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2.14 "Recalling that the (24) vector edges of the vector equilibrium (25 great cicles) exactly equal the radial explosive forces, while the [31 great circle) icosahedron's 30 external edges are longer and more powerful than its 30 radial vectors, yet each has an excess of one great circle, which great circle must have two polar vertexes of spin, we encounter once more the excess two polar vertexes characterizing all topological systems, and witness the excess of embracingly cohering forces in contradistinction to the explosively disintegrative forces of universe." (I, 1052.31]
3.9 "There are only three possible cases of fundamental omnisymmetrical, omnitrianguläted, least-effort structural systems in nature: the tetrahedron, with three triangles at each vertexi the octahedron, with four triangles at each vertex; and the icosahedron, with five triangles at each vertex." (I, 532.41)
4.16 "Four sets of axes of spin....These four sets of (50) unique topological aspects of the vector equilibrium provide four different sets of symmetrically positioned polar axes of spin to generate 25 great circles of the vector equilibrium."(I. 450.11) (Compare with 3 sets of 62 features of icosahedron generating 31 great circles)
5.4 "We discover that an icosahedron is the first degree of contraction of the vector equilibrium. We never catch the vector equilibrium in its true existence in reality: it is always going one way or the other. When we go to the icosahedron, we get to great realities. In the icosahedron, we get to a very prominent fiveness: around every vertex you can always count five." (I, 461.03)
5.5 "The fundamental fiveness of the icosahedron is split two ways, with 2 1/2going one way (the outside-out way) and 2 1/2 going the other way (the inside-out way)... It is then in transforming from a positive two-and-one-halfness to a negative two-and-one-halfness that the intertransformable vector-equilibrium-to- icosahedron, icosahedron-to-vector-equilibrium, equilibrious-to-disequilibriousness attains sumtotally and only dynamically a spherical fiveness."(II, 1053.12-15)
6.12 "If we assume that the vertexes are points of discharge, then we see how the six great circles (of the 31) of the icosahedron -- which never get near its own vertexes -- may represent the way residual (energy) charge will always remain held on the surface of the icosahedron....The icosahedron makes it possible to have individuality in Universe. The vector equilibrium never pauses at equilibrium, but our consciousness is caught in the icosahedron when mind closes the switch. The icosahedron's function in Universe may be to throw the switch of cosmic energy into a local shunting circuit. In the icosahedron energy gets itself locked up even more by the six great circles..." (I, 458.05-11)
6.13 "The rational spherical excess of six degrees (of the icosahedron's 120 -- 60 plus and 60 minus -- similar tetrahedral components) is symmetrically distributed to each of the three central and three surface angles of each of the 120 tetrahedral components of the spherical icosahedron. This sixness phenomenon tantalizingly suggests its being the same transformative sixness as that which is manifest in the cosmically constant sixfoldness of vectors of all the topological accountings..." (II, 1043.01-02)
7.2 "The seven unique cosmic axes of symmetry describe all of crystallography....
Vector equilibrium: Icosahedron: 1. Square face centrepoints 3 5. Triangular face centrepoints 10 2. Triangular face " 4 6. Midedges 15 3. Vertexes 6 4. Midedges 12 7. Vertexes 6 Total great circles 25 Total great circles 31 Grand total (*25) 56 Axes of symmetry 1 through 6 result in great circles through the same 12 vertexes. Great circles generated by. the 7th go through no vertexes (I, 1042.05)
7.3 "The prime generation of the seven axes of symmetry are the seven unique perpendiculars to the faces of the seven possible truncations of the tetrahedron." (II. 104.11)
7.4 "The trigonometric identification of the great-circle trajectories of the seven axes of symmetry with the 120 basic disequilibrium LCD triangles of the spherical icosahedron." (II, 251.29)
11.1 "The primary and secondary icosa symmetries altogether comprise 121 - 11 great circles." (II, 987.132)
20.6 "There is, for instance, the minimum twentyfoldness of the ticosahedron's 20 equiangular, triangular (ergo, structural) facets, which constitute the highest common unit-angle, unit-edge, and unit-vertex structural denominator of universal structural systems. The icosahedron encloses the most volume with the least energy investment as matter or work." (I, 1055.03)
25.4 "When the nucleus of the vector equilibrium is collapsed, or contracted, permitting the 12 vertexes to take the icosahedral conformation, the 12 points of contact of the system go out of register so that the 12 vertexes that accommodate the 25 (of the 31) great circles of the icosahedron no longer constitute the shortest routes of travel of the energy....The icosahedron, in fact, can only occur as a single shell of 12 vertexes remote from the vector equilibrium's multi-unlimited-frequency, concentric-layer growth...but it provides the most economical route between a chain of tangent icosahedra.., as well as for energy locked up on its surface to continue to make orbits of their own in local travel around that single sphere's surface."(I, 458.02-3)
31.2 "The 31 great circles of the icosahedron always shunt the energies into local holding great-circle orbits, while the vector equilibrium (25 great circles) opens the switching to omniuniverse energy travel. The icosahedron is red-light, non-go; whereas vector equilibrium is green light, go. The six (of the 31) great circles of the icesahedron act as holding patterns for energies." (II, 1132.02)
31.3 "In this composite spherical matrix we see all the 25 primary vector equilibrium great circles and two sets skewed-positive and negative of the icosahedron's
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