BUCKYVERSE

954.00 Mite as the Couplers Asymmetrical Octant Zone Filler

(see drawings section)

954.01 The Coupler is the asymmetric octahedron to be elucidated in Secs. 954.20 through 954.70. The Coupler has one of the most profound integral functionings in metaphysical Universe, and probably so in physical Universe, because its integral complexities consist entirely of integral rearrangeability within the same space of the same plus and/or minus Mites. We will now inspect the characteristics and properties of those Mites as they function in the Coupler. Three disparately conformed, nonequitriangular, polarized half-octahedra, each consisting of the same four equivolumetric octant zones occur around the three half-octants’ common volumetric center. These eight octant zones are all occupied, in three possible different system arrangements, by identical asymmetrical tetrahedra, which are Mites, each consisting of the three AAB Modules.

954.02 Each of these \sfrac{1}{8} octant-zone-filling tetrahedral Mite’s respective surfaces consists of four triangles, CAA, DEE, EFG^{1} and EFG^{2}, two of which, CAA and DBB, are dissimilar isosceles triangles and two of which, EFG^{1} and EFG2, are right triangles. (See Illus. 953. 10.) Each of the dissimilar isosceles triangles have one mutual edge, AA and BB, which is the base respectively of both the isosceles triangles whose respective symmetrical apexes, C and D, are at different distances from that mutual baseline.

954.03 The smaller of the mutually based isosceles triangle’s apex is a right angle, D. If we consider the right-angle-apexed isosceles triangle DBB to be the horizontal base of a unique octant-zone-filling tetrahedron, we find the sixth edge of the tetrahedron rising perpendicularly from the right-angle apex, D, of the base to C (FF), which perpendicular produces two additional right triangles, FGE^{1} and FGE^{2}, vertically adjoining and thus surrounding the isosceles base triangle’s right-angled apex, D. This perpendicular D (FF) connects at its top with the apex C of the larger isosceles triangle whose baseline, AA, is symmetrically opposite that C apex and congruent with the baseline, BB, of the right-angle-apexed isosceles base triangle, BBD, of our unique octant-filling tetrahedral Mite, AACD.

954.04 The two vertical right triangles running between the equilateral edges of the large and small isosceles triangles are identical right triangles, EFG1 and EFG2, whose largest (top) angles are each 54and whose smaller angles are 35each.

90

54

35

180

954.05 As a tetrahedron, the Mite has four triangular faces: BBD, AAC, EFG1, and EFG2. Two of the faces are dissimilar isosceles triangles, BBD and/L4C; ergo, they have only two sets of two different face angles eachB, D, A, and C one of which, D, is a right angle.

954.06 The other two tetrahedral faces of the Mites are similar right triangles, EFG, which introduce only two more unique angles, E and F, to the Mite’s surface inventory of unique angles.

954.07 The inventory of the Mite’s twelve corner angles reveals only five different angles. There are two As and two Fs, all of which are 54 each, while there are three right angles consisting of oneZ> and two Gs. There are two Bs of 45each, two Es of 35each, and one C of 70. (See drawings section.)

954.08 Any of these eight interior octant, double-isosceles, three-right-angled-tetrahedral domainsMites(which are so arrayed around the center of volume of the asymmetrical octahedron) can be either a positively or a negatively composited allspace-filling tetrahedron.

954.09 We find the Mite tetrahedron, AACD, to be the smallest, simplest, geometrically possible (volume, field, or charge), allspace-filling module of the isotropic vector matrix of Universe. Because it is a tetrahedron, it also qualifies as a structural system. Its volume is exactly Vsth that of its regular tetrahedral counterpart in their common magnitude isotropic vector matrix; within this matrix, it is also only \sfrac{1}{24}th the volume of its corresponding allspace-filling cube, \sfrac{1}{48}th the volume of its corresponding allspace-filling rhombic dodecahedron, and \sfrac{1}{6144}th the volume of its one other known unique, omnidirectional, symmetrically aggregatable, nonpolarized-assemblage, unit-magnitude, isotropic-vector-matrix counterpart, the allspace-filling tetrakaidecahedron.

954.10 Allspace-Filling Hierarchy as Rationally Quantifiable in Whole Volume Units of A or B Quanta Modules

                   *Quanta*

Synergetics’ Module Type Symmetrical or
Name Volume Polyhedron Asymmetrical
Mite Tetrahedron Asymmetrical
Syte (3 types) Tetrahedron Asymmetrical
Kites
Lites
Bites
Coupler Octahedron Asymmetrical
Cube Cube Simple Symmetrical
Rhombic Rhombic
Dodecahedron Dodecahedron Complex Symmetrical
Tetrakaidecahedron ,432 Tetrakaidecahedron Complex Symmetrical

954.20 Coupler: The basic complementarity of our octahedron and tetrahedron, which always share the disparate numbers 1 and 4 in our topological analysis (despite its being double or 4 in relation to tetra = 1), is explained by the uniquely asymmetrical octahedron, the Coupler, that is always constituted by the many different admixtures of AAB Quanta Modules; the Mites, the Sytes, the cube (72 As and Bs), and the rhombic dodecahedron (144 As and Bs).

954.21 There are always 24 As or Bsin our uniquely asymmetrical octahedron (the same as one tetra), which we will name the Coupler because it occurs between the respective volumetric centers of any two of the adjacently matching diamond faces of all the symmetrical, allspace-filling rhombic dodecahedra (or 144 As and Bs). The rhombic dodecahedron is the most-faceted, identical-faceted (diamond) polyhedron and accounts, congruently and symmetrically, for all the unique domains of all the isotropic-vector-matrix vertexes. (Each of the isotropic-vector-matrix vertexes is surrounded symmetrically either by the spheres or the intervening spaces-between-spheres of the closest-packed sphere aggregates.) Each rhombic dodecahedron’s diamond face is at the long-axis center of each Coupler (vol. = 1) asymmetric octahedron. Each of the 12 rhombic dodecahedra is completely and symmetrically omnisurrounded byand diamond-face-bonded with other such rhombic dodecahedra, each representing one closest-packed sphere and that sphere’s unique, cosmic, intersphere-space domain lying exactly between the center of the nuclear rhombic dodecahedron and the centers of their 12 surrounding rhombic dodecahedra the Couplers of those closest-packed-sphere domains having obviously unique cosmic functioning.

954.22 A variety of energy effects of the A and B Quanta Module associabilities are contained uniquely and are properties of the Couplers, one of whose unique characteristics is that the Coupler’s topological volume is the exact prime number one of our synergetics’ tetrahedron (24 As) accounting system. It is the asymmetry of the Bs(of identical volume to the As) that provides the variety of other than plusness and minusness of the all-A-constellated tetrahedra. Now we see the octahedra that are allspace filling and of the same volume as the As in complementation. We see proton and neutron complementation and non-mirror-imaging interchangeability and intertransformability with 24 subparticle differentiabilities and 2, 3, 4, 6, combinationsenough to account for all the isotopal variations and all the nuclear substructurings in omnirational quantation.

954.30 Nuclear Asymmetric Octahedra: There are eight additional asymmetric octahedra Couplers surrounding each face of each Coupler. It is probable that these eight asymmetric nuclear octahedra and the large variety of each of their respective constituent plus and minus Mite mix may account for all the varieties of intercomplex complexity required for the permutations of the 92 regenerative chemical elements. These eight variables alone provide for a fantastic number of rearrangements and reorientations of the A and B Quanta Modules within exactly the same geometric domain volume.

954.31 It is possible that there are no other fundamental complex varieties than those accounted for by the eight nuclear Coupler-surrounding asymmetrical octahedra. There is a mathematical limit of variationwith our friend octave coming in as before. The Coupler may well be what we have been looking for when we have been talking about “number one.” It is quite possibly one nucleon, which can be either neutron or proton, depending on how you rearrange the modules in the same space.

954.32 There are enough coincidences of data to suggest that the bombardment-produced energy entities may be identified with the three energy quanta modules two A Quanta Modules and one B Quanta Moduleallspace-filler complexities of associability, all occurring entirely within one uniquely proportioned, polarized, asymmetrical, nonequilateral, eighttriangle-faceted polyhedronthe Coupler within whose interior only they may be allspace-fillingly rearranged in a large variety of ways without altering the external conformation of the asymmetrical, octahedral container.

954.40 Functions of the Coupler: In their cosmic roles as the basic allspace-filling complementarity pair, our regular tetrahedron and regular octahedron are also always identified respectively by the disparate numbers 1 and 4 in the column of relative volumes on our comprehensive chart of the topological hierarchies. (See Chart 223.64.) The volume value 4being 22 extemdash also identifies the prime number 2 as always being topologically unique to the symmetrical octahedron while, on the same topological hierarchy chart, the uniquely asymmetrical allspace-filling octahedron, the Coupler, has a volume of 1, which volume-1-identity is otherwise, topologically, Uniquely identified only with the non-allspace-filling regular symmetrical tetrahedron.

954.41 The uniquely asymmetrical octahedron has three XYZ axes and a center of volume, K. Its X and Y axes are equal in length, while theZ axis is shorter than the other two. The uniquely asymmetrical octahedron is always polarly symmetrical around its short Z axis, whose spin equatorial plane is a square whose diagonals are the equilengthed X and Y axes. The equatorially spun planes of both theX and Y axes are similar diamonds, the short diagonal of each of these diamonds being the Z axis of the uniquely asymmetrical octahedron, while the long diagonal of the two similar diamonds are theX and Y axes, respectively, of the uniquely asymmetrical octahedron.

954.42 The uniquely asymmetrical octahedron could also be named the polarly symmetrical octahedron. There is much that is unique about it. To begin with the “heart,” or center of volume of the asymmetrical octahedron (knowable also as the polarly symmetrical octahedron, of geometrical volume 1), is identified by the capital letter K because K is always the kissing or tangency point between each and every sphere in all closest-packed unit radius sphere aggregates; and it is only through those 12 kissing (tangency) points symmetrically embracing every closest-packed sphere that each and all of the 25 unique great circles of fundamental crystallographic symmetry must passthose 25 great circles being generated as the 3, 4, 6, 12 = 25 great circle equators of spin of the only-four-possible axes of symmetry of the vector equilibrium. Therefore it is only through those volumetric heart K points of the uniquely asymmetrical octahedra that energy can travel electromagnetically, wavelinearly, from here to there throughout Universe over the shortest convex paths which they always follow.

954.43 The uniquely asymmetrical octahedron is always uniformly composed of exactly eight asymmetrical, allspace-filling, double-isosceles tetrahedra, the Mites, which in turn consist of AAB three-quanta modules each. Though outwardly conformed identically with one another, the Mites are always either positively or negatively biased internally in respect to their energy valving (amplifying, choking, cutting off, and holding) proclivities, which are only “potential” when separately considered, but operationally effective as interassociated within the allspace-filling, uniquely asymmetrical octahedron, and even then muted (i.e., with action suspended as in a holding pattern) until complexes of such allspace-filling and regeneratively circuited energy transactions are initiated.

954.44 The cosmically minimal, allspace-filling Mites’ inherent bias results from their having always one A + and one Atriple-bonded (i.e., face-bonded) to constitute a symmetrical isosceles (two-module) but non-allspacefilling tetrahedron to either one of the two external faces, of which either one B + or one B can be added to provide the allspace-filling, semisymmetrical double-isosceles, triple right-angled, three-moduled Mite, with its positive and negative bias sublimatingly obscured by the fact that either the positive or the negative quantum biasing add together to produce the same overall geometrical space-filling tetrahedral form, despite its quanta-biased composition. This obscurity accounts for its heretofore unbeknownstness to science and with that unbeknownstness its significance as the conceptual link between the heretofore remote humanists and the scientists’ cerebrating, while with its discovery comes lucidly conceptual comprehension of the arithmetical and geometrical formings of the whole inventory of the isotopes of all the atoms as explained by the allspace-filling variety of internal and external associabilities and reorientings permitted within and without the respective local octantfilling of the, also in-tum, omni-space-filling, uniquely asymmetrical octahedron, the Coupler.

954.45 As learned in Sections 953 and 954, one plus-biased Mite and one minus-biased Mite can be face-bonded with one another in three different allspace-filling ways, yet always producing one energy-proclivity-balanced, six-quanta-moduled, double-isosceles, allspace-filling, asymmetrical tetrahedron: the Syte. The asymmetric octahedron can also be composed of four such balanced-bias Sytes (4 As+ , 2 and 2 Bs1 + , 1). Since there are eight always one-way-or-the-other-biased Mites in each uniquely asymmetrical octahedron, the latter could consist of eight positively biased or eight negatively biased Mites, or any omnigeometrically permitted mixed combination of those 16 (2^{4}) cases.

954.46 There are always 24 modules (16 As and 8 Bsof which eighths are always positive and the eight other Xs are always negative, while the eight Bs consist of any of the eight possible combinations of positives and negatives) * in our uniquely asymmetrical octahedron. It is important to note that this 24 is the same 24-module count as that of the 24-/1-moduled regular tetrahedron. We have named the uniquely asymmetrical octahedron the Coupler.

954.47 We give it the name the Coupler because it always occurs between the adjacently matching diamond faces of all the symmetrical allspacefilling rhombic dodecahedra, the “spherics” (of 96 As and 48 Bs). The rhombic dodecahedron has the maximum number (12) of identical (diamond) faces of all the allspace-filling, unit edge length, symmetrical polyhedra. That is, it most nearly approaches sphericity, i.e., the shortest-radiused, symmetrical, structural, polyhedral system. And each rhombic dodecahedron exactly embraces within its own sphere each of all the closest-packed unit radius spheres of Universe, and each rhombic dodecahedron’s volumetric center is congruent with the volumetric center of its enclosed sphere, while the rhombic dodecahedron also embracingly accounts, both congruently and symmetrically, for all the isotropic-vector-matrix vertexes in closest-packed and all their “between spaces.” The rhombic dodecahedra are the unique cosmic domains of their respectively embraced unit radius closest-packed spheres. The center of area, K, of each of the 12 external diamond faces of each rhombic dodecahedron is always congruent with the internal center of volume (tangent sphere’s kissing points), K, of all the allspace-filling uniquely asymmetrical octahedra.

954.48 Thus the uniquely asymmetrical octahedra serve most economically to join, or couple, the centers of volume of each of the 12 unit radius spheres tangentially closest packed around every closest packed sphere in Universe, with the center of volume of that omnisurrounded, ergo nuclear, sphere. However the asymmetrical, octahedral coupler has three axes (Y, Y, M), and only its X axis is involved in the most economical intercoupling of the energy potentials centered within all the closest-packed unit radius spheres. The Y and M axes also couple two alternative sets of isotropic-vector-matrix centers. The M axis coupling the centers of volume of the concave vector equilibria shaped between closest-packed sphere spaces, and the Y axis interconnecting all the concave octahedral between spaces of unit-radius closest-packed sphere aggregates, both of which concave between-sphere spaces become spheres as all the spheresas convex vector equilibria or convex octahedratransform uniformly, sumtotally, and coincidentally into concave-between-unit-radius-sphere spaces. The alternate energy transmitting orientations of the locally contained A and B Quanta Modules contained within the 12 couplers of each nuclear set accommodate all the atomic isotope formulations and all their concomitant side effects.

 8 all plus   0 minus

 plus         minus
 plus         minus
 plus         minus
 plus         minus
 plus         minus
 plus         minus
 plus         minus
 plus         minus

These combinations accommodate the same bow-tie wave

patterns of the Indigs (see Sec. 1223).

This eight-digited manifold is congruent with the Indig bow-tie waveanother instance of the congruence of number and geometry in synergetics. Because of the prime quanta functioning of the allspace-filling Mites, we observe an elegant confirmation of the omniembracing and omnipermeative pattern integrities of synergetics.

954.49 We also call it the Coupler because its volume = 1 regular tetrahedron = 24 modules. The Couplers uniquely bind together each rhombic dodecahedron’s center of volume with the centers of volume of all its 12 omniadjacent, omniembracing, rhombic dodecahedral “spherics.”

954.50 But it must be remembered that the centers of volume of the rhombic dodecahedral spherics are also the centers of each of all the closest-packed spheres of unit radius, and their volumetric centers are also omnicongruent with all the vertexes of all isotropic vector matrixes. The Couplers literally couple “everything,” while alternatively permitting all the varieties of realizable events experienced by humans as the sensation of “free will.”

954.51 We see that the full variety of energy effects made by the variety of uniquely permitted A-and-B-Module rearrangeabilities and reassociabilities within the unique volumetric domain of the Coupler manifest a startling uniqueness in the properties of the Coupler. One of the Coupler’s other unique characteristics is that its volume is also the exact prime number 1, which volumetric oneness characterizes only one other polyhedron in the isotropic-vector-matrix hierarchy, and that one other prime-number-one-volumed polyhedron of our quantum system is the symmetric, initial-and-minimal-structural system of Universe: the 24-module regular tetrahedron. Here we may be identifying the cosmic bridge between the equilibrious prime number one of metaphysics and the disequilibrious prime number one of realizable physical reality.

954.52 It is also evidenced that the half-population ratio asymmetry of the B Modules (of identical volume to the A Modules) in respect to the population of the A Modules, provides the intramural variety of rearrangements other than the 1/i plus-and-minusnessof the all-A-Module-constellated regular tetrahedron.

954.53 The Coupler octahedron is allspace-filling and of the same 24- module volume as the regular tetrahedron, which is not allspace-filling. We go on to identify them with the proton’s and neutron’s non-mirror-imaged complementation and intertransformability, because one consists of 24 blue A Modules while the other consists of sixteen blue As and eight redBs, which renders them not only dissimilar in fundamental geometric conformation, but behaviorally different in that the As are energy-inhibiting and theBs are either energy-inhibiting or energy-dissipating in respect to their intramural rearrangeabilities, which latter can accommodate the many isotopal differentiations while staying strictly within the same quanta magnitude units.

954.54 When we consider that each of the eight couplers which surround each nuclear coupler may consist of any of 36 different AAB intramural orientations, we comprehend that the number of potentially unique nucleus and nuclear-shell interpatternings is adequate to account for all chemical element isotopal variations, as well as accommodation in situ for all the nuclear substructurings, while doing so by omnirational quantation and without any external manifestation of the internal energy kinetics. All that can be observed is a superficially static, omniequivectorial and omnidirectional geometric matrix.

954.55 Again reviewing for recall momentum, we note that the unique asymmetrical Coupler octahedron nests elegantly into the diamond-faceted valley on each of the 12 sides of the rhombic dodecahedron (called spheric because each rhombic dodecahedron constitutes the unique allspace-filling domain of each and every unit radius sphere of all closest-packed, unit-radius sphere aggregates of Universe, the sphere centers of which, as well as the congruent rhombic dodecahedra centers of which, are also congruent with all the vertexes of all isotropic vector matrixes of Universe).

954.56 Neatly seated in the diamond-rimmed valley of the rhombic dodecahedron, the unique asymmetrical octahedron’s Z axis is congruent with the short diagonal, and its Y axis is congruent with the long diagonal of the diamond-rimmed valley in the rhombic dodecahedron’s face into which it is seated. This leaves the X axis of the uniquely asymmetrical octahedron running perpendicular to the diamond face of the diamond-rimmed valley in which it so neatly sits; and its X axis runs perpendicularly through the K point, to join together most economically and directly the adjacent hearts (volumetric centers) of all adjacently closest-packed, unit radius spheres of Universe. That is, the X axes connect each nuclear sphere heart with the hearts of the 12 spheres closest-packed around it, while the Y axis, running perpendicularly to theX axis, most economically joins the hearts (volumetric centers) of the only circumferentially adjacent spheres surrounding the nuclear sphere at the heart of the rhombic dodecahedron, but not interconnecting with those nuclear spheres’ hearts. Thus the Y axes interlink an omnisymmetrical network of tangential, unit-radius spheres in such a manner that each sphere’s heart is interconnected with the hearts of only six symmetrically interarrayed tangentially adjacent spheres. This alternate interlinkage package of each-with-six, instead of six-with-twelve, other adjacent spheres, leaves every other space in a closest-packed, isotropic-vector-matrixed Universe centrally unconnected from its heart with adjacent hearts, a condition which, discussed elsewhere, operates in Universe in such a way as to permit two of the very important phenomena of Universe to occur: (1) electromagnetic wave propagations, and (2) the ability of objects to move through or penetrate inherently noncompressible fluid mediums. This phenomenon also operates in such a manner that, in respect to the vertexes of isotropic vector matrixes, only every other one becomes the center of a sphere, and every other vertex becomes the center of a nonsphere of the space interspersing the spheres in closest packing, whereby those spaces resolve themselves into two types concave vector equilibria and concave octahedra. And, whenever a force is applied to such a matrix every sphere becomes a space and every space becomes a sphere, which swift intertransforming repeats itself as the force encounters another sphere, whereby the sphere vanishes and the resulting space is penetrated.

954.57 We now understand why the K points are the kinetic switch-off- and-on points of Universe.

954.58 When we discover the many rearrangements within the uniquely asymmetric Coupler octahedra of volume one permitted by the unique self-interorientability of the A and B Modules without any manifest of external conformation alteration, we find that under some arrangements they are abetting the X axis interconnectings between nuclear spheres and their 12 closest-packed, adjacently-surrounding spheres, or the Y axis interconnectings between only every other sphere of closest-packed systems.

954.59 We also find that the A and B Module rearrangeabilities can vary the intensity of interconnecting in four magnitudes of intensity or of zero intensity, and can also interconnect the three X and Y and M systems simultaneously in either balanced or unbalanced manners. The unique asymmetric octahedra are in fact so unique as to constitute the actual visual spin variable mechanisms of Dirac’s quantum mechanics, which have heretofore been considered utterly abstract and nonvisualizable.

954.70 The Coupler: Illustrations: The following paragraphs illustrate, inventory, sort out, and enumerate the systematic complex parameters of interior and exterior relationships of the 12 Couplers that surround every unit-radius sphere and every vertexial point fix in omni-closest-packed Universe, i.e., every vertexial point in isotropic vector matrixes.

954.71 Since the Coupler is an asymmetric octahedron, its eight positive or negative Mite (AAB module), filled-octant domains introduce both a positive and a negative set of fundamental relationships in unique system sets of eight as always predicted by the number-of-system-relationships formula: N2 N , which with the system number eight has 28 relationships.

954.72 There being three axestheX, Y, andAf sets of obverse-reverse, polar-viewed systems of eighteach eight has 28 relationships, which makes a total of three times 28 = 84 integral axially regenerated, and 8 face-to-face regenerated K-\.o-K couplings, for a total of 92 relationships per Coupler. However, as the inspection and enumeration shows, each of the three sets of 28, and one set of 8 unique, hold-or-transmit potentials subgroup themselves into geometrical conditions in which some provide energy intertransmitting facilities at four different capacity (quantum) magnitudes: 0, 1, 2, 4 (note: 4 = 22), and in three axial directions. The X X axis transmits between or interconnects every spheric center with one of its 12 tangentially adjacent closest-packed spheres.

954.73 The YY axis transmits between or interconnectsany two adjacent of the six octahedrally and symmetrically interarrayed, concave vector equilibria conformed, ‘tween-space, volumetric centers symmetrically surrounding every unit-radius, closest-packed sphere.

954.74 The MM axis interlinks, but does not transmit between, any two of the cubically and symmetrically interarrayed eight concave octahedra conformed sets of ‘tween-space, concave, empty, volumetric centers symmetrically surrounding every unit-radius, closest-packed sphere in every isotropic vector matrix of Universe.

954.75 The eight X-to-X, face-to-face, couplings are energizingly interconnected by one Mite each, for a total of eight additional interconnections of the Coupler.

954.76 These interconnections are significant because of the fact that the six concave vector equilibria, YY axis-connected ’tween-spaces, together with the eight concave octahedral ‘tween-spaces interconnected by theMM axis, are precisely the set of spaces that transform into spheres (or convex vector equilibria) as every sphere in closest-packed, unit-radius, sphere aggregates transforms concurrently into either concave vector equilibria ‘tweenspaces or concave octahedra ‘tween-sphere spaces.

954.77 This omni-intertransformation of spheres into spaces and spaces into spheres occurs when any single force impinges upon any closest-packed liquid, gaseous, or plasmically closest-packed sphere aggregations.

954.78 The further subdivision of the A Modules into two subtetrahedra and the subdividing of the B Modules into three subtetrahedra provide every positive Mite and every negative Mite with seven plus-or-minus subtetrahedra of five different varieties. Ergo 92 \times 7 = 644 possible combinations, suggesting their identification with the chemical element isotopes.