466.00 Energy-valve Functioning of Outer Shell of Nuclear Domains
Fig. 466.00 Fig. 466.01 |
466.01 An earlier version of Fig. 466.01 was first published by the author in 1944: it illustrates the energy-valving aspects of the closest-packed spheres interfunctionings as they occur within the three-frequency, 92-ball outer layer of the vector equilibrium as it "jitterbuggingly" skew-transforms into the icosahedral state, then returns to the vector equilibrium state, passes through, and again transforms to the alternately skewed icosahedral state^{__} repeat and repeat. |
466.05 Fig. C is a plan view of the closest-sphere-packing manifestation of any one of the vector equilibrium's four pairs of nuclear tetrahedra as they commence to torque in the jitterbug process. An isometric sketch of this net 39-ball aggregation is given at Fig. 466.31 Note that this torqued pair of nuclear tetrahedra employs three of the vector equilibrium's six axes. The two unengaged axes of the equator are starved and inoperative. |
466.10 High-frequency Sphericity Approaches Flatness |
466.11 Where we have six balls in a planar array closest packed around one nucleus, we produce six top and six bottom concave tetrahedral valleys surrounding the nucleus ball. We will call the top set of valleys the northern set and the bottom set the southern set. Despite there being six northern valleys we find that we can nest only three close- packed (triangulated) balls in the valleys. This is because we find that the balls nesting on top of the valleys occupy twice as much planar area as that afforded by the six tetrahedral valleys. Three balls can rest together on the top in omni-close-packed tangency with one another and with the seven balls below them; and three balls can similarly rest omniintertangentially in the bottom valleys as their top and bottom points of tangency bridge exactly across the unoccupied valleys, allowing room for no other spheres. This produces the symmetrical nuclear vector equilibrium of 12 closest-packed spheres around one. (See Fig. 466.13A.) |
466.12 The three balls on the top can be lifted as a triangular group and rotated 60 degrees in a plane parallel to the seven balls of the hexagonal equatorial set below them; this triangular group can be then set into the three previously vacant and bridged-over valleys. As this occurs, we have the same 12 spheres closest packed around one with an overall arrangement with the two triangular sets of three on the top, three on the bottom, and six around the equator. The top and the bottom triangular sets act as poles of the system, which^{__} as with all systems^{__} has inherent free spinnability. In both of the two alternate valley occupations the northern polar triangle is surrounded alternately by three squares and three triangles, reading alternately^{__} triangle, square, triangle, square, triangle, square. (See Fig. 466.13B.) |
Fig. 466.13 |
466.13 In one polar triangular valley occupation the squares of the northern hemisphere will be adjacent to the triangles of the southern hemisphere. This is the vector- equilibrium condition. In the alternate valley nesting position at the equator the equatorial edges of the squares of the northern hemisphere will abut the squares of the southern hemisphere, and the triangles of the northern hemisphere will abut those of the southern, producing a polarized symmetry condition. In the vector-equilibrium condition we have always and everywhere the triangle-and-square abutments, which produces a four- dimensional symmetry system. (See Sec. 442 and Fig. 466.13C.) |
466.14 There is then a duality of conditions of the same 12 nucleus-surrounding first omni-inter-closest-packed layer: we have both a polarized symmetry phase and an equilibrious symmetry phase. Under these alternate conditions we have one of those opportunities of physical Universe to develop a pulsative alternation of interpatterning realizations, whereby the alternations in its equilibrium phase do not activate energy, while its polarized phase does activate energetic proclivities. The equilibrious phase has no associative proclivities, while the polarized phase has associative proclivities. In the polarized phase we have repulsion at one end and attraction at the other: potential switchings on and off of energetic physical Universe. (See Figure 466.13D.) |
466.17 In very-high-frequency nuclear systems the approach to flatness from the four planes to five planes tends to induce a 360-degreeness of the sums of the angles around the critical 12 vertexes^{__} in contrast to the 300degree condition existing in both the unfrequenced vector equilibrium and icosahedron. That is what Fig. 466.01 is all about. |
466.18 In Figs. 466.01 and 466.41 there is introduced an additional 60 degree equilateral triangle, in surroundment of every directly-nuclear-emanating vertex K. The 12 vector-equilibrium K vertexes are always in direct linear relationship with the system nucleus (see Sec. 414). The additional degrees of angle produced by the high-frequency local flattening around K vertexes introduces a disturbance-full exterior shell condition that occasions energetic consequences of a centrifugal character. |
466.20 Centrifugal Forces |
466.30 Nuclear Tetrahedra Pairs: Closest-sphere-packing Functions |
Fig. 466.31 |
466.31 In Fig. 466.01-C is a plan view of the closest-sphere-packing manifestation of any one of the vector equilibrium's four pairs of nuclear tetrahedra as they commence to torque in the jitterbug process. An isometric sketch of this net 39-ball aggregation is given in Fig. 466.31. Note that this torqued, north-south-pole, axial pair of tetrahedra employs three of the vector equilibrium's six axes. The other three unengaged axes lying in the equator are starved and inoperative^{__} angularly acceleratable independently of the north-south axial motion. |
466.32 In Fig. 466.01-C we see the internal picture from the nucleus to the vertexes displaying the hexagonal pattern emerging at F^{3}. |
466.33 There can be only one pair of tetrahedra operative at any one time. The other three pairs of tetrahedra function as standby auxiliaries, as in the triangular-cammed, in- out-and-around, rubber cam model described in Secs. 465.01 and 465.10. |
466.35 In the outer layer of 92 balls^{__} two of which are extracted for the axis of spin^{__}there are eight triangular faces. There are four balls in the center of each of the six square faces. |
6 × 4 = 24. 92 - 24 = 68. 68/8 = 8 l/2. |
We need 20 balls for a pair of complete polar triangles. |
68 - 20 = 48. 48/8 = 6; a pair of 6s = 12. Thus there are only 12 available where 20 are required for a polar pair. In any one hemisphere the vertex balls A, B, C used by a polar triangle make it impossible to form any additional polar units. |
466.40 Universal Section of Compound Molecular Matrix |
466.42 This compound molecular matrix grid provides a model for molecular compounding because it accommodates more than one tetrahedron. |
466.43 This matrix is not isotropic. It is anisotropic. It accommodates the domain of a nucleus. |
Next Section: 470.00 |