The spatial structure configuration can be defined based on the close packing of polyhedra. A polyhedron is a three dimensional solid made of at least four sides (S) which intersect each other along the edges (E) and vertices (V). Leonhard Euler found the following relationship between the number of sides, vertices and edges of a polyhedron:
S+V=E+2
The platonic polyhedra (after Plato who introduced them in 300 B.C.) have surfaces made of regular polygons. These polyhedra are: Tetrahedron (made of triangles) with S=4,V=4, and E=6; Hexahedron or cube (made of squares) with S=6, V=8, and E=12; Octahedron (made of triangles) with S=8, V=6, and E=12; Dodecahedron (made of pentagons) with S=12, V=20, and E=30; and Icosahedron (made of triangles) with S=20, V=12, and E=30. Note that only Tetrahedron, Octahedron and Icosahedron are stable when subjected to external forces. Polyhedra such as tetrahedra, octahedra, and cubes can be connected to each other to create spatial structural forms. Assuming that the spatial structure has enough supports, if it is made of stable polyhedra the entire structure will be stable.
