A set of polyhedrons have shapes capable of fitting together, in one or more ways, into a solid geometric shape such as a rectangular solid or more specifically, a cube. The polyhedrons include five-sided polyhedrons made up of a regular tetrahedron and an irregular tetrahedron abutted together as one solid; alternately, the two separate tetrahedra can be included in lieu of one or more of the five-sided polyhedrons, for assembly in the puzzle. The set of polyhedrons includes separate irregular tetrahedra and may include a regular octahedron. Preferably each shape of polyhedron is in a different color. In a preferred embodiment, the polyhedrons are all solid throughout and are of the same density, and that density is preferably the same density as water to enable the teaching of certain relationships. The set of polyhedrons function not only as a puzzle, for fitting into a transparent housing such as a cube, but also for educational purposes in teaching geometry.

A cubic puzzle construction utilizes a mathematical technique of dissecting a physical cube into a finite number of pieces to yield a block puzzle capable of the illusion of matter being created and destroyed. The component pieces are assembled in two different ways to produce the same cubic shape. However, one method of assembly requires the use of an additional piece or pieces while the second method omits these. In both methods the rigid pieces fit easily, without gaps or overlaps, to completely fill the same rigid container.

Complementary geometric construction modules, each derived from a rectangular prism, with end faces formed obliquely to each other and to the longitudinal axis of the prism, with the two oblique faces touching each other at a point on the longitudinal edge of the prism, each module forming a hexahedron, each being the reverse or mirror-shape of the other, and providing bilateral symmetry when the two corresponding faces on the modules, are in full contact with each other; the modules in multiple sets adapted to be formed into a wide variety of sculptured architectural shapes, unique in appearance.

A geometric block system for constructing a regular rhombic dodecahedron having twelve identical rhombic faces, the system consisting of eight identical first blocks each being one-quarter of a regular tetrahedron and eight identical second blocks each being one-eights of a regular octahedron. The regular tetrahedron has six edges of length "a" and four identical equilateral triangular faces with sides of length "a". Each first block has one cubic unit of volume and has an apex at a point corresponding with the center of gravity of the tetrahedron and has first, second, third and fourth triangular faces. The first face is equilateral triangular with edges of length .intg.a"; the second, third and fourth faces are isosceles triangular with one edge of length "a" and two edges of length "b" equal to a .sqroot.6/4. The regular octahedron has eight edges of length "a" and eight identical equilateral triangular faces with sides of length "a". Each second block has two cubic units of volume and has an apex at a point corresponding with the center of gravity of said octahedron and has fifth, sixth, seventh and eighth triangular faces. The fifth face is equilateral triangular with edges of length "a"; the sixth, seventh and eighth faces are isosceles triangular with one edge of length "a" and two edges of length "c" equal to a/.sqroot.2. Each identical rhombic face has four edges of length "b". The first and second blocks may be assembled from respective subdivision blocks as described.

Construction of buildings by assembling prefabricated elements. The volumes constructed are the sum of elementary volumes resulting from the division of a right prism whose height is a dimension U which is taken as unit and whose base is an equilateral triangle whose sides are equal to 2 U, this division being made through a plane passing through one side of one of the bases and the apex of the other base in line with the apex opposite the said side.