951.00 AllspaceFilling Tetrahedra 
951.01 The tetrahedra that fill allspace by themselves are all asymmetrical. They are dynamic reality onlyforeachmoment. Reality is always asymmetrical. 
951.10 Synergetic AllspaceFilling Tetrahedron: Synergetic geometry has one cosmically minimal, allspacefilling tetrahedron consisting of only four A Quanta Modules and two B Quanta Modules^{__}six modules in all^{__}whereas the regular tetrahedron consists of 24 such modules and the cube consists of 72. (See Illus. 950.12.) 
953.00 Mites and Sytes: Minimum Tetrahedra as ThreeModule Allspace Fillers 
Fig. 953.10 
953.10 Minimum Tetrahedron: Mite: Two A Quanta Modules and one B Quanta Module may be associated to define the allspacefilling positive and negative sets of three geometrically dissimilar, asymmetric, but unit volume energy quanta modules which join the volumetric center hearts of the octahedron and tetrahedron. For economy of discourse, we will give this minimum allspacefilling AAB complex threequanta module's asymmetrical tetrahedron the name of Mite (as a contraction of Minimum Tetrahedron, allspace filler). (See drawings section.) 
953.20 Positive or Negative: Mites can fill allspace. They can be either positive (+) or negative (), affording a beautiful confirmation of negative Universe. Each one can fill allspace, but with quite different energy consequences. Both the positive and negative Mite Tetrahedra are comprised, respectively, of two A Quanta Modules and one B Quanta Module. In each Mite, one of the two A s is positive and one is negative; the B must be positive when the Mite is positive and negative when the Mite is negative. The middle A Quanta Module of the MB wedgeshaped sandwich is positive when the Mite and its B Quanta Module are negative. The Mite and its B Quanta Module have like signs. The Mite and its middle A Quanta Module have unlike signs. 
953.21 If there were only positive Universe, there would be only Sytes (see Sec. 953.40. But Mites can be either plus or minus; they accommodate both Universes, the positive and the negative, as well as the halfpositive and halfnegative, as manifestations of fundamental complementarity. They are true rights and lefts, not mirror images; they are inside out and asymmetrical. 
953.22
There is a noncongruent, ergo mutually exclusive,
tripartiteness (i.e., two As
and one B in a wedge sandwich) respectively unique to
either the positive or the negative
world. The positive model provides for the interchange
between the spheres and the
spaces.^{4} But the Mite permits the same kind of exchange
in negative Universe.
(Footnote 4: See Sec. 1032.10.) 
953.23 The cube as an allspace filler requires only a positive world. The insideout cube is congruent with the outsideout cube. Whereas the insideout and outsideout Mites are not congruent and refuse congruency. 
953.24 Neither the tetrahedron nor the octahedron can be put together with Mites. But the allspacefilling rhombic dodecahedron and the allspacefilling tetrakaidecahedron can be exactly assembled with Mites. Their entire componentation exclusively by Mites tells us that either or both the rhombic dodecahedron and the tetrakaidecahedron can function in either the positive or the negative Universe. 
953.25 The allspacefilling functions of the (+) or () AAB threemodule Mite combines can operate either positively or negatively. We can take a collection of the positives or a collection of the negatives. If there were only positive outsideout Universe, it would require only one of the three alternate sixmodule, allspacefilling tetrahedra (see Sec. 953.40) combined of two A (+), two A (), one B (+), and one B () to fill allspace symmetrically and complementarily. But with both insideout and outsideout worlds, we can fill all the outsideout world's space positively and all the insideout world's space negatively, accommodating the inherent complementarity symmetry requirements of the macromicro cosmic law of convex world and concave world, while remembering all the time that among all polyhedra only the tetrahedron can turn itself inside out. 
953.30 Tetrahedron as ThreePetaled Flower Bud: Positive or negative means that one is the insideout of the other. To understand the insideouting of tetrahedra, think of the tetrahedron's four outside faces as being blue and the four inside faces as being red. If we split open any three edges leading to any one of the tetrahedron's vertexes, the tetrahedron will appear as a threepetaled flower bud, just opening, with the triangular petals hinging open around the common triangular base. The opening of the outsideblue insidered tetrahedron and the hinging of all its blue bud's petals outwardly and downwardly until they meet one another's edges below the base, will result in the whole tetrahedron's appearing to be red while its hidden interior is blue. All the other geometrical characteristics remain the same. If it is a regular tetrahedron, all the parts of the outsidered or the outsideblue regular tetrahedron will register in absolute congruence. 
953.40 Symmetrical Tetrahedron: Syte: Two of the AAB allspacefilling, three quanta module, asymmetric tetrahedra, the Mites^{__}one positive and one negative^{__}may be joined together to form the sixquantamodule, semisymmetrical, allspacefilling Sytes. The Mites can be assembled in three different ways to produce three morphologically different, allspacefilling, asymmetrical tetrahedra: the Kites, Lites, and Bites, but all of the same sixmodule volume. This is done in each by making congruent matching sets of their three, alternately matchable, righttriangle facets, one of which is dissimilar to the other two, while those other two are both positivenegative mirror images of one another. Each of the three pairings produces one sixquanta module consisting of two A (+), two A (), one B (+), and one B (). 
953.50 Geometrical Combinations: All of the wellknown Platonic, Archimedean, Keplerian, and Coxeter types of radially symmetric polyhedra may be directly produced or indirectly transformed from the whole unitary combining of Mites without any fractionation and in whole, rational number increments of the A or B Quanta Module volumes. This prospect may bring us within sight of a plenitudinous complex of conceptually discrete, energyimporting, retaining, and exporting capabilities of nuclear assemblage components, which has great significance as a specific closedsystem complex with unique energybehaviorelucidating phenomena. In due course, its unique behaviors may be identified with, and explain discretely, the inventory of highenergy physics' present prolific production of an equal variety of strange smallenergy "particles," which are being brought into splitsecond existence and observation by the ultrahighvoltage accelerator's bombardments. 
953.60 Prime Minimum System: Since the asymmetrical tetrahedron formed by compounding two A Quanta Modules and one B Quanta Module, the Mite, will compound with multiples of itself to fill allspace and may be turned inside out to form its noncongruent negative complement, which may also be compounded with multiples of itself to fill allspace, this minimum asymmetric system^{__}which accommodates both positive or negative space and whose volume is exactly 1/8th that of the tetrahedron, exactly 1/32nd that of the octahedron, exactly 1/160th that of the vector equilibrium of zero frequency, and exactly 1/1280th of the vector equilibrium of initial frequency ( = 2), 1280 = 2^{8} × 5^{__}this Mite constitutes the generalized nuclear geometric limit of rational differentiation and is most suitably to be identified as the prime minimum system; it may also be identified as the prime, minimum, rationally volumed and rationally associable, structural system. 
Fig. 954.00A Fig. 954.00B 
954.00 Mite as the Coupler's Asymmetrical Octant Zone Filler 
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 halfoctahedra, each consisting of the same four equivolumetric octant zones occur around the three halfoctants' 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 l/8 octantzonefilling 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 EFG^{2}, 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 rightangleapexed isosceles triangle DBB to be the horizontal base of a unique octantzonefilling tetrahedron, we find the sixth edge of the tetrahedron rising perpendicularly from the rightangle 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 rightangled 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 angleapexed isosceles base triangle, BBD, of our unique octantfilling 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, EFG^{1} and EFG^{2}, whose
largest (top) angles are each 54° 44' and whose smaller
angles are 35° 16' each.

954.05 As a tetrahedron, the Mite has four triangular faces: BBD, AAC, EFG^{1}, and EFG^{2}. Two of the faces are dissimilar isosceles triangles, BBD and AAC; ergo, they have only two sets of two different face angles each^{__}B, 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° 44' each, while there are three right angles consisting of one D and two Gs. There are two Bs of 45° 00' each, two Es of 35° 16' each, and one C of 70° 32'. (See drawings section.) 
954.08 Any of these eight interior octant, doubleisosceles, threerightangled tetrahedral domains^{__}Mites^{__}(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), allspacefilling module of the isotropic vector matrix of Universe. Because it is a tetrahedron, it also qualifies as a structural system. Its volume is exactly l/8th that of its regular tetrahedral counterpart in their common magnitude isotropic vector matrix; within this matrix, it is also only 1/24th the volume of its corresponding allspacefilling cube, 1/48th the volume of its corresponding allspacefilling rhombic dodecahedron, and 1/6144th the volume of its one other known unique, omnidirectional, symmetrically aggregatable, nonpolarizedassemblage, unit magnitude, isotropicvectormatrix counterpart, the allspacefilling tetrakaidecahedron. 
954.10
AllspaceFilling Hierarchy as Rationally Quantifiable
in Whole Volume Units of A or B Quanta Modules

954.10A
AllspaceFilling Hierarchy as Rationally Quantifiable
in Whole Volume
Units of A or B Quanta Modules

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 Bs in 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, allspacefilling rhombic dodecahedra (or 144 As and Bs). The rhombic dodecahedron is the mostfaceted, identicalfaceted (diamond) polyhedron and accounts, congruently and symmetrically, for all the unique domains of all the isotropicvector matrix vertexes. (Each of the isotropicvectormatrix vertexes is surrounded symmetrically either by the spheres or the intervening spacesbetweenspheres of the closestpacked sphere aggregates.) Each rhombic dodecahedron's diamond face is at the longaxis center of each Coupler (vol. = 1) asymmetric octahedron. Each of the 12 rhombic dodecahedra is completely and symmetrically omnisurrounded by^{__}and diamondfacebonded with^{__}12 other such rhombic dodecahedra, each representing one closestpacked sphere and that sphere's unique, cosmic, interspherespace domain Lying exactly between the center of the nuclear rhombic dodecahedron and the centers of their 12 surrounding rhombic dodecahedra^{__}the Couplers of those closestpackedsphere 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 allA 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 nonmirrorimaging interchangeability and intertransformability with 24 subparticle differentiabilities and 2, 3, 4, 6, combinations^{__}enough to account for all the isotopal variations and all the nuclear substructurings in omnirational quantation. 
Next Section: 954.30 