retention ring 1476 and the same fastener 1470 alone for insertion into hexagons in FIGURES 129 - 201. FIGURES 180 illustrates an elevated close-up sectional view of slotted 1472 fastener 1470 in FIGURES 171a, 171b 179 and 181. FIGURE 181 illustrates an elevated close-up sectional view of the slotted fastener end 1471 and bolt relieve 1478 and retention ring 1476,1479 in FIGURES 171a, 171b 179 and 180. FIGURES 182 illustrates an elevated close-up sectional view of the slotted fastener end and retention ring profile in FIGURES 171a, 171b 179-181. Slotel472 compresses when taper 1475 compresses arainst protruded ring 1479 in 1476 structure. This spring effect and retention cavity 1473 in FIGURE 182 is all that is needed to compression retain the fastner 1470.

FIGURE 183 illustrates a tilted elevated view of one full hexagon 3- triangle monolith 1500 in FIGURE 170 for viewing hexagon tube structure 1485 assembled. FIGURE 184 illustrates bottom elevated view of two assembled hexagon 3- triangle monolith 1500 in FIGURE 183 assembled face to face male triangles 1401 inserted into female triangles 1401. FIGURE 185 illustrates top elevated inside face view of two full hexagons aligned showing the pattern of S-Groves and triangles and a third full

hexagon partially assembled from hexagons of FIGURES 183. FIGURE 186 illustrates top elevated inside face view of four full hexagons 1500 aligned showing the pattern of S- Grooves and triangles and the forth hexagon assembled face to face on the other three hexagon of FIGURES 183.

FIGURE 187 illustrates top elevated inside face view of one full hexagon 1550 with alternate circular S-Groves 1553 and 1552 rather than equilateral triangle S- grooves with a radiant fluid tube 1551 extending from the perimeter of the hexagon 1550.

FIGURE 188 illustrates top elevated inside face view of two full hexagon with alternate circular S-Groves mating the faces in alignment and assembled. FIGURE 189 illustrates an exploded side view of the components of one full hexagon with alternate circular S- Groves assembled including the ribs and dowels of FIGURES 178. Circle S-Groove assembly 1552, spacer circular structure 1555, and 1556 radiant fluid tubing curves, and finished hexagon surface 1557 are all in FIGURES 187-189.

FIGURE 190 illustrates an elevated isometric view one tube bundle hinge 1570 with alternating tube structure 1571,1572, 1573,1574. 1576, and 1576 configured to mate to the hexagon tube structures in FIGURES 192-204 with tube edges in FIGURE 192-204 which illustrates a series of assembled rotated views of FIGURE 190.

FIGURE 192 illustrates a seal 1579 partially removed form the face of a pair of hexagons derivative halves 1411,1412 cut along the points of the hexagon of FIGURE 129-130.

FIGURE 193 illustrates a rotated view of FIGURE 192 showing the locking tube inserts 1581 the edge tubes 1580 of FIGURE 192-204. FIGURE 194 illustrates a view of FIGURE 192 exploded open and the 2-triangle halves 1411, 1412 rotated 90-degrees to show the edge tube detail 1571a, 1571a, 1571a, 1571a that mate to each other and lock together when rod inserts 1581 are inserted into the alternating matching tubes segments 1571a, 1571a, 1571a, 1571a for FIGURE 192-204. FIGURE 195 illustrates a view of FIGURE 192 exploded open and the 2-triangle half is rotated 180-degrees to show the edge tube detail and mating alignment that locks together when rod inserts are inserted into the alternating matching tube segments for FIGURE 192-204. FIGURE 196 illustrates a close up view of hinge in FIGURE 190 and 191 assembled to hexagons in FIGURES 193-204. FIGURE 197 is FIGURE 196. FIGURE 198 illustrates a view of

FIGURE 192 exploded open and the 2-triangle half is rotated 180-degrees and separated to for hinge assembly on hexagon edge tube alternating segments by rod insertion into the alternating matching tube segments in FIGURE 192-204.

FIGURE 199 illustrates a finished corner 1588 that provides overlapped edges 1589 to finished the face edges of the hexagon including locking hinge male tube bundle 1585 into hinge spaces between hinge corners forming 90-degree angles. FIGURE 200 illustrates a rotated outside view of the finishing corner in FIGURE 199. FIGURE 201 illustrates a rotated inside view of the finishing corner 1590 in FIGURE 199 and 200 with a void space 1587 between hinge 1588 matching tube bundles 1586 for insertion in the void spaces in a subassembly of corners in FIGURES 134-139 and FIGURE 149 assembled corner. Fastener 1470 could be inserted to secure any of the hinges or tubes in this invention.

FIGURE 202 illustrates an inside top view of one-half hexagon 3-triangle monolith 1411,1412 in FIGURE 190-198 cut along the points into hexagon derivative half with hexagon edge tube segments 1415,1416 aligned at an angle by FIGURE 140 offset rods 1413,1414 which form a curve or tube when half a meter hexagons are hinged and arrayed around the central point 22-times providing 3501-milimeter (mm) radius.

FIGURE 203 illustrates a rotated close-up edge view of FIGURE 202. FIGURE 204 is the same as FIGURE 202. FIGURE 205-208 illustrates outside view of a tube assembled from two layers of hexagons outside array 1600 and inside array 1601 each tapered into the center relative to the tube axis 1609 providing a tube assembly from an inside hexagon smaller and tapered toward the center of tube relative to the outside larger hexagon scaled larger relative to the one circumferential dimension in tube 1607. FIGURE 206 illustrates one-half of FIGURE 205. FIGURE 207 illustrates the taper of the hexagons relative to the circumferential dimension the axial dimension related to a 1-meter hexagon (measured flat to flat edge) remains the same. FIGURE 208 illustrates a view of a hexagonal taper geometry before a bullion cut is made by a surface like 1607 to make curved hexagon blocks 1600,1601 in FIGURE 207. In FIGURE 208 hexagon tapered structure 1606 is tapered on surfaces 1610a, 1610b relative to the axial segment length 1609 and tapered surface 1611 is tapered to the line segment 1609 relative to the flat hexagon edge only; the

surfaces 1610a, 1610b shape block source structure 1606 surface 1611 providing a match to additional arrays of the same tapered block 1606. FIGURE 209 illustrates tubes for bullion cutting fastener holes in the hexagons of FIGURE 207 with the same taper.

FIGURE 210 illustrates tube arrays 1653 for alternative hexagon structure that can easily be curved around the centerlines of the tubes 1653 providing an infinite curve with end tube segments 1651,1650a, 1650b aligned for mating to assemblies of hexagons. FIGURE 210 illustrates the mating edges 1651 to tubes 1650a and tube segment 1650b of the hexagons when two hexagons are assembled and tube edge segments 1650a, 1650b insert to male/female edge tube voids 1651. These tubes can be co molded to surface 1653 so when the surface is curved the tubes curve with eh bend in the surface forming tubes. Open ends of the tubes can have smaller tubes inserted to connect one open tube edge with another making a very stiff integrated ridged structure.

FIGURE 212 is a tube hexagon assembly with a weight inserted into hexagon array 1630 one-third of the way down the length of the fuselage. The opposing end 1631 is scalloped with part of the hexagons removed to let air flow exit with less friction. These large rings can be propelled through the air at great distances. Rocket propellant of other propulsion can drive this rotating fuselage through the air.

An innovation is needed to manufacture optimally engineered building blocks that snap together by hand to create any shape of conventional building assembly. Advanced material developers need a common shape to make market penetration into consumers that do not appreciate new technical details. In order for new materials to make it to the marketplace a standard size building block and shape need to be developed.

Hexagon/triangle block materials need to be purchased with FEA-Superelement engineering data locating each block in an assembly.

Human imagination of building designs cannot currently be analyzed rapidly, because of random fastening, unsymmetrical shapes, and limited difficult to shape material choices.

FEA-superelement based symmetrical material shapes with common fasteners can convert human engineering imagination directly to"real life"structures that are safe and predicable when assembled exactly as the superelement code suggests would be the most optimized final assembly. Many materials exist that are difficult and expensive to shape into useful buildings or structures and this innovation in Table 1.1 teaches how to tile these different materials into optimized assemblies where a variety of materials applied together provide utility (Ref. 1).

There is an inherent relationship between shape and the ability to predict material behavior. The stiffness matrix for a substructure is commonly referred to as a "superelement". A formula of the stiffness matrix of a substructure is a superelement, which in this case is a hexagon/triangle substructure element. The stiffness structures are modeled by constant stiffness matrices and therefore it is desirable to have the substructures behave in a linier, elastic manner (Ref. 2,3, 4,5, 6). The selection of S- Groove male/female hexagon/triangle fasteners overlapping S-Groves, offsetting hexagons, and locking in the block faces were based on the need for a robust fastener directed at holding blocks together for linier force transfers between blocks; obtaining an accurate FEA-Superelement result.

Salient characteristics of the hexagon/triangle building block are: A sole building block ; meeting building needs with one inventory item. A sole building block assembly is rapidly optimized by one engineering"formula". No power equipment is needed to assemble building blocks. A material library list is provided; changing assembled functions. Utility functions are packaged inside hexagon/triangles (climate control, solar voltaic...) No cutting is needed to construct a building. No fasteners are needed to hold one blocks face to another. Extra fasteners located in the apex of the equilateral triangles of the hexagon are optional. Blocks can be light enough for one person to lift and large enough to build rapidly. Block materials in the shape of a hexagon/triangle need to be purchased with FEA-Superelement engineering data locating each block. New future materials for rebuild updates need to mate up to old blocks. The block cannot have difficult complex fasteners to remove, because future rebuild materials will not be the sameSubsystems can be packaged inside hexagon/triangles. Fuel cells, solar cells, climate control, heat reflective infrared paints, lighting, noise cancellation (unimorphic ultrasonic wafers), wiring, plumbing, and other functions can be packaged inside hexagon/triangle for plug-in delivery of technology to Do-It-Yourself (DIY) customers. Technical expertise for these multi-functional hexagon/triangles can remain in the source-factories. A library list of materials is made available.

1-meter hexagon/triangles are new metric standard blocks that build out into standard North American and Global metric building code dimensions. Over time, individuals can build and rebuild their shelter needs to adapt to natural environmental changes of building- sites and human population pressures.

Virtually any structural material can be integrated into hexagon/triangles. Material selections will change based on climatic, building-site environment, and application. The library list of materials available is relative to material suppliers providing stress analysis of each material in the composite shape of the hexagonal superelement shape. It is a goal to select sustainable composites where decades from now the original hexagon blocks will

mate with brand new hexagon parts made of new material technologies-updating the old with new elements.

Those who wish to build"Green"have a wish list of building materials for which few companies have supplied product. Hexagon/triangle blocks can satisfy the need for a major part of this"Green"list : Light-Translucent walls and roofs for a more sunlight penetrating building. Bamboo and strawboard composite for allergy reduction. Thermal plastic for easy recycling. 3-Dimensional color polymer composite options that resist showing attrition. Thermal reflective infrared coating integrated into the multiple block wall layers. Curved building blocks for roof and walls. Thermal storage and recovery material integration (phase change salts). Water adsorbent materials for water-making.

Wire integrated into the building block. Plumbing integrated into the building block. Solar cells integrated into the building block. Fire resistant materials.

The present invention has been described in relation to a preferred embodiment and several alternate preferred embodiments. One of ordinary skill, after reading the foregoing specification, may be able to affect various other changes, alterations, and substitutions or equivalents thereof without departing from the concepts disclosed. It is therefore intended that the scope of the Letters Patent granted hereon be limited only by the definitions contained in the appended claims and equivalents thereof.