BUCKYVERSE

973.00 Basic Tetrahedra as Volumetric Modules

973.01 Basic Tetrahedron: Each Basic Tetrahedron (Mite)[^33] is semi-symmetric, four of its six edges consisting always of two pairs of equal-length edges and only two being of odd lengths. The Mite itself consists of six entirely asymmetric Modules, four of which are dissimilar to the other two:

973.10 Regular Tetrahedron: The Plato-identified “regular” (i.e., omnisymmetric) tetrahedron is comprised entirely of A Modules: 12 positive As and 12 negatives, but the symmetric, “regular,” Platonic, equiangled, equi-edged tetrahedron cannot by itself fill allspace as could the cube, the rhombic dodecahedron, and the tetrakaidecahedronnone of which allspacefilling forms have self-stabilizing structural-conformation integrity, not being comprised of triangles, which alone can stabilize pattern.

973.11 The “regular” Platonic tetrahedron may be combined with the octahedron to fill allspace.

973.12 The volumes of all the symmetrical Platonic polyhedra, except the icosahedron and its pentagonal dodecahedron, are whole, low-order-number multiples of the “regular” Platonic tetrahedron, consisting itself of 24 modules, making that tetrahedron seemingly the “basic unit of measure” of all polyhedra. The inability of that “regular” tetrahedron to fill all cosmic space turns our comprehensive, cosmic-coordinate-system exploration to the consideration of the least common divisor aggregates of the A and B Modules.

973.20 Functions of A and B Quanta Modules and Sytes: The/ and B Quanta Modules are omnitriangulated and individually asymmetric but not maximally asymmetric. The A Quanta Module has three of its 12 total angles at 90 degrees, and the B Quanta Module has two 90-degree angles. The/ Quanta Module has a 30-degree and a 60-degree angle. TheB Quanta Module has two 45-degree angles.

973.21 These angles all represent low-order whole fractions of unity: $\sfrac
{1}, \sfrac, \sfrac, \sfrac, and \sfracof unity in a planar circle; all the other angles of the/ andB$ Quanta Modules are unit and symmetric central angles of the tetrahedron and octahedron.

973.22 The variety of their mixability produces what need be only momentary bewilderment and only an illusion of “disorder” occasioned initially by the subtlety and muchness of the unfamiliar.

973.23 This brings us to consider the only superficially irregular, only semiasymmetric Syte as possibly being the most separately universal structural-system entity.

973.24 The Syte, consisting of only six modules and filling allspace in a threefold intertransformable manner, is found to be far more universal and “primitive” than the regular tetrahedron. The Mite is the single most universal and versatile structural componentsave for its own subcomponents, the A and B Quanta Modules, which of unit volume and non-mirror-imaged complementation do indeed initially provide, singly or in complementation, the beginnings of all cosmic structuring.

973.25 The Syte’s six Modules are always subdivided into two sets of three Modules eachtwo As, one Bof which two sets of the three Modules each are identically dimensioned both angularly and linearly, but one is inside out of the other. Therefore, one set of three Modules extemdash two As, one Bis positively outside-outed, and the other is negatively inside-outed.

973.30 Particle and Wave Involvement: Particle Quanta Equation: (Prime numbers 2 and 5)

10F^{2}+ 2

973.31 Wave Quanta Equation: (Prime numbers 2, 5, and 3)

10 (2+ 12\frac{F^{2}- F}{2})

973.32 One is particle involvement; the other is total involvement. Inadvertently, they correlate the sphere and all the other polyhedra rationally.

973.33 The difference is the difference between using the tetrahedron as volumetric unity, while the physicist has always been using the cubic centimeter of water and then only lifting it in one direction, against gravity, against the imagined plane of the world. On the other hand, synergetics moves omnidirectionally, inwardly, outwardly, and aroundly.