986.410 T Quanta Module |
Fig. 986.411A Fig. 986.411B Fig. 986.411C |
986.411 The respective 12 and 30 pentahedra OABAB of the rhombic dodecahedron and the triacontahedron may be symmetrically subdivided into four right-angled tetrahedra ABCO, the point C being surrounded by three right angles ABC, BCO, and ACO. Right- angle ACB is on the surface of the rhombic-hedra system and forms the face of the tetrahedron ABCO, while right angles BCO and ACO are internal to the rhombic-hedra system and from two of the three internal sides of the tetrahedron ABCO. The rhombic dodecahedron consists of 48 identical tetrahedral modules designated ABCO^{d}. The triacontahedron consists of 120 (60 positive and 60 negative) identical tetrahedral modules designated ABCO^{t}, for which tetrahedron ABCO^{t} we also introduce the name T Quanta Module. |
986.412 The primitive tetrahedron of volume 1 is subdivisible into 24 A Quanta Modules. The triacontahedron of exactly tetravolume 5, has the maximum-limit case of identical tetrahedral subdivisibility^{__}i.e., 120 subtetra. Thus we may divide the 120 subtetra population of the symmetric triacontahedron by the number 24, which is the identical subtetra population of the primitive omnisymmetrical tetrahedron: 120/24=5. Ergo, volume of the A Quanta Module = volume of the T Quanta Module. |
Fig. 986.413 |
986.413
The rhombic dodecahedron has a tetravolume of 6, wherefore
each of its 48
identical, internal, asymmetric, component tetrahedra
ABCO^{d} has a regular tetravolume of
6/48 = 1/8 The regular tetrahedron consists of 24 quanta
modules (be they A, B, C, D,^{5} *
or T Quanta Modules; therefore ABCO^{d}, having l/8-tetravolume,
also equals three quanta
modules. (See Fig.
986.413.)
(Footnote 5: C Quanta Modules and D Quanta Modules are added to the A and B Quanta Modules to compose the regular tetrahedron as shown in drawing B of Fig. 923.10.) |
986.414 The vertical central-altitude line of the regular, primitive, symmetrical tetrahedron may be uniformly subdivided into four vertical sections, each of which we may speak of as quarter-prime-tetra altitude units-each of which altitude division points represent the convergence of the upper apexes of the A, B, C, D, A', B', C', D', A", B", C", D" . . . equivolume modules (as illustrated in Fig. 923.10B where^{__}prior to the discovery of the E "Einstein" Module^{__}additional modules were designated E through H, and will henceforth be designated as successive ABCD, A'B'C'D', A"B"C"D" . . . groups). The vertical continuance of these unit-altitude differentials produces an infinite series of equivolume modules, which we identify in vertical series continuance by groups of four repetitive ABCD groups, as noted parenthetically above. Their combined group-of- four, externally protracted, altitude increase is always equal to the total internal altitude of the prime tetrahedron. |
986.415 The rhombic triacontahedron has a tetravolume of 5, wherefore each of its 120 identical, internal, asymmetric, component tetrahedra ABCO^{t}, the T Quanta Module, has a tetravolume of 5/120 = 1/24 tetravolume^{__}ergo, the volume of the T Quanta Module is identical to that of the A and B Quanta Modules. The rhombic dodecahedron's 48 ABCO^{d} asymmetric tetrahedra equal three of the rhombic triacontahedron's 120 ABCO^{t} , T Quanta Module asymmetric tetrahedra. The rhombic triacontahedron's ABCOt T Quanta Module tetrahedra are each 1/24 of the volume of the primitive "regular" tetrahedron^{__}ergo, of identical volume to the A Quanta Module. The A Mod, like the T Mod, is structurally modeled with one of its four corners omnisurrounded by three right angles. |
986.416 1 A Module = 1 B Module = 1 C Module = 1 D Module = 1 T Module = any one of the unit quanta modules of which all the hierarchy of concentric, symmetrical polyhedra of the VE family are rationally comprised. (See Sec. 910). |
986.417 I find that it is important in exploratory effectiveness to remember^{__}as we find an increasingly larger family of equivolume but angularly differently conformed quanta modules^{__}that our initial exploration strategy was predicated upon our generalization of Avogadro's special-case (gaseous) discovery of identical numbers of molecules per unit volume for all the different chemical-element gases when individually considered or physically isolated, but only under identical conditions of pressure and heat. The fact that we have found a set of unit-volume, all-tetrahedral modules^{__}the minimum-limit structural systems^{__}from which may be aggregated the whole hierarchy of omnisymmetric, primitive, concentric polyhedra totally occupying the spherically spun and interspheric accommodation limits of closest-packable nuclear domains, means that we have not only incorporated all the min-max limit-case conditions, but we have found within them one unique volumetric unit common to all their primitive conformational uniqueness, and that the volumetric module was developed by vectorial^{__}i.e., energetic^{__}polyhedral-system definitions. |
986.418 None of the tetrahedral quanta modules are by themselves allspace-filling, but they are all groupable in units of three (two A's and one B^{__}which is called the Mite) to fill allspace progressively and to combine these units of three in nine different ways^{__}all of which account for the structurings of all but one of the hierarchy of primitive, omniconcentric, omnisymmetrical polyhedra. There is one exception, the rhombic triacontahedron of tetravolume 5^{__}i.e., of 120 quanta modules of the T class, which T Quanta Modules as we have learned are of equivolume to the A and B Modules. |
Fig. 986.419 |
986.419 The 120 T Quanta Modules of the rhombic triacontahedron can be grouped in two different ways to produce two different sets of 60 tetrahedra each: the 60 BAAO tetrahedra and the 60 BBAO tetrahedra. But rhombic triacontahedra are not allspace-filling polyhedra. (See Fig. 986.419.) |
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