987.050 Intercommensurable Functions of Jitterbug

987.051 The vector equilibrium of tetravolume-20 = prime 5 x prime 2^{2}, is rationally coordinate with the tetrahedron representing the prime number 1 and w ith the octahedron representing the prime number 2. But the 20-tetra-volume ($5
\times 2^) VEis inherently incommensurable with the icosahedron, which represents the prime number 5 compounded with V2 even though theVE$ and icosa are concentrically and omnisymmetrically intertransformable (see Secs. 461.02-06).

987.052 The mathematical span between the second power of 2, (2^{2}= 4) and the second root of 2, (V2)which is the s ame proportional relationship as that existing between V2 and 1is th e constant proportional accommodating median between tetra 1 and octa 2 and between the first two prime numbers: between the most primitive odd and even, betwee n the most primitive yes and no of the primitive binary systemergo, of all computer mathematics.

987.053 The 2 as constant proportional equity median is clearly evidenced as each of the VE’s six square unit-length-vector-edged faces jitter-buggingly transform into the two unit-vector-edged equilateral triangles. We recall that the diagonal of each square was the hypotenuse of a right-angle-apexed, unit-vector-edged isosceles triangle whose hypotenuse jitterbuggin gly contracted in length to the length of each of the unit-vector edges. We have the well-known formula for the second power of the hypotenuse equaling the sum of the second powers of the right triangle’s right-angle sides, and since the right- angle-apexed isosceles triangle’s sides were of unit-vector length = 1, the secon d powers of both equal 1. The sum of their second powers was 2, and the length of the square’s hypotenuse diagonal = VT. Ergo, the total linear alteration of the VE >icosa was the contraction of V2. This introduces one of nature’s most profound incommensurability equations, wherein image

987.054 Proportionately expressed this equation reads: VE : icosa = 2: V?= V2 : 1 Fractionally expressed the equation reads: VE _ 2_ V2 icosa V2 1 Thus we have a sublime equation of constant proportionality of otherwise inherently incommensurate value sets.

987.055 In the jitterbug, as the 20-tetravolume VE contracts symmetrically through the icosahedral phase with a tetravolume o f 18.51 229587, and then ever symmetrically contracts to the bivalent octahedral phase of tetra-volume-4, the six-membered axis of the concentric system does not rotate while the other 18 nonaxis “equatorial” members rotate around the axis. (Fig. 460.08.)

987.056 As the system contraction continues beyond the octahedron stage of tetravolume-4, the axis also torques and contracts as the octahedron either (1) contracts symmetrically and rotationally into the regular tetrahedron of tetravolume-1 (or counterrotates into the alternate regular tetrahedron of tetra volume-1), or (2) flattens by contraction of its axis to form zerovolume, edge-congruent pair of triangular patterns; thereafter the triangle’s three corners are foldable alternately into the quadrivalent positive or the quadrivalent negative regular tetrahedron of tetravolume-1.

987.057 Since all 24 internal radiation vectors had been removed before the jitterbugging, leaving only the 24 external gravitation vectors, the transformation is systematically comprehensive and embraces all the complex unities of the VE and icosa and their only-proportionally-equatable, separately rational, geometrical membership sets. Though the tetra and icosa are incommensurable with each other, the octahedron is transformatively com mensurable with either.

987.058 The inherent volumetric incommensurability of VE and icosa (and their respective four- and three-unique-symmetrical-g reat-ci rcle-system sets), compounded with the ability of the octahedron to intertransformably interconnect these two otherwise incommensurables, produces the energetic oscillations, resonances, and intertransformings of the eternally regenerative Universe. This eternal disquietude regeneration of Universe is also accommodated by the fact that the tetra and VE are a priori incommensurable with the icosa. Despite this the rhombic triacontahedron of tetravolume-5 (as a product of the icosa’s 15-great-circle cleavaging), while under the oscillatory pressuring, is volumetrically and rationally coordinate with the tetrahedron and the state we speak of as matterand when it is under the negative tensive pressure of the oscillatory Universe, it transforms from matter to radiation. (See scenario of T and E Modules at Sec. 986.)