420.00 Isotropic Vector Matrix

420.01 When the centers of equiradius spheres in closest packing are joined by most economical lines, i.e., by geodesic vectorial lines, an isotropic vector matrix is disclosed“isotropic” meaning “everywhere the same,” “isotropic vector” meaning “everywhere the same energy conditions.” This matrix constitutes an array of equilateral triangles that corresponds with the comprehensive coordination of nature’s most economical, most comfortable, structural interrelationships employing 60-degree association and disassociation. Remove the spheres and leave the vectors, and you have the octahedron-tetrahedron complex, the octet truss, the isotropic vector matrix.

420.02 The isotropic vector matrix is four-dimensional and 60-degree- coordinated. It provides an omnirational accounting system that, if arbitrarily accounted on a three-dimensional, 90-degree basis, becomes inherently irrational. The isotropic vector matrix demonstrates the ability of the symmetrically and asymmetrically terminaled, high-frequency energy vectors to accommodate the structuring of any shape. (See Sec. 932, “Constant Volume.”)

420.03 Our extension of the Avogadro hypothesis (Sec. 410) generalizes that all energy conditions are the same. Inasmuch as vectors describe energy conditions, this would mean a volumetric aggregation of vectors in a structural complex in which all of the interacting vectors would have to be of the same length and all of their intersecting angles would have to be the same. This state of omnisameness of vectors stipulates the “isotropic,” meaning everywhere the same. This prescribes an everywhere state of equilibrium.