936.00 Volumetric Variability with Topological Constancy 
936.10 Symmetrical and Asymmetrical Contraction 
936.11 An octahedron consists of 12 vector edges and two units of quantum and has a volume of four when the tetrahedron is taken as unity. (See Table 223.64.) Pulling two ends of a rope in opposite directions makes the rope's girth contract precessionally in a plane at 90 degrees to the axis of purposeful tensing. (Sec. 1054.61.) Or if we push together the opposite sides of a gelatinous mass or a pneumatic pillow, the gelatinous mass or the pneumatic pillow swells tensively outward in a plane at 90 degrees to the line of our purposeful compressing. This 90degree reaction^{__}or resultant^{__}is characteristic of precession. Precession is the effect of bodies in motion upon other bodies in motion. The gravitational pull of the Sun on the Earth makes the Earth go around the Sun in an orbit at degrees to the line of the EarthSun gravitational interattraction. The effect of the Earth on the Moon or of the nucleus of the atom upon its electron is to make these interattractively dependent bodies travel in orbits at 90 degrees to their mass interattraction force lines. 
Fig. 936.12 
936.12 The octahedron represents the most commonly occurring crystallographic conformation in nature. (See Figs. 931.10 and 1054.40.) It is the most typical association of energyasmatter; it is at the heart of such association. Any focused emphasis in the gravitational pull of the rest of the Universe upon the octahedron's symmetry precesses it into asymmetrical deformation in a plane at 90 degrees to the axis of exaggerated pulling. This forces one of the 12 edge vectors of the octahedron to rotate at 90 degrees. If we think of the octahedron's three XYZ axes and its six vertexes, oriented in such a manner that X is the north pole and X' is the south pole, the other four vertexes^{__}Y, Z, Y', Z'^{__}all occur in the plane of, and define, the octahedron's equator. The effect of gravitational pull upon the octahedron will make one of the four equatorial vectors disengage from its two adjacent equatorial vertexes, thereafter to rotate 90 degrees and then rejoin its two ends with the north pole and south pole vertexes. (See Fig. 936.12 and color plate 6.) 
936.14 The precessional effect has been to rearrange the energy vectors themselves in such a way that we have gone from the volumefour quanta of the symmetrical octahedron to the volumethree quanta of the asymmetric tetraarcarray segment of an electromagnetic wave pattern. Symmetric matter has been entropically transformed into asymmetrical and directionally focused radiation: one quantum of energy has seemingly disappeared. When the radiation impinges interferingly with any other energy event in Universe, precession recurs and the threequantum electromagnetic wave retransforms syntropically into the fourquantum octahedron of energyasmatter. And vice versa. Q.E.D. (See Fig. 936.14.) 
Fig. 936.16 
936.16 See the Iceland spar crystals for the octahedron's double vectoredge image. 
Fig. 936.19 
936.19 As we tense the octahedron, it strains until one vector (actually a double, or unityastwo, vector) yields its end bondings and precesses at 90 degrees to transform the system into three doublebonded (facebonded) tetrahedra in linear arc form. This tetra arc, embryonic, electromagnetic wave is in neutral phase. The seemingly annihilated^{__}but in fact only separatedoutquantum is now invisible because vectorless. It now becomes invisibly facebonded as one invisible tetrahedron. The separatedout quantum is face bonded to one of the furthermost outward triangular faces occurring at either end of the tetraarc array of three (consisting of one tetra at the middle with each of the two adjacent tetra facebonded to it); the fourth invisible tetrahedron is facebonded to one or the other of the two alternatively vacant, alternatively available furthermost end faces of the tetra arc group. With this fourth, invisible tetrahedral addition the overall triplebonded tetrahedral array becomes either rightwardly or leftwardly spiraled to produce a four tetrahedron tetrahelix, which is a potential, event embryo, electromagneticcircuitry gap closer. Transmission may thereafter be activated as a connected chain of the inherently fourmembered, individuallink continuity. This may explain the dilemma of the wave vs the particle. (See Sec. 973.30, Fig. 936.19, and color plates 6 and 7.) 
936.20 Conceptual Conservation and Annihilation 
937.00 Geometry and Number Share the Same Model 
937.10 Midway Between Limits 
937.11 The grand strategy of quantum mechanics may be described as progressive, numerically rational fractionating of the limit of total energy involved in eternally regenerative Universe. 
937.12 When seeking a model for energy quanta conservation and annihilation, we are not surprised to find it in the middle ranges of the geometrical hierarchy of prime structural systems^{__}tetrahedron, octahedron, and icosahedron (see Sec. 610.20). The tetrahedron and icosahedron are the two extreme and opposite limit cases of symmetrical structural systems: they are the minimummaximum cosmic limits of such prime structures of Universe. The octahedron ranks in the neutral area, midway between the extremes. 
937.14 The tetrahedron has three triangles around each vertex; the octahedron has four; and the icosahedron has five. The extremelimit cases of structural systems are vertexially locked by odd numbers of triangular gears, while the vertexes of the octahedron at the middle range have an even number of reciprocating triangular gears. This shows that the octahedron's three great circles are congruent pairs^{__}i.e., six circles that may seem to appear as only three, which quadrivalent doubling with itself is clearly shown in the jitterbug model, where the 24 vector edges double up at the octahedron phase to produce 12 doublecongruent vector edges and thus two congruent octahedra. (See Fig. 460.08D.) 
Fig. 937.20 
937.20 Doubleness of Octahedron 
937.21 The octahedron always exhibits the quality of doubleness. When the octahedron first appears in the symmetrical contraction of the vector equilibrium jitterbug system, it appears with all of its vectors doubled (see Fig. 460.08D 460.08D). It also takes two sets of three great circles each to fold the octahedron. You might think you could do it with one set of three great circles, but the foldability of the octahedron requires two sets of three great circles each. (See Secs. 835 and 836.) There are always six great circles doubled up in the octahedron to reappear only as three. (See Fig. 937.20.) 
937.22
And we also recall that the octahedron appears as
the prime number 2 in the
geometrical hierarchy, while its volume is 4 when the
tetrahedron is taken as volumetric
units (see Table
223.64).
1, 4, 3, 6, 18.51, and 20.

937.30 Octahedron as Sphere of Compression 
937.31
The slenderness ratio in gravitationally tensed functioning
has no minimum
overall limit of its structuralsystem length, as compared
to the diameter of the system's
midlength cross section; ergo,

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