1033.41 Asymmetrical Contraction of Vector Equilibrium: Quantum Loss
1033.41 The vector equilibrium contraction from tetravolume 20 to the tetravolume 4 of the octahedron may be accomplished symmetrically (as just described in Sec. 1033.30) by altogether collapsing the unstable six half- octahedra and by symmetrical contraction of the 12 radii. The angular collapsing of the 12 radii is required by virtue of the collapsings of the six half-octahedra, which altogether results in the eight regular tetrahedra being concurrently reduced in their internal radial dimension, while retaining their eight external equiangular triangles unaltered in their prime-vector-edge lengths; wherefore, the eight internal edges of the original tetrahedra are contractively reduced to eight asymmetric tetrahedra, each with one equiangular, triangular, external face and with three right-angle-apexed and prime-vector-base-edged internal isosceles-triangle faces, each of whose interior apexes occurs congruently at the center of volume of the symmetrical octahedron—ergo, each of which eight regular-to-asymmetric-transformed tetrahedra are now seen to be our familiar Eighth-Octahedra, each of which has a volume of
{2}= 4$), the resulting octahedron equals tetravolume-4.
1033.42 This transformation may also have been accomplished in an alternate manner. We recall how the jitterbug vector equilibrium demonstrated the four-dimensional freedom by means of which its axis never rotates while its equator is revolving (see Sec. 460.02). Despite this axis and equator differentiation the whole jitterbug is simultaneously and omnisymmetrically contracting in volume as its 12 vertexes all approach their common center at the same radial contraction rate, moving within the symmetrically contracting surface to pair into the six vertices of the octahedron—after having passed symmetrically through that as-yet-12-vectored icosahedral stage of symmetry. With that complex concept in mind we realize that the nonrotating axis was of necessity contracting in its overall length; ergo, the two-vertex-to-two-vertex- bonded “pair” of regular tetrahedra whose most-remotely-opposite, equiangular triangular faces’ respective centers of area represented the two poles of the nonrotated axis around which the six vertices at the equator angularly rotated—three rotating slantwise “northeastward” and three rotating “southeastward,” as the northeastward three spiraled finally northward to congruence with the three corner vertices of the nonrotating north pole triangle, while concurrently the three southeastward-slantwise rotating vertices originally situated at the VE jitterbug equator spiral into congruence with the three comer vertices of the nonrotating south pole triangle.
1033.43 As part of the comprehensively symmetrical contraction of the whole primitive VE system, we may consider the concurrent north-to-south polar-axis contraction (accomplished as the axis remained motionless with respect to the equatorial motions) to have caused the two original vertex-to-ver- tex regular polar tetrahedra to penetrate one another vertexially as their original two congruent center-of-VE-volume vertices each slid in opposite directions along their common polar-axis line, with those vertices moving toward the centers of area, respectively, of the other polar tetrahedron’s polar triangle, traveling thus until those two penetrating vertices came to rest at the center of area of the opposite tetrahedron’s polar triangle—the planar altitude of the octahedron being the same as the altitude of the regular tetrahedron. (See Figs. 1033.43 and 1033.47.)
1033.44 In this condition they represent the opposite pair of polar triangles of the regular octahedron around whose equator are arrayed the six other equiangular triangles of the regular octahedron’s eight equiangular triangles. (See Fig. 1033.43.) In this state the polarly combined and—mutually and equally—interpenetrated pair of tetrahedra occupy exactly one-half of the volume of the regular octahedron of tetravolume-4. Therefore the remaining space, with the octahedron equatorially surrounding their axial core, is also of tetravolume-2—i.e., one-half inside-out (space) and one-half inside-in (tetracore).
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Fig. 1033.43 Two Opposite-Paired Tetrahedra Interpenetrate in Jitterbug Contraction: As one axis remains motionless, two polar-paired, vertex-joined tetrahedra progressively interpenetrate one another to describe in mid-passage an octahedron, at C, and a cube-defining star polyhedron of symmetrical congruence at D. (Compare Fig. 987.242A.)
1033.45 At this octahedron-forming state two of the eight vertices of the two polar-axis tetrahedra are situated inside one another, leaving only six of their vertices outside, and these six—always being symmetrically equidistant from one another as well as equidistant from the system center—are now the six vertices of the regular octahedron.
1033.46 In the octahedron-forming state the three polar-base, comer-to- apex-connecting-edges of each of the contracting polar-axis tetrahedra now penetrate the other tetrahedron’s three nonpolar triangle faces at their exact centers of area.
1033.47 With this same omnisymmetrical contraction continuing—with all the external vertices remaining at equal radius from the system’s volumetric center—and the external vertices also equidistant chordally from one another, they find their two polar tetrahedra’s mutually interpenetrating apex points breaking through the other polar triangle (at their octahedral-forming positions) at the respective centers of area of their opposite equiangular polar triangles. Their two regular-tetrahedra-shaped apex points penetrate their former polar-opposite triangles until the six mid-edges of both tetrahedra become congruent, at which symmetrical state all eight vertices of the two tetrahedra are equidistant from one another as well as from their common system center. (See Fig. 987.242A.)
1033.48 The 12 geodesic chords omniinterconnecting these eight symmetrically omniarrayed vertices now define the regular cube, one-half of whose total volume of exactly 3-tetravolumes is symmetrically cored by the eight-pointed star core form produced by the two mutually interpenetrated tetrahedra. This symmetrical bore star constitutes an inside-in tetravolume of 1V2, with the surrounding equatorial remainder of the cube-defined, insideout space being also exactly tetravolume IV2. (See Fig. 987.242A.)
1033.490 In this state each of the symmetrically interpenetrated tetrahedra’s eight external vertices begins to approach one another as each opposite pair of each of the tetrahedra’s six edges—which in the cube stage had been arrayed at their mutual mid-edges at 90 degrees to one another—now rotates in respect to those mid-edges—which six mutual tetrahedra’s mid-edge points all occur at the six centers of the six square faces of the cube.
1033.491 The rotation around these six points continues until the six edge-lines of each of the two tetrahedra become congruent and the two tetrahedra’s four vertices each become congruent—and the VE’s original tetravolume 20 has been contracted to exactly tetravolume 1.
1033.492 Only during the symmetrical contraction of the tetravolume-3 cube to the tetravolume-1 tetrahedron did the original axial contraction cease, as the two opposing axis tetrahedra (one inside-out and one outside-out) rotate simultaneously and symmetrically on three axes (as permitted only by four- dimensionality freedoms) to become unitarily congruent as tetravolume-1—altogether constituting a cosmic allspace-filling contraction from 24 to 1, which is three octave quanta sets and 6x4 quanta leaps; i.e., six leaps of the six degrees of freedom (six inside-out and six outside-out), while providing the prime numbers 1,2,3,5 and multiples thereof, to become available for the en- tropic-syntropic, export-import transactions of seemingly annihilated—yet elsewhere reappearing—energy quanta conservation of the eternally regenera- live Universe, whose comprehensively closed circuitry of gravitational embracement was never violated throughout the 24 compaction.