950.21 Because the cube is the basic, prime-number-three-elucidating volume, and because the cube’s prime volume is three, if we assess space volumetrically in terms of the cube as volumetric unity, we will exploit three times as much space as would be required by the tetrahedron employed as volumetric unity. Employing the extreme, minimum, limit case, ergo the prime structural system of Universe, the tetrahedron (see Sec. 610.20), as prime measure of efficiency in allspace filling, the arithmetical-geometrical volume assessment of relative space occupancy of the whole hierarchy of geometrical phenomena evaluated in terms of cubes is threefold inefficient, for we are always dealing with physical experience and structural systems whose edges consist of events whose actions, reactions, and resultants comprise one basic energy vector. The cube, therefore, requires threefold the energy to structure it as compared with the tetrahedron. We thus understand why nature uses the tetrahedron as the prime unit of energy, as its energy quantum, because it is three times as efficient in every energetic aspect as its nearest symmetrical, volumetric competitor, the cube. All the physicists’ experiments show that nature always employs the most energy-economical strategies.
Figure 15: Fig. 950.12 Three Self-Packing, Allspace-Filling, Irregular Tetrahedra: There are three self-packing irregular tetrahedra that will fill allspace without need of any complementary shape (not even with the need of right- and left-hand versions of themselves). One, the Mite, has been proposed by Fuller (A). The other two are described by Coxeter in his book Regular Polytopes, p. 71 and are called the trirectangular tetrahedron (B) and the tetragonal disphenoid, or isosceles tetrahedron since it is bounded by four congruent isosceles triangles (C). All three of these tetrahedra can be subdivided into component A and A Quanta Modules. The Mite has a population of two Bs and four A and the tetragonal disphenoid is simply a somewhat different arrangement of the same components. The trirectangular tetrahedron consists of two A and oneB Modules. (It is of interest to note that theB Module may be either right- or lefthanded. See the remarks of Arthur L. Loeb.) Two trirectangular tetrahedra will combine to form either of the other two tetrahedra. The edge dimensions given above are all with respect to a “unity”-edged regular tetrahedron. The self-packing, allspace-filling, irregular tetrahedron of synergetics is also known as the Mite. It is composed of four/ Quanta Modules and two B Quanta Modules.Figure 15: Fig. 950.12 Three Self-Packing, Allspace-Filling, Irregular Tetrahedra: There are three self-packing irregular tetrahedra that will fill allspace without need of any complementary shape (not even with the need of right- and left-hand versions of themselves). One, the Mite, has been proposed by Fuller (A). The other two are described by Coxeter in his book Regular Polytopes, p. 71 and are called the trirectangular tetrahedron (B) and the tetragonal disphenoid, or isosceles tetrahedron since it is bounded by four congruent isosceles triangles (C). All three of these tetrahedra can be subdivided into component A and A Quanta Modules. The Mite has a population of two Bs and four A and the tetragonal disphenoid is simply a somewhat different arrangement of the same components. The trirectangular tetrahedron consists of two A and oneB Modules. (It is of interest to note that theB Module may be either right- or lefthanded. See the remarks of Arthur L. Loeb.) Two trirectangular tetrahedra will combine to form either of the other two tetrahedra. The edge dimensions given above are all with respect to a “unity”-edged regular tetrahedron. The self-packing, allspace-filling, irregular tetrahedron of synergetics is also known as the Mite. It is composed of four/ Quanta Modules and two B Quanta Modules.