90560-The-Disequilibrium-120-LCD-Triangle

905.60 The Disequilibrium 120 LCD Triangle

905.61 The icosahedral spherical great-circle system displays:

12 vertexes surrounded by 10 converging angles;

20 vertexes surrounded by 6 converging angles;

30 vertexes surrounded by 4 converging angles

12 x 10 = 120

20x6 =120

30x4 =120

360 converging angle sinuses.

905.62 According to the Principle of Angular Topology (see Sec. 224), the 360 converging angle sinuses must share a 720-degree reduction from an absolute sphere to a chorded sphere: \sfrac{72O\degree}{360\degree}= 2\degree. An average of 2 degrees angular reduction for each corner means a 6 degrees angular reduction for each triangle. Therefore, as we see in each of the icosahedron’s disequilibrious 120 LCD triangles, the well-known architects and engineers’ 30triangle has been spherically opened to 36a “spherical excess,” as the Geodetic Survey calls it, of 6 degrees. All this spherical excess of 6 degrees has been massaged by the irreducibility of the 90-degree and 60-degree corners into the littlest corner. Therefore, 30> 36 in each of the spherical icosahedron’s 120 surface triangles.

905.63 In subsiding the 120 spherical triangles generated by the 15 great circles of the icosahedron from an omnispherical condition to a neospheric 120-planar-faceted polyhedron, we produce a condition where all the vertexes are equidistant from the same center and all of the edges are chords of the same spherical triangle, each edge having been shrunk from its previous arc length to the chord lengths without changing the central angles. In this condition the spherical excess of 6 degrees could be shared proportionately by the 90, 60, 30flat triangle relationship which factors exactly to 3:2:1. Since 6= ¹/ao of 180, the 30 quanta of six each in flatout triangles or in the 120 LCD spherical triangles’ 186 degrees, means one additional quantum crowded in, producing 31 quanta.

905.64 Alternatively, the spherical excess of 6 degrees (one quantum) may be apportioned totally to the biggest and littlest corners of the triangle, leaving the 60-degree, vector equilibrium, neutral corner undisturbed. As we have discovered in the isotropic vector matrix nature coordinates crystallographically in 60 degrees and not in 90 degrees. Sixty degrees is the vector equilibrium neutral angle relative to which life-in-time aberrates.

Basic Draftsman’s Triangle (Flat) (minus 5) = 30

Flatout >1 Quanta
*Module Triangle *
*35
60
84
180

(unchanged) = 60

(plus 5) = 90

180

905.65 By freezing the 60-degree center of the icosahedral triangle, and by sharing the 6-degree, spherical-planar, excess reduction between the 36-degree and 90-degree corners, we will find that the A Quanta Modules are exactly congruent with the 120 internal angles of the icosahedron. The minus 5 closely approximates the one quantum 6+ of spherical excess apparent at the surface, with a comparable nuclear deficiency of 5. (See Table 905.65.)

image

Table 905.65

905.66 The Earth crust-fault angles, steel plate fractionation angles, and ship’s bow waves all are roughly the same, reading approximately 70-degree and 110-degree complementation.

Dihedral angle of octahedron = 109= 2 x 54

Dihedral angle of tetrahedron = 70

180

x 2–60

+ 54

109

If 5= unity; 54= 60- 1 quantum; and 70= 60+ 2 quanta.

Obviously, the 70and 109relate to the “twinkle angle” differential from 60(cosmic neutral) and to the 109central angle of the spherical tetrahedron. (See also Sec. 1051.20.)