953.00 Mites and Sytes: Minimum Tetrahedra as Three-Module Allspace Fillers
953.10 Minimum Tetrahedron: Mite: Two A Quanta Modules and one B Quanta Module may be associated to define the allspace-filling 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 allspace-filling AAB complex three-quanta module’s asymmetrical tetrahedron the name of Mite (as a contraction of Minimum Tetrahedron, allspace filler). (See drawings section.)
Figure 16: Fig. 950.31 Tetrahedra and Octahedra Combine to Fill Space: Regular tetrahedra alone will not fill space, but when four tetrahedra (A) are grouped to define a larger tetrahedron (B), the resulting central space is an octahedron (C). Therefore tetrahedra and octahedra will combine to fill all the space. If the volume of the smaller tetrahedron is equal to one then the volume of the larger tetrahedron is eight, i.e. edge length two to the third power (2 × 2 × 2). (When we double the linear dimension of a figure we always increase its volume eight-fold.) If the volume of the large tetrahedron is eight the central octahedron must have a volume of exactly four, while the small tetrahedra each equal one. The volume of a pyramid is */s the base area times the height. Therefore the A-octahedron (D) has exactly the same volume as its corresponding tetrahedron, further proof that the regular octahedron has exactly four times the volume of a regular tetrahedron of the same edge length.Figure 16: Fig. 950.31 Tetrahedra and Octahedra Combine to Fill Space: Regular tetrahedra alone will not fill space, but when four tetrahedra (A) are grouped to define a larger tetrahedron (B), the resulting central space is an octahedron (C). Therefore tetrahedra and octahedra will combine to fill all the space. If the volume of the smaller tetrahedron is equal to one then the volume of the larger tetrahedron is eight, i.e. edge length two to the third power (2 × 2 × 2). (When we double the linear dimension of a figure we always increase its volume eight-fold.) If the volume of the large tetrahedron is eight the central octahedron must have a volume of exactly four, while the small tetrahedra each equal one. The volume of a pyramid is */s the base area times the height. Therefore the A-octahedron (D) has exactly the same volume as its corresponding tetrahedron, further proof that the regular octahedron has exactly four times the volume of a regular tetrahedron of the same edge length.
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 As 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 AAB wedge-shaped 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 half-positive and half-negative, 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[^32]. But the Mite permits the same kind of exchange in negative Universe.
953.23 The cube as an allspace filler requires only a positive world. The inside-out cube is congruent with the outside-out cube. Whereas the inside-out and outside-out Mites are not congruent and refuse congruency.
953.24 Neither the tetrahedron, the octahedron, nor the cube can be put together with Mites. But the allspace-filling rhombic dodecahedron and the allspace-filling 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 allspace-filling functions of the (+) or () AAB three-module 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 outside-out Universe, it would require only one of the three alternate six-module, allspace-filling 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 inside-out and outside-out worlds, we can fill all the outside-out world’s space positively and all the inside-out world’s space negatively, accommodating the inherent complementarity symmetry requirements of the macro-micro 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 Three-Petaled Flower Bud: Positive or negative means that one is the inside-out 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 three-petaled flower bud, just opening, with the triangular petals hinging open around the common triangular base. The opening of the outside-blue-in-side-red 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 outside-red or the outside-blue regular tetrahedron will register in absolute congruence.
953.40 Symmetrical Tetrahedron: Syte: Two of the AAB allspacefilling, three-quanta module, asymmetric tetrahedra, the Mitesone positive and one negativemay be joined together to form the six-quanta-module, semisymmetrical, allspace-filling Sytes. The Sytes can be assembled in three different ways to produce three morphologically different, allspace-filling, asymmetrical tetrahedra: the Kites, Lites, and Bites, but all of the same six-module volume. This is done in each by making congruent matching sets of their three, alternately matchable, right-triangle facets, one of which is dissimilar to the other two, while those other two are both positive-negative mirror images of one another. Each of the three pairings produces one six-quanta module consisting of two A(+), two A(-), one B(+), and one B(-).
953.50 Geometrical Combinations: All of the well-known 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 Aor B Quanta Module volumes. This prospect may bring us within sight of a plenitudinous complex of conceptually discrete, energy-importing, -retaining, and -exporting capabilities of nuclear assemblage components, which has great significance as a specific closed-system complex with unique energy-behavior-elucidating phenomena. In due course, its unique behaviors may be identified with, and explain discretely, the inventory of high-energy physics’ present prolific production of an equal variety of strange small-energy “particles,” which are being brought into split-second existence and observation by the ultrahigh-voltage 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 systemwhich accommodates both positive or negative space and whose volume is exactly \sfrac{1}{8}th that of the tetrahedron, exactly \sfrac{1}{32}nd that of the octahedron, exactly \sfrac{1}{160}th that of the vector equilibrium of zero frequency, and exactly \sfrac{1}{1280}th of the vector equilibrium of initial frequency (= 2), $1280 = 2^\times 5$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.