To provide a polyhedron structure favorable to the framework of a celestial body observing dome.

Frame members 2 consisting of inside and outside two frame pieces 3, 4, are arranged on each side of a tetrahedron?, and cylindrical bodies 5 are arranged at the center points of respective frame members pieces 2, thereby the frame pieces 3, 4 of the frame members 2 are freely rotatively engaged with each other centering around these cylindrical bodies 5. At each vertex of the tetrahedron, the ends of the inside fame pieces 3 of the respective frame members 2 are connected to be freely opened and closed to the ends of the outside frame pieces 3, 4 of the other frame member 2 while being slidably brought into contact from the inner side with the outside frame piece 4 of one frame member 2 out of two frame members 2 passed through the vertexes of the tetrahedron, and at the same time, the ends of the outside frame pieces 4 of the respective frame members 2 are connected to be freely opened and closed with the ends of the inside frame pieces 3 of one frame members 2 while being slidably brought into contact from the outer side with the inside frame piece 3 of the other frame member 2 out of the other two frame members 2 passed through the vertexes of the tetrahedron. Hereby, a polyhedron structure 1 can be freely contracted and expanded.