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Title:
METHOD OF CONSTRUCTING FLAT BUILDING BLOCK MODULES
Document Type and Number:
WIPO Patent Application WO/1994/013896
Kind Code:
A1
Abstract:
A plurality of modular construction blocks (100) extending in three dimensions completely and substantially space-filling structure of arbitrary shape and volume is provided, each of the blocks (100) comprising a plurality of surfaces (34): wherein each of the blocks (100) is generally flat and wherein each of the blocks is characterized by a flat face (5), the flat face (5) having a geometric shape determined by a face of a polyhedron (5a) selected from a group of space filling polyhedrons (5a) which when appropriately combined, substantially and completely fill the arbitrary volume of space; wherein generally transverse to the flat face (5) of each block is a plurality of peripheral sides (4) extending the block in a dimension perpendicular to the flat face of the block.

Inventors:
GYUREC ERNESTO DANIEL (US)
PRONSATO ANTONIO CARLOS
Application Number:
PCT/US1992/010634
Publication Date:
June 23, 1994
Filing Date:
December 08, 1992
Export Citation:
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Assignee:
POWER RINGS INC (US)
GYUREC ERNESTO DANIEL (US)
International Classes:
A63F9/12; F16S1/02; F16S1/14; G09B1/38; G09B23/04; G09B25/04; (IPC1-7): E04B1/32
Foreign References:
US3974600A1976-08-17
US4723382A1988-02-09
US4593908A1986-06-10
US3965626A1976-06-29
US4253268A1981-03-03
US3461574A1969-08-19
US4682450A1987-07-28
US4496155A1985-01-29
US4789370A1988-12-06
US3645535A1972-02-29
US4323245A1982-04-06
US3687500A1972-08-29
US3940100A1976-02-24
US3777359A1973-12-11
US3564758A1971-02-23
US3698124A1972-10-17
US3783571A1974-01-08
US4686800A1987-08-18
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Claims:
IN THE CLAIMS :
1. A plurality of modular construction blocks extending in three dimensions from a combination of which blocks a three dimensional completely and substantially spacefilling structure of arbitrary shape and volume is provided, each said block comprising a plurality of surfaces: wherein each said block is generally flat; wherein each said block is characterized by a flat face, said flat face having a geometric shape determined by a face of a polyhedron selected from a group of space¬ filling polyhedrons, which when appropriately combined, substantially and completely fill said arbitrary volume of space; wherein generally transverse to said flat face of each block is a plurality of peripheral sides extending said block in a dimension perpendicular to said flat face of said block, each one of said peripheral sides determined by a surface defined within said selected polyhedron by a point within said selected polyhedron and at least two surface points of said selected polyhedron, said peripheral side being a truncated portion of said surface within said selected polyhedron, so that said threedimensional spacefilling structure may be provided by assembling a plurality of said modular blocks, connected together along their peripheral sides with the result that the amount of material necessary to provide said threedimensional spacefilling structure is reduced.
2. The plurality of modular construction blocks of Claim 1 wherein said selected polyhedron is a tetrahedron.
3. The plurality of modular construction blocks of Claim 1 wherein each said block is comprised of a first and second portion, said first portion being defined as that portion of said block on a first side of said flat face and said second portion being defined as that portion of said block on an opposing second side of said flat face, said first portion defined from a first selected polyhedron of said plurality of spacefilling polyhedrons and said second portion defined from a second different type of polyhedron of said plurality of spacefilling polyhedrons.
4. The plurality of modular construction blocks of Claim 1 wherein said face of said selected polyhedron is treated as having an infinite number of vertices arranged in a circle on said face, said circle being tangent to each side of said face, and wherein said dihedral sectional plane within said polyhedron defining said peripheral sides being a conic surface.
5. The plurality of modular construction blocks of Claim 4 wherein said selected polyhedron is selected from the group of polyhedrons consisting of a cube, tetrahedron, tetragonal octahedron, rhombic dodecahedron, regular octahedron and combinations thereof.
6. The plurality of modular construction blocks of Claim 1 wherein a substantial portion of the interior of each said block is hollow, said peripheral sides forming a contiguous skeletal structure.
7. The plurality of modular construction blocks of Claim 1 further comprising means for connecting each said construction block to a plurality of other ones of said construction blocks along said peripheral sides of said construction blocks.
8. The plurality of modular construction blocks of Claim 7 wherein said means for connecting is a pair of symmetrical and opposing prisms generally extending perpendicular to one of said peripheral sides of each said block and attached to said corresponding side of said block.
9. The plurality of modular construction blocks of Claim 8 wherein said pair of prisms is a pair of opposing triangular prisms having their corresponding apical edge opposed and generally aligned to form a slot connector.
10. The plurality of modular construction blocks of Claim 8 wherein said pair of prisms is a pair of opposing half cylinders, said half cylinders having a half cylindrical surface, said half cylindrical surfaces being opposed and symmetrically aligned with each other to form a slot connector.
11. A plurality of modular construction blocks for use in constructing a completely and substantially three dimensional spacefilling structure of arbitrary shape, each said block comprising a plurality of exterior surfaces; wherein said surfaces include a flat face generally parallel to and coextensive with a planar face of a selected spacefilling imaginary polyhedron; and wherein said surfaces of said flat face include peripheral sides of said block, said peripheral sides arranged and configured to connect with corresponding peripheral sides of another one of said modular blocks similarly corresponding to an adjacent face of said selected imaginary polyhedron, said modular block being connected to adjacent modular blocks along said peripheral sides.
12. The plurality of modular construction blocks of Claim 11 wherein said selected imaginary polyhedron is selected from the group of polyhedrons consisting of a cube, tetrahedron, tetragonal, tetrahedron, rhombic, dodecahedron, regular octahedron, cuboctrahedron and combinations thereof.
13. The plurality of modular construction blocks of Claim 11 wherein each block is provided with an infinite number of said peripheral sides so that said peripheral sides comprise a generally circular cross section in the plane of said planar extension of said modular block.
14. The plurality of construction blocks of Claim 11 further comprising fastening means for connecting said blocks to each other and wherein each block is connected to other ones of said blocks by said fastening means only at points on said peripheral sides of said blocks and not at apexes of said blocks.
15. The plurality of construction blocks of Claim 14 where said fastening means comprises: a triangular, flat connector having three connecting points; and a square, flat connector having four connecting points, wherein said plurality of construction blocks are fastened together only at their peripheral sides with the use of only selected ones of said triangular and square flat connectors to form said arbitrarily shaped three dimensional spacefilling structure.
Description:
METHOD OF CONSTRUCTING FLAT BUILDING BLOCK MODULES

5 Background of the Invention i Field of the Invention

_

This invention generally relates to modular building construction, and specifically to a method of making dihedrally connected building blocks and a built-in slot 10 connector to erect or to make the structure of buildings, billboards, towers, roads, runways, dams, bridges, shore and offshore structures, furniture and their respective scale models for testing and design.

These scale model building blocks modules also can be 15 profitable if used as teachers' aids and toys. Prior Art

The construction of buildings by a plurality of similar simply polyhedral members, generally rectangular prisms, is a practice followed since ancient times for two main reasons. 20 The obvious advantage is the low cost mass production of those members as is explained in Bardot's U.S. Patent No. 3,777,359, the less obvious advantage is the low cost construction of scale models for testing and design. There are three main disadvantages of the simple brick: 25 They are too massive, too heavy.

They are assembled only into prismatic structures.

They are weakly connected.

Up to now, those disadvantages had been alleviated, but at a cost to the main advantages. The solution to the

30 massiveness problem by making holes in the members creates conduits when assembled. However, those conduits are not connected, but parallel.

The second disadvantage has been partially overcome by making complex polyhedrons, see Hervath, U.S. Patent No.

35 3,783,571. However, this second problem is not widely seen as solved. Most designers are still exploring the mysteries of

the cube structure; NASA space station structure, for example, having an expensive and very sophisticated system designed to be assembled into 46 different polyhedral arrangements, is conservatively cubical. The third and perhaps most elusive problem, the weakness of the connection, had been attacked economically by perfecting a tongue and groove holding and locking system, see Silvius 1 U.S. Patent No. 3,687,500, for a dihedral slot connection.

The building blocks of the art known as space structures are a different case. They are vertexically connected frames (see Pearce's U.S. Patent No. 3,600,825). These structures dispel the general problems discussed above, but bring with them problems of their own, such as low tolerance edge members* length. Space structures may be visualized as a plurality of assembled polyhedral bricks from which everything has been removed except a small portion along the edges; those edge- members are connected at the vertexeε or corners of the polyhedrons. Space structures, generally, have two main component parts, a member and a connector. The member is an elongated prism or a tube whose cross section center is the edge of the polyhedrons, and the connector, usually ball shaped, is at the vertex of the polyhedrons. The space structure member, in principle, can be easily mass produced by extrusion of simple molding. The multiple connector, on the other hand, has eluded heretofore inexpensive solutions. For this problem, classical space structures, regardless of their high strength-to-weight ratio and the immense variety of shapes they can form, had been relegated in architecture usually to trusses or to secondary functions such as canopies. In the construction toy industry, space structures have been shadowed by the simple, face- connected, square, prismatic building blocks. Another problem associated with this ingenious solution is the need of highly specialized managerial workers, notably

in McCormick's astonishing dihedral structures disclosed in U.S. Patent No. 4,686,800. Objects of the Invention

It is a principal object of the present invention to unite the advantages of the bricks with those of the space structures: low cost production (extrusion, simple molding) , low cost test scale modeling, high strength-to-weight ratio, maximum variety of polyhedral arrangement and low cost structural design and erection labor. Summary of the Invention

In on aspect of the invention, there is provided a plurality of modular construction blocks extending in three dimensions, from a combination of the blocks, a three dimensional, co plety and substantially space-filling structure of arbitrary shape and volume is provided. Each of these blocks comprise a plurality of surfaces. Furthermore, each block is generally flat and characterized by a flat face with a geometric shape determined by a face of a polythetron selected from a group of space-filling polyhedrons, which when appropriately combined, substantially and completely fill the arbitrary volume of space. Generally transverse to the flat face of each block is a plurality of peripheral side extending the block in a dimension perpendicular and the flat face of the block. Each one of the peripheral sides is determined by a surface defined within the selected polyhedron by a point within the selected polyhedron and at least the surface points of the polyhedron. The peripheral side is a trancated portion of the surface within the selected polyhedron, so that the three-dimensional space-filling structure may be provided by assembling a plurality of the modular blocks, connected together along their peripheral sides with the result that the amount necessary to provide the structure is reduced.

In a preferred embodiment of this aspect of the invention, the selected polyhedron is a tetratedron.

In another embodiment of this aspect of the invention, each block is comprised of a first and second portion. The

In another embodiment of this aspect of the invention, each block is comprised of a first and second portion. The first portion is defined as that portion of the block on the first side of the flat face and the second portion is defined as the portion of the block on an opposing second side of the flat face. The first portion is defined from a first selected polyhedron of the plurality of space-filling polyhedrons and the second portion is defined from a second, different type of polyhedron of the plurality of space-filling polyhedrons. In another preferred embodiment of this aspect of the invention the face of the selected polyhedron is treated as having an infinite number of vertices arranged in a circle on the face. The circle is tangent to each side of the face, and the dihedral sectional plane within the polyhedron defining the peripheral sides is a conic surface.

In another preferred embodiment of this aspect of the invention, the selected polyhedron is selected from the group of polyhedrons consisting of a cube, tetrahedron, tetragonal octahedron, rhombic dodecahedron, regular octahedron and combinations thereof.

In another preferred embodiment of this aspect of the invention, a substantial portion of the interior of each the block is hollow; the peripheral sides forming a contiguous skeletal structure. Another preferred embodiment of this aspect of the invention further comprises a means for connecting each construction block to a plurality of other construction blocks along the peripheral sides of the construction blocks. This means for connecting is preferably a pair of symmetrical and opposing prisms generally extending perpendicular to one of the peripheral sides of each the block and attached to the corresponding side of the block.

The pair of prisms can also be a pair of opposing triangular prisms having their corresponding apical edge opposed and generally aligned to form a slot connector.

Alternatively, the pair of prisms can also be a pair of opposing half cylinders. The half cylinders described have a

half cylindrical surface, and half cylindrical surfaces is opposed and symmetrically aligned with each other to form a slot connector.

In another aspect of the invention, there is a plurality of modular construction blocks for use in constructing a completely and substantially three dimensional space-filling structure of arbitrary shape. Each block comprises a plurality of exterior surfaces.

These surfaces include a flat face generally parallel to and coextensive with a planar face of a selected space-filling imaginary polyhedron. Furthermore, these surfaces include peripheral sides of the block, whereby the peripheral sides are arranged and configured to connect with corresponding peripheral sides of another modular blocks similarly corresponding to an adjacent face of the selected imaginary polyhedron. The modular block is connected to adjacent modular blocks along the peripheral sides.

In a preferred embodiment of this aspect of the invention, the selected imaginary polyhedron is selected from the group of polyhedrons consisting of a cube, tetrahedron, tetragonal, tetrahedron, rhombic, dodecahedron, regular octahedron, cuboctrahedron and combinations thereof.

In another preferred embodiment of this aspect of the invention, each block is provided with an infinite number of the peripheral sides so that the peripheral sides comprise a generally circular cross section in the plane of the planar extension of the modular block.

Another preferred embodiment of this aspect of the invention further comprises a fastening means for connecting the blocks to each other. Each block is connected to other blocks by the fastening means only at points on the peripheral sides of the blocks and not at the apexes of the blocks. In addition, the fastening means may also comprise: a triangular, flat connector having three connecting points; and a square, flat connector having four connecting points. Here, the plurality of construction blocks are fastened together only at their peripheral sides with the use of only

selected triangular and square flat connectors to form the arbitrarily shaped three dimensional space-filling structure.

Brief Description of the Drawings FIGS. 1 to 5 show the perspective view of three successive hypothetical manufacturing stages, the extraction of pyramids from six polyhedrons, the making of frustums from the said pyramids and the creation of solid modules from the said frustums. FIG. 6 shows a chart of the top views and common cross sections of the ten solid modules from FIGS. 1 to 5 and 7, both pyramidal and conical genera.

FIG. 7 shows the perspective view of three successive hypothetical steps, the extraction of cones from two cubes, the making of frustums from the said cones and the creation of a solid module from the said frustums.

FIG. 8 shows a perspective view of the cuboctahedron- octahedron structure made by a plurality of pyramidal solid modules connected together by their trapezoidal faces. FIG. 9 shows a perspective view of the cuboctahedron- octahedron structure made by polarized conical solid modules connected together at their marks.

FIG. 10 shows a perspective view of the making of pyramidal and conical skeletal modules. FIG. 11 shows two cross sections, "A" and "B," and a perspective view of four modules, one pyramidal and one conical with an "A" cross section, and two conical, one solid and one skeletal with a "B" cross section.

FIG. 12 shows a top view of a "universal" conical, skeletal module.

FIG. 13 shows a perspective view depicting five types of slots connected to five types of modules.

FIG. 14 shows a perspective view depicting two modules, one pyramidal with an "A" connector and one conical with a "B" connector.

FIG. 15 shows a perspective view depicting prior art and present invention built-in slot connectors.

FIG. 16 shows a perspective view depicting two "A" integral slot connectors.

FIG. 17 shows a perspective view depicting two "B" integral slot connectors. FIG. 18 shows a perspective view depicting four frustums, two seven-sided and two infinite-sided and two modules made from the said frustums.

FIG. 19 shows a perspective view depicting four truncated frustums, two modules made with the said frustums and three cross sections depicting the truncation.

FIG. 20 shows a perspective view depicting four rounded frustums, two modules made with the said frustums, and three cross sections depicting the rounding.

FIG. 21 is a chart of the reference symbols used in FIGS. 1 to 20.

Overview of the Invention These and other objects are derived from a new method for creating modular building blocks units together with a new dihedral slot connector for erecting geometrical structures.

As the study of a method applicable to any polyhedron is more fruitful than the individual description of a number of building blocks made with the said method, this approach will be used. The method of the present invention has evolved along two branches, pyramidal and conical. But, because cones are a class of pyramids, to clarify and amplify the concept, the method will be presented in a single description. The method of manufacture is described in hypothetical steps as a guide for the design of modular building block units — modules for short. Solid Pyramidal Modules (see FIGS. 1 to 6)

First, we choose a couple of concave face congruent polyhedrons, preferably space-fillers. We shall call them original polyhedrons. Second, by connecting any internal point and the vertexes, we divide the original polyhedrons into as many pyramids as the polyhedrons have faces. We then

create pyramids having a polygonal base, which is face of the original polyhedrons.

Third, we make frustums of the said pyramids; this is done by removing the top parts of the pyramids in a plane between the base and the apex. Fourth, gluing the frustums by their congruent larger bases, we create a solid pyramidal module. The core of the new method is the creation of a building block by the bonding of the two frustums by their congruent bases. Connecting the vertexes with the center of the volume, the original cube generates six pyramids of square base. The original tetrahedron generates four pyramids of triangular base. The original octahedron generates eight pyramids of triangular base. The original cuboctahedron creates six square pyramids and eight triangular pyramids. The original tetragonal octahedron generates eight isosceles pyramids. The frustums of those pyramids are half of the solid pyramidal modules.

Therefore, solid pyramidal modules are frustums (of pyramids having the original polyhedron polygonal face for base and the original polyhedron center for apex) glued by their bases to other identical or different frustums with congruent bases.

Skeletal Pyramidal Modules

A hole or holes through the module's bases provides a means to make an erected structure.

We shall call the solid modules, from which a central portion has been removed, skeletal pyramidal modules (see FIG.

10) .

Distinctive Angle We shall call the angle (sum of two polyhedrons' dihedrals) , drawn by a cross section perpendicular to the side of the modules (see FIG. 6 A2 , B2, C2, D2 , E2 for modules' cross sections) the distinctive angle.

Solid Conical Modules The other preferred type of module to be made with the present invention method (see FIG. 7 in the cube example) is constructed by two conical frustums glued by their bases. The

conical frustums are cones having the original polyhedron center point for the apex and a circle for the base. These circles are inscribed, tangent at each side of the polygonal face of the original polyhedron and tangent also to neighboring circles.

It is imperative in this kind of module to mark it where the circle is touching the polygon side because these are the places where a module will be connected, according to the present method, to other modules (see FIG. 6 A3, B3, C3, D3, E3, F3 for a top view of the conical module, and FIG. 9 for a perspective view of an assembled polyhedron) . In most conical modules we do not know, without marks, where the sides are. The conical module is limited by the fact that a circle can be inscribed in a limited number of polygons. However limited, conical modules may prove useful because of their simpler design. Skeletal Modules

By means of a hole or holes through the bases or the extensive removal through the plane central portion, the designer may achieve lighter modules, skeletal modules of the two genera, pyramidal and conical (see FIG. 10) , which allows for the separate construction of the module's sides by industrial processes other than molding, such as extrusion or metal sheet bending and for the making of holes through the sides to use a bolt-like fastener to hold the modules to other of like shape. Two Cross Sections

Solid and skeletal modules have, within the present method, two preferred embodiments represented by cross sections that we shall call "A" and "B" (see FIG. 11) . "A" is a truncation of the distinctive angle. The "B" cross section mainly applies to the conical modules. It is a semicircle or, in the skeletal configuration, could be a circle.

The conical modules are assembled according to the present method by means of wrapping a fastener through holes in the member or magnetically. Single Description (see FIGS. 19 and 20)

Cones have been studied and defined as pyramids with an infinite sided base; therefore, both genera of the method can be reduced to one and, because the core of the method, the union of the frustums by their congruent base, has not been previously explored, we think we have the right and duty to expose the following simpler and wider description of the method:

1. The union of two frustums by their congruent base.

2. The removal of a central portion through the plane section of the frustum.

3. The making of holes through the peripheral side of the frustum.

4. The truncation of the peripheral edge of the frustum. 5. The rounding of the peripheral side of the frustum.

6. The magnetization of the frustum.

7. The magnetization of the module. Built-in Dihedral Slot Connectors

Until this point, modules have had the need of an fastener, adhesive or magnetic, to be attached, connected, to be assembled or erected structurally. Now, referring to FIG. 13, there is a fundamental leap that allows the modules to connect onto another perpendicularly intersecting body as does the type of connector developed first by Beck's U.S. Patent No. 2,894,934.

The built-in dihedral slot connectors (slot connectors, for short) are not part of the method, but is the preferred embodiment to be built into the modules created by the present invention. "A" and "B" Connectors

The present invention slot connectors are of two types, one more suited for the "A" cross section (see FIG. 16) , we shall call the "A" connector; the other, which is round (see FIG. 17) , we shall call the "B" connector. The "A" connector is an improvement over previous slot-connector designs (U.S. Patent Nos. 3,177,611, 3,698,124, 3,940,100, etc.) consist mainly in augmenting the surface of contact between

connectors, and with "B" connectors, the improvement comprises the easily radially deformable shape of the cylinder when pressed on a line parallel to the axis of the connector. The connectors are preferably located where the conical modules are marked, or at the middle of a conical skeletal "B" cross- section module. This is a configuration easily adaptable to a wide variety of different processes such as inflatable toy modules and iron building construction modules.

Detailed Description of the Preferred Embodiments

The present invention has two aspects. One is a module defined by a hypothetical method to make building block modules (modules for short) ; the other is an apparatus, an integral slot connector for the perpendicular connection of two flat members. Because the modules made with this method are flat members, both parts conveniently complement each other.

The Hypothetical Method of Manufacture Used to Define the Structure of the Modules To facilitate reading, we created mnemonic charts. See

FIG. 21. The method may be described as along two genera, Pyramidal and Conical. Both genera comprise steps to create modular construction units which may be interconnected with others of like shape by means of a fastener, magnetically or connected by means of other modules of like shape to erect a hollow polyhedral structure after being provided by an integral connector.

The method may also be described along one single line because cones are a class of pyramids. This freer description may help to produce modules that, when connected to others of like shape, create results beyond polyhedral structures.

We decided to expose the method in its two forms in the belief that a double description could clarify subtle relationships between the two types of structures. Pyramidal Modules

The preferred embodiment of the present invention will now be described in connection with FIGS. 1 to 5. The first

step is to choose a couple of polyhedrons (original polyhedrons) . These may be two equal polyhedrons such as cubes 1 (FIG. 1) , rhombic dodecahedrons 4 (FIG. 3) or tetragonal octahedrons 6 (FIG. 6) ; or they may be two different polyhedrons such as a regular tetrahedron 2 and a regular octahedron 3 (FIG. 2) ; or they may be two different polyhedrons with two different faces such as a cuboctahedron 5 (FIG. 4) and an octahedron 3 (FIGS. 2 and 4) ; or they may be a combination involving three or four different polyhedrons (four different polyhedrons is the limit for regular and irregular space-filling systems) .

In any case, we first choose two of them with congruent faces — common faces — such as the square FA1 of the cube 1 or the right triangle FA2-3 in the tetrahedron 2 structure. We will begin by choosing polyhedrons that form the more simple structures, triangular and rectangular prisms. We may continue with regular space-fillers, then semi-regular space- fillers, and finally get to the most irregular polyhedrons such as the wonderful Buckminεter Fuller's "Quanta Modules." After choosing the original polyhedrons, we have to select a point inside them, not a point on the surface. If this, point is at the center, equidistant to all faces, as in all our examples, the modules will be simpler; experimental or toy modules may require an eccentric point. The center point is usually found, in regular and semi-regular polyhedrons, at the intersection of lines connecting the vertexes, connecting the centers of the faces or connecting the vertexes with the centers of the faces.

Referring to FIGS. 1 to 5, the second step of the present new method involves the mental sectioning of the original polyhedrons 1, 2, 3, 4, 5, 6 into pyramids PY1, PY2 , PY3 , PY4 , PY4S, PY5T, PY6 defined by segments between the central points CP1, CP2, CP3 , CP4 , CP5, CP6 and their respective vertexes VE1, VE2, VE3, VE4 , VE5, VE6. The step may also be expressed as the creation of pyramids PY1, PY2 , PY3 , PY4 , PY5S, PY5T, PY6 having them the central points CP1, CP2 , CP3 , CP4 , CP5, CP6 of the original polyhedrons 1, 2, 3, 4, 5, 6 for apex and

the original polyhedrons faces FA1, FA2-3, FA4, FA1-FA2-3, FA6 for base.

From the cube 1, the tetrahedron 2, the octahedron 3, the rhombic dodecadehron 4 and the tetragonal octahedron 6 is extracted one type of pyramid respectively, but from the cuboctahedron 5 two types of pyramids are extracted: one square PY5S and one triangular PY5T. Three different pyramids from one polyhedron is the limiting case for regular or semi- regular space-filler polyhedrons. The third step is the making of frustums, FR1, FR2, FR3,

FR4, FR5S, FR5T, FR6 from the extracted pyramids PY1, PY2, PY3, PY4, PY5, PY6. This is accomplished by removing the top portion TP1, TP2, TP3, TP4, TP5S, TP5T, TP6 after a plane sectioning between the apex CP1, CP2, CP3, CP4, CP5, CP6 and the base FA1, FA2-3, FA4, FA1-FA2-3, FA6 of the said pyramids PY1, PY2, PY3, PY4, PY5S, PY5T, PY6. Because the thickness of the module is produced by this sectioning, the designer should consider it a significant design variable. The sectioning may be parallel to the base, as in our examples, creating regular trapezoidal peripheral faces PF1, PF2, PF3, PF4, PF5S, PF5T, PF6.

The fourth step, the creation of the modules, is the heart of the method. Mentally joining one original polyhedron's frustum, FR1, FR2, FR3, FR5, FR5S, FR5T, FR6 with the other original polyhedron's frustum FR1, FR2, FR3, FR5, FR5S, FR5T, FR6 by their congruent base FA1, FA2-3, FA4, FA6 forms a third body: the modules Ml, M2-3, M4, M5S, M5T, M6. As a result of the union of the frustums, the common base's polygon FA1, FA2-3, FA4, FA6 (in all of its combinations) forms the peripheral edges PE1, PE2-3, P34, PE5S, PE5T, PE6. The cube 1 system's module Ml is made by the union of two equal frustums FR1. The tetrahedron 2/octahedron 3 system's module M2-3 is made by the union of two different frustums FR2 and FR3. The cuboctahedron 5/octahedron 3 systems have one square module M5S made from the union of two equal frustums FR5S and triangular module M5T made from the union of two different frustums FR3 and FR5T. The rhombic dodecahedron 4

system's module M4 is made by the union of two equal frustums FR4. The tetragonal octahedron 6 module M6 is made by the union of two equal frustums FR6.

An interesting column, Buckminster Fuller's "Tetrahelix, " is made with a module formed by two tetrahedrons' frustums FR2. Summing up, original polyhedrons 1, 2, 3, 4, 5, 6 are divided into pyramids PY1, PY2 , PY3 , PY4, PY5S, PY5T, PY6, from which are removed top portions TP1, TP2 , TP3 , TP4, TP5S, TP5T, TP6, forming frustums FR1, FR2 , FR3, FR4 , FR5S, FR5T, FR6 that joined by their bases FA1, FA2-3, FA5, FA6 form examples of solid pyramidal modules Ml, M2-3, M4 , M5S, M5T, M6 with their distinctive angles DAI, DA2-3, DA4 , DA5S, DA5T, DA6 along their peripheral faceted side PFl, PF2 , PF3 , PF4 , PF5S, PF5T, PF6 and their peripheral edges PE1, PE2-3, PE4 , PE5S, PE5T, PE6. The fifth step is described in connection with FIG. 11. It comprises the truncation of the peripheral polygonal edge 6 of the module 1 creating a peripheral side 2 between the peripheral faces 10, that is one wall (in a built structure) of a conduit along the edges of the polyhedron. We shall call this truncation an "A" cross section; this truncation is useful also in molding and in avoiding chipping.

The following steps are described in connection with FIG.

10. The sixth step creates another conduit in the built structure, this time bigger and perpendicular to the face of the original polyhedron. It makes skeletal modules SMI and SM2-3 by the removal through the plane of the modules of a portion, small 11 or large 11', but never reaching or modifying the peripheral faces PFl, PF2 or PF3 and their distinctive angle. This step is crucial; the designer creates with it conduits not only to get access into the structure but also as a holder of tubes or spheres, as in Haug's U.S. Patent No. 3,940,100.

The seventh step is the making of holes 8 through the peripheral faceted sides PF2 , PF3 of the module M2-3 for the use of a rivet or a bolt-nut 12 fastener to hold the module to others of like shape.

Conical Modules

There is another type of module visualized by a similar method. They are modules made joining two conical frustums by their equal circular bases. They are, as the pyramidal modules, aimed to be assembled into hollow polyhedral structures.

The first step is to choose two polyhedrons. They may be identical or different, but they must pass three conditions: (1) their faces must be congruent; (2) have at least bilateral symmetry (this condition leaves out entire families of scalene tetrahedron space-fillers) ; and (3) a point on the face must be equidistant to the sides, a circle inscribed in them must touch each one of the sides (this condition leaves out, for example, elongated rectangles and truncated triangles) . We may choose any of the polyhedrons of FIGS. 1 to 5, but for the present new method example we will refer to cubes, as shown in FIG. 7.

The second step is to choose a volume point or the central volume point CPl in each of the polyhedrons 100. The third step is to inscribe a circle 30 on the faces

FA1. The circle 30 must be tangent to the sides 50 of the faces FA1 and tangent to their neighbor circles 30 in a point usually, but not necessarily, at the middle of the sides 50.

The tetragonal octahedron circle, for example, is inscribed in an isosceles triangle and touches two sides and two neighbor circles off the side respective centers.

The fourth step involves the construction of cones 6 equal to those defined by the said volume central points CPl and their respective inscribed circles 30. The cones may be regular, with their apex CPl in a line perpendicular to the center of the base or irregular, such as the cone of the tetragonal octahedron.

The fifth step is to make frustums 70 from the said cones 60 by removing the top portions 80 after sectioning the said cones 60 through a plane 130 that goes between the base 9 and the apex CPl. The preceding steps guide the construction of

a couple of base congruent frustum of cones extracted from two face congruent polyhedrons.

The sixth step is the creation of modules 100 by mentally joining the said frustums 70 from one original polyhedron 100 with the said frustums 70 from the other original polyhedron 100 by their larger congruent bases 90.

The seventh step is to make marks 120 to indicate where the circles were tangent 110 to the edges 50 of the original polyhedrons 100 to show the place where a module must be attached to others of like shape to be erected.

The next two steps, eighth and ninth, are described in relation with FIG. 11. They are to truncate the peripheral edge 62, to remove the tip of the distinctive angle 72, and to make a single peripheral side 22 between the peripheral sides 10, useful in molding and to avoid chipping.

The last steps are described in relation with FIG. 10.

The tenth step is to remove, through the module's plane, a central portion, either a small portion 133 or large portion 33, but never reaching or modifying the peripheral sides 14. As a result of this step we obtain skeletal modules.

The eleventh step is to make holes 8 through the peripheral sides 14 where indicated by the marks of the seventh step to attach the modules by means of a fastener, according to the present invention. There is a further simplifying preferred embodiment of the method for conical modules; it will be described in relation to FIG. 11.

The twelfth step consists in the rounding of the peripheral edge 72, represented in a module's cross section as a semicircle 82 tangent to the peripheral faces 102; this is the "B" cross section. This step, together with the tenth, makes a modules from an inexpensive ring 4; a fact that may take today's sophisticated space frame technology to market areas untaught before.

The module 101 top view depicted in FIG. 12, holed between angles of thirty degrees 201, twenty-five degrees 301 and thirty-five degrees 401 disposed in ninety degree specular arrangement may be assembled, according to the invention, into

five space-filling structures by means of a wire fastener, and may be used in concrete reinforcing, not only as the ultimate reinforcement of the concrete, but also as scaffolding and holder of the forms. The modules are somewhat flat, rigid elements; their embodiments are determined by two types of sections: those of the plane and those of the thickness or cross section. The plane sections of a module results in polygons; the middle plane section is the face of the original polyhedron. The cross section (perpendicular to the sides towards the center) has an angle that is the sum of two original polyhedron bisected dihedrals.

As a guide for the drafting of modules, the designer of advanced modules may create, for the manufacture modules, a chart of top views (face sections) and cross sections of the modules such as the one depicted in FIG. 6, which shows the six modules from FIGS. 1 to 5 top views Al, A3, Bl, B3 , Cl, C3, Dl, D3, El, E3, Fl, F3 (they represent both faces of the modules, therefore no hidden lines are shown) and cross sections A2 , B2 , C2 , D2 , E2 (each one represents all the polygons' sides, with the exception, in these examples, of the tetragonal octahedron 6 where two cross sections A2 , E2 represent three sides 7g, 7g, 5g) . The cross sections are the same for both pyramidal and conical modules; they have two acute angles 5c, 6c, 7c, 8c, 9c, each one half the size of the original polyhedron's dihedral (s) , and the sum of those angles forms distinctive angles, in the sense that you can differentiate two pyramidal square or triangular modules by these angles. Each top view shows two polygonal perimeters, one external (face of the original polyhedrons 5a, 5d, 6a, 6d, 7a, 7d, 8a, 8d, 9a, 9d, 10a, 10) and one internal (which is not critical) 5al, 5dl, 6al, 6dl, 7al, 7dl, 8al, 8dl, 9al, 9dl, lOal, lOdl. Both perimeters have the same number of sides and the same angles between sides. The sides and angles of the conical module top views are hypothetical and represented by a broken line 5ah, 5alh, 6ah, 6alh, 7ah, 7alh, 8ah, 8alh, 9ah,

9alh, 10ah, lOalh. At some convenient point on the lines from the tangential points 5f, 6f, 7f, 8f, 9f, lOf to the plane center 5e, 6e, 7e, 8e, 9e, lOe, a mark or hole 11, 11a, lib, lie, lid, lie shall be made to indicate where to attach one module to another according to the present invention method.

The following list shows approximate proportional lengths and angles from FIG. 6. Angles are mandatory, but some lengths are given to conform with volume standards given by

Peter Pearce's book, "Structure in Nature in a Strategy for Design."

5g= the unity (u)

6g= (u) times square root of 2

7g= (u) times square root of 3 divided by 2

5b= 90-degree angle 6b= 60-degree angle

7b= 70-degree angle

8b= 110-degree angle

5c= 45-degree angle

6c= 35-degree angle 9b= 55-degree angle

7c= 62.5-degree angle Modules Single Description

The present invention method will now be described to give more freedom to the designer referring to frustums of unspecified amount of sides and dihedral angles, unspecified in the same sense we may call unspecified the amount of spokes a wheel could have from the hub to the rim and in the mathematical sense being the infinite sided polyhedron, a circle for frustums not necessarily related to predetermined polyhedrons; the method of the present invention works with any frustum, with any pair of frustums of congruent base.

Removals, holes, truncations and rounding will be done in the frustum instead of being performed in the constructed module.

This wider method may help to create some complexity, but also unexpected wonder and beauty.

Although frustums always have one base larger than the other, we will name them for further clarity.

This description will be done in connection with FIG. 18 as follows:

A method to produce a relatively flat module from two frustums 1, 1.1, having each frustum two opposite bases 2.0, 3.0, 2.1, 3.1, one larger 3.0, 3.1 than the other 2.0, 2.1

(each base may have from three to infinite edges) , one peripheral faceted side 4.0 (with as many facets as the bases

2.0, 3.0, 2.1, 3.1 has edges) between the bases, and one critical peripheral edge 5.0 between the larger base 3.0 and the peripheral side 4; being one frustum's larger base 3 congruent to the other frustum's larger base 3.1.

The method comprises the following steps:

(a) The making of holes 7 through the said frustums' bases 2.0, 2.1, 3.0, 3.1 in order to allow access to the structure, connect one module to another and eventually connect one frustum to another making skeletal frustums.

(b) The making of holes 8 through the said frustums' peripheral sides 4.0 in order to connect one module to another. (c) The congruent union of the said 1.0, 1.1 frustums' bases by their said larger congruent bases 3.0, 3.1 forming a module 6.0.

The method further comprises two additional steps described in connection with FIGS. 19 and 20, respectively: (d) The truncation of the said frustums 1.0 critical peripheral edge 7.0 through planes perpendicular 6.0 to the larger base 3.0, creating a new faceted side 2.0 between the peripheral side 4.0 and the large base 3.0.

(e) The convex circular rounding of the said frustums' peripheral side 9.0 in such a manner that part of the cross section of the frustum shows a quarter of a circle defining the rounding.

The center 11.0 of that hypothetical circle is on the large base 10.0 and the length of its radius 12.0 is equal to the distance between the frustum's bases 13.0 and 10.0.

Assembling of Modules

The assembling or erecting of the modules will be described now in connection with FIGS. 8 and 9. To erect the modules into a building structure is to reverse the process of its construction, a process in which the volume loses an interior portion and it is divided into as many units, or pyramids, as the polyhedron has faces.

The pyramidal module has two peripheral sides 302 divided into as many trapezoids 502 as the plane section of the module has sides. For the modules to be assembled, erected into polyhedral structures, its trapezoids 502 must be congruent bonded — attached to other module trapezoids.

The conical module in FIG. 9 has two peripheral sides 61 divided by a peripheral edge 71 — the module is marked 81 radially and/or holed 91 to show the lines 101 on the peripheral edge that must be shared by the modules to be assembled, and erected into polyhedral structures. The conical modules may be held together by means of a wire-like fastener 111 or may be held magnetically 131. These magnetic ring modules may be provided by one or more insulators 121. FIG. 9 shows a type of structure, a cuboctahedron-octahedron system that may be assembled with polarized 131 modules without insulators 121, the modules must be circularly magnetized 131 (perpendicular to the bases 14) . Integral Dihedral Slot Connectors

Until this point, the present invention module sides are connected parallel to each other by means of a fastener intersecting them at ninety degrees. Now, a new type of module, with a built-in connector, will substitute the fastener. This new module will intersect others at ninety degrees, as depicted in the schematic perspective view of FIG. 13.

Another reason why we have selected the five structural systems depicted in FIGS. 1 to 5 will become apparent. The five systems interact, making what we may call three super- systems.

In reference to FIG. 13, the cube-system 24 intersecting connector 14 is a smaller cube module. The rhombic dodecahedron system 44 intersecting connector is a smaller regular tetrahedron module 34. The cuboctahedron-octahedron system 64 intersecting connector is a smaller tetragonal octahedron module 54. And the tetragonal octahedron system 94 intersecting connectors are of two kinds: the cuboctahedron- octahedron-square module 74 and the cuboctahedron-octahedron- triangle module 84. For the purpose of a 90-degree intersecting connection, the present invention has two preferred embodiments; they are depicted in a perspective view in FIG. 14. One, more suited for the pyramidal module with "A" cross section 15, we will call it "A" connector 25. The other, of a round configuration, more apt for the conical module 45 (here, in a simplified cross section) , we will call it "B" connector 35. They are depicted in comparison with prior art in FIG. 15. It may be said that prior art slot connector are in integral connector for perpendicularly connecting two relatively flat members 26 of equal thickness essentially by making an opening 16 slightly larger than the width of the member if the member is undeformably rigid.

The opening 16 should be slightly smaller if the material is somewhat deformable and we want a grip or locking between the parts. The connectors are also integral connectors 35 for perpendicularly connecting two relatively flat members 45 of equal thickness; also the rules for the openings size apply.

The "A" type will be described in relation to FIG. 16.

It is an integral connector for connecting two undeformable rigid flat members 57. The connector comprises a slightly smaller shape 17 than two triangular prisms 27 spatially oriented to share their longitudinal right angle edges 37 (ultimately, because the prisms are smaller than the described prisms 27, and there is a gap between prisms 27 instead of touching) . The prisms have their larger faces 47 mutually parallel, the member 57 attached to the said larger faces 47 and to two coplanar prisms' triangular faces 67; the said prisms' common

edge 37 is a line in the middle plane 77 section of the member

57. To accomplish a smoother connection and avoid chipping, the front end faces' 87 shorter edges 97 and the right angle edge 37 should be obviously rounded or truncated. The advantage of the "A" connector over prior art is its minimization of weakening of the member and enlarging the surface of contact. Because the right angle edge 37 results in the "B" connector when rounded up to semicircle, the following description in reference to FIG. 17 is intended as further clarification. The "B" connector is an integral connector for connecting two deformable rigid, flat members

58. It comprises a shape 18 slightly larger than two semicircular prisms 28 spatially oriented to mutually face their curved faces 38, having their flat, rectangular faces 48 mutually parallel at a distance equal to the diameter of the prisms' semicircle multiplied by the square root of two (because ultimately the prisms are larger than described here, the distance between rectangular faces is smaller) . The member 58 is attached to the said prisms' rectangular faces 48 and to two coplanar semicircular faces 68. For the purpose of a smoother connection, the semicircular front end faces' 78 curved edges 18 should be rounded or truncated.

In building block scale modeling, the problem of inexpensive locking, gripping or snap action is very important. The present "B" connector solution gives a large margin of manufacture tolerance.

The contact lines 88 between connectors are radius of a semi-cylinder. Cylinders, when pushed in a surface line parallel to its cross section center, deform easily, which is what the designer looks for in a slow-wear holding system.

The "B" connector is now ready to interconnect with the "A" connector; if it is not in our interest to unit the systems, the "B" connector will improve in strength by means of a bridge 98 between the closer points of the prisms' curved faces 38 from the longitudinal middle 108 toward the member, being the bridge never thicker than the gap between prisms. The design concepts of the "B" connector are presented without

scale considerations mainly, but not limited to, in use with the present invention. It is in the hands of the designers to complete them with a proprietary specification in a variety of markets. It is expected that our method will combine with new specific inventions in a wide range of industries and markets. The present invention encourages the construction of hollow modules, such as inflated units made out of two equal flexible sheets welded in such perimeters that, when inflated, they resemble conical cross section "B" skeletal with "B" connectors modules. For advanced constructive applications, the designer may look for known data published in Coxeter's "Regular Polytopes," Buckminεter Fuller's "Synergetics," Arthur Loeb's "Space Structures" and the above-mentioned book of Pearce. In a less advanced stage, the designer may use school texts or our basic examples. For amusing (puzzle) applications, the designer may create proprietary data or a system for creating such data.