611.00 Structural Quanta

611.01 If the system’s openings are all triangulated, it is structured with minimum effort. There are only three possible omnisymmetrical, omnitriangulated, least-effort structural systems in nature. They are the tetrahedron, octahedron, and icosahedron. When their edges are all equal in length, the volumes of these three structures are, respectively, one, requiring one structural quantum;/owr, requiring two structural quanta; and 18.51, requiring five structural quanta. Six edge vectors equal one minimum-structural system: 6 edge vectors = 1 structural quantum.

611.02 Six edge vectors = one tetrahedron. One tetrahedron = one structural quantum.

1 Tetrahedron (volume 1) = 6 edge vectors = 1 structural quantum;

1 Octahedron (volume 4)= 12 edge vectors = 2 structural quanta;

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Icosahedron

Fig. 610.20 The Three Basic Structural Systems in Nature with Three, Four or Five Triangles at Each Vertex:

There are only three possible cases of fundamental omnisymmetrical, omnitriangulated, least-effort structural systems in nature: the tetrahedron with three triangles at each vertex, the octahedron with four triangles at each vertex, and the icosahedron with five triangles at each vertex. If there are six equilateral triangles around a vertex we cannot define a three-dimensional structural system, only a “plane. ” The left column shows the minimum three triangles at a vertex forming the tetrahedron through to the six triangles at a vertex forming an “infinite plane.” The center column shows the planar polyhedra. The right column shows the same polyhedra in spherical form.

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Fig. 612.11

1 Icosahedron (volume 18.51) = 30 edge vectors = 5 structural quanta.

Therefore:

with tetrahedron, 1 structural quantum provides 1 unit of volume;

with octahedron, 1 structural quantum provides 2 units of volume; with icosahedron, 1 structural quantum provides 3.7 units of volume.