Interconnectable space filling model

DETAILED DESCRIPTION OF PREFERRED EMBODIMENT Referring to the above drawings, FIGS.
1 through 10 illustrate the how to make triangular panels that snap together at the edges to form tetrahedra 5.
FIGS.
11 through 20 show a very similar process for making panels that snap together at the edges to form octahedra 6.
A tetrahedra 5, as in FIG.
1, is a regular platonic solid whose surface is composed of four identical equilateral triangles.
An octahedra 6, as in FIG.
11, is a regular Platonic solid whose surface is composed of eight identical equilateral triangles.
The equilateral triangles of the octahedra 6 and tetrahedra 5 of the present invention must be the same size.
Proto-panels 10, frustums of the regular Platonic solids, are formed from regular tetrahedra 5 and octahedra 6 by conceptually slicing off a portion of each face.
This conceptual slice is parallel to each face and creates equilaterally shaped proto-panels 10, each with an inner face 11, an outer face 12 and three equal length edge surface 13.
While the thickness of the proto-panels 10 may vary, preferably the proto-panel thickness to outer face edge length ratio should be less than 1:5.
FIGS.
2 and 12 show the conceptual formation of proto-panels 10 by slicing Platonic solids at a plane parallel to their triangular base.
FIGS.
3 and 13 illustrate the formation proto-panels 10 from the remaining faces.
The volume of space where the proto-panels 10 overlap form beams 15 that run along the edges of the solids.
This is illustrated in FIGS.
4 and 14.
The cross sections of the beams 15 for both the octahedron 6 and tetrahedron 5 are rhombi, FIGS.
6 and 16.
The beam cross sectional rhombi have angles arc cosine(1/3) and arc cosine(-1/3), which are approximately 70.
5.
degree.
and 109.
5.
degree.
.
The beams created by the shared volume of two panels for the tetrahedron and octahedron are slightly different.
They both have the same cross section but are mitered differently.
The 30.
degree.
miters for the tetrahedron meet at an edge of the tetrahedron which lies on the acute angle of the rhombus cross section