905.50 Repeatability and Split Personality of Tetrahedron

905.51 Having completed the expansive-contractive, could-be, quantum jumps, we will now consider the rotatability of the tetrahedron’s six-edge axes generation of both the two spherical tetrahedra and the spherical cube whose “split personality’s”, four-triangle-defining edges also perpendicularly bisect all of both of the spherical tetrahedron’s four equiangled, equiedged triangles in a three-way grid, which converts each of the four equiangled triangles into six right-angle spherical trianglesfor a total of 24, which are split again by the spherical octahedron’s three great circles to produce 48 spherical triangles, which constitute the 48 equilibrious LCD Basic Triangles of omni-equilibrious eventless eternity (see Sec. 453).

905.52 The spherical octahedron’s eight faces become skew-subdivided by the icosahedron’s 15 great circles’ self-splitting of its 20 equiangular faces into six-each, right spherical triangles, for an LCD spherical triangle total of 120, of which 15 such right triangles occupy each of the spherical octahedron’s eight equiangular facesfor a total of 120which are the same 120 as the icosahedron’s 15 great circles.

905.53 The disequilibrious 120 LCD triangle = the equilibrious 48 LCD triangle \times 2\sfrac{1}{2}. This 2\sfrac{1}{2}+ 2\sfrac{1}{2}= 5; which represents the icosahedron’s basic fiveness as split-generated into $2\sfrac
{1}by their perpendicular, mid-edge-bisecting 15 great circles. Recalling the six edge vectors of the tetrahedron as one quantum, we note that6 4- 6 + %is1 + 1 + \sfrac= 2\sfrac; and that 2\sfrac\times 6 = 15$ great circles. (This half-positive and half negative dichotomization of systems is discussed further at Sec. 1053.30ff.)

905.54 We find that the split personality of the icosahedron’s 15-great- circle splittings of its own 20 triangles into 120, discloses a basic asymmetry caused by the incompleteness of the 2, where it is to be seen in the superimposition of the spherical icosahedron upon the spherical vector equilibrium. In this arrangement the fundamental prime number fiveness of the icosahedron is always split two ways: 2 positive phase and 2 negative phase. This half-fiving induces an alternate combining of the half quantum on one side or the other: going to first three on one side and two on the other, and vice versa.

905.55 This half-one-side/half-on-the-other induces an oscillatory alternating 120-degree-arc, partial rotation of eight of the spherical tetrahedron’s 20 equiangled triangles within the spherical octahedron’s eight triangles: 8 \times 2\sfrac{1}{2}= 20. We also recall that the vector equilibrium has 24 internal radii (doubled together as 12 radii by the congruence of the four-great-circle’s hexagonal radii) and 24 separate internal vector chords. These 24 external vector chords represent four quanta of six vectors each. When the vector equilibrium jitterbuggingly contracts toward the octahedral edge-vector doubling stage, it passes through the unstable icosahedral stage, which is unstable because it requires six more edge-vectors to hold fixed the short diagonal of the six diamond-shaped openings between the eight triangles. These six equilength vectors necessary to stabilize the icosahedron constitute one additional quantum which, when provided, adds 1 to the 4 of the vector equilibrium to equal 5, the basic quantum number of the icosahedron.