1033.70 Geometrical 20-ness and 24-ness of Vector Equilibrium

1033.701 The maximum somethingness of the VE’s 20-ness does not fill allspace, but the 24-tetravolume Duo-tet Cube (short name for the doubletetrahedron cube) does fill allspace; while the tetravolume-4-ness of the exterior octahedron (with its always-potential one-quantum annihilability) accommodates and completes the finite energy-packing inventory of discontinuous episodic Physical Scenario Universe.

1033.702 The three interior octahedra are also annihilable, since they vanish as the VE’s 20-ness contracts symmetrically to the quadrivalent octahedron jitterbug stage of tetravolume 4: an additive 4-tetravolume octahedron has vanished as four of the VE’s eight tetrahedra (four inside-out, four outside-out) also vanish, thereby demonstrating a 16-quanta-annihilation accomplished without impairment of either the independent motion of the system’s axial twoness or its convergent-divergent, omniconcentric symmetry.

1033.703 The four of the 24-ness of the Duo-tet Cube (which is an/² cube: the double tetrahedron) accounts for the systemic four-dimensional planes of four-dimensional symmetry as well as for the ever-regenerative particle four-ness of the quark phenomena characterizing all high-energy-systembombardment fractionability.

1033.704 24 \times 4 = 96. But the number of the self-regenerative chemical elements is 92. What is missing between the VE 92 and the/² Duo-tet Cube’s 96 is the fourness of the octahedron’s function in the annihilation of energy: 92 + 4 = 24 x 4 = 96. The four is the disappearing octa set. The 24 is the second-power 24 unique indig turnabout increment. (See Fig. 1223.12.)

1033.71 We have three expendable interior octa and one expendable exterior octa. This fact accommodates and accounts both the internal and externa! somethingness-to-nothingness annihilations terminally occurring between the 1—>20—>1—>20 at the macroinvolution and microevolution initiating nothingness phases, between which the total outside-out 1—>20 quanta and the total inside-out 20—> 1 quanta intertransformabilities occur.

1033.72 The final jitterbug convergence to quadrivalent tetravolume-1 outside-out and tetravolume-1 inside-out is separated by the minimum-nothingness phases. This final conversion is accomplished only by torquing the system axis to contract it to the nothingness phase between the three-petal, triangular, inside-out and outside-out phases. (See Secs. 462.02, 464.01 and 464.02.)

1033.73 The Quantum Leap: Between the maximum nothingness and the minimum nothingness we witness altogether five stages of the 4-tet- ravolume octa vanishment in the convergent phase and five such 4-tet- ravolume octa growth leaps in the divergent phase. These five—together with the interior and exterior octa—constitute seven octa leaps of four quanta each. The/² of the inherent multiplicative two of all systems provides the eighth fourness: the quantum leap. (Compare Sec. 1013.60.)

1033.74 It requires 24-ness for the consideration of the total atomic behavior because the vector equilibrium is not allspace-fillingly complete in itself. It requires the exterior, inside-out, invisible-phase, eightway-fractionated, transformable octahedron superimposed on the VE’s eight equiangular, triangular faces to complete the allspace-filling, two-frequency Duo-tet Cube’s eight symmetrically arrayed and most-economically interconnected corners’ domain involvement of 24 tetravolumes.

1033.741 The VE’s involvement domain of 24 symmetrical, allspacefilling tetravolumes represents only one of the two alternate intertransformation domains of closest-packed, unit-radius spheres transforming into spaces and spaces intertransforming into spheres: ergo, it requires 48-tetravolumes to accommodate this phenomenon. To allow for each of these 48-tetravolume domains to accommodate their respective active and passive phases, it requires 96-tetravolumes. F² tetravoluming, which is as yet primitive, introduces an allspace-filling, symmetrical cube of 192-tetravolumes as an essential theater of omniatomic primitive interarrayings.

1033.75 The total primitively nucleated Duo-tet Cube’s double-tetra unique increment of allspace filling is that which uniquely embraces the whole family of local Universe’s nuclearly primitive intertransformabilities ranging through the 24—>1 and the 1—>24 cosmic hierarchy of rational and symmetrical “click-stop” holding patterns or minimum-effort self-stabilization states.

1033.76 The Duo-tet Cube (the maxicube) occurring between micronothingness and macronothingness shows how Universe intertransformably accommodates its entropic-syntropic energy-quanta exportings and importings within the two-frequency, allspace-filling minireality of special-case Universe. Thus the entropic-syntropic, special-case Physical Universe proves to be demonstrable within even the most allspace-crowding condition of the VE’s maximum-something 20-ness and its exterior octahedron’s even-more- than-maximum-something 4-tetravolume nothingness.

1033.77 This 24-ness is also a requisite of three number behavior requirements as disclosed in the min-max variabilities of octave harmonics in tetrahedral and VE cumulative closest-packing agglomerations at holistic shell levels as well as in all second-powering “surface” shell growths, as shown in three different columns in Fig. 1223.12.