¶ Icosahedron: Subtriangulation
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Index Entry
Of the three fundamental structures the tetrahedron contains the least volume with the most surface and is therefore the strongest structure per unit of volume. Whereas the icosahedron gives the most volume with the least surface; and though least strong, it is stable and gives the most efficient volume per units of invested structure. That is the reason I decided to develop the triangulated icosahedron as the fundamental volume-controlling device of man. I decided also to obtain high local strength on the icosahedron by subtriangulating its twenty basic spherical triangles with locally superimposed tetrahedra-- i.e., an octahedron-tetrahedron truss-- which would take highly concentrated local loads or impacts with minimum effort, while the surrounding rings of triangles would swiftly distribute and diminishingly inhibit the outward waves of stresses from the point of concentrated loading.
