986.720 Absolute Constancy: Cheese Polyhedra

986.721 My first observation of the polyhedral hierarchy was introduced in Sec. 223.64, Table 224.20, and Fig. 400.30. That hierarchy may be considered as cheese polyhedra in which there is an experimental redemonstrability of absolute constancy of areal, volumetric, topological, and symmetry characteristics, which constancy is exclusively unique to triangles and tetrahedra and is maintained despite any and all asymmetrical aberrations of those triangles and tetrahedra, as caused

by perspective distortion;

by interproportional variations of relative lengths and angles as manifest in isosceles, scalene, acute, or obtuse system aspects (see quadrangular versus triangular accounting in Figs. 990.01 and 100.301.),

by truncatings parallel to triangle edges or parallel to tetrahedron faces; or

by frequency modulations,

in contradistinction to complete loss of symmetry and topological constancy of all polygons other than the triangle and of all polyhedra other than the tetrahedron as caused by any special-case, time-size alterations or changes of the perspective point from which the observations of those systems are taken.

986.722 In connection with this same cheese tetrahedron recall we remember (1) that we could push in on the face A of the tetrahedron at a given rate of radial contraction of the system, while pulling out face# at a matching rate of radial expansion of the system, which “couple” of local alterations of the system left the tetrahedron unaltered in shape or size throughout the transformation (Sec. 623) and just as it was both before and after the “coupled” transformings took place, the only altered consequence of which was that the tetrahedron’s center of volume had migrated; and we remember (2) that we could also push in on the same tetrahedron’s face C and pull out on face/) at a coupled rate other than the coupled rate of radial expansion and contraction ofthe/1-B face-coupling s intercomplementary transformings; by all of which we learn that the tetrahedron can accommodate two disparate rates of change without in any way altering its own size and only altering its center-of-volume positioning in respect to any other system components of the local Universe consideration. (See color plate 26.)

986.723 It must be noted, however, that because of the generalized nonsimultaneity of cosmic events, there exists an inherent lag between the pushing in of face A and the pulling out of face B, which induces an inherent interim wave-depression or a wave-breaking pulsating of the coupling functionings of the tetrahedron’s accommodation of transmission of two disparately frequenced energetic communications.

986.724 Second, I recallas in Secs. 920.01 and 921.10 and Fig. 923.10that the tetrahedron is the quantum of energy.

986.725 Third, I recall that the single-tuned-length axis of the edge-axis- rotatable tetrahedron’s two nonaxis polar vertexes may be deployed to connect up with any two other points in Universe without altering the tetrahedron s unit volume or its tuned-axis length. (See Sec. 961.30.)

986.726 Fourth, I recall that the tetrahedron’s 24 A Modules and the latter’s B, C, D; A, B, C, D; A", B", C", D" …a (see Fig. 986.726, which is a detail and relabeling of Fig. 923.10B) together with the T and E Modules provide transformative significance of being the constant-unit-volume progression of ever-more-asymmetrically-transforming stages of the constant-unit-volume tetrahedra, with the uniform-stage transforming being provided by five of the six edges of each of the constant-volume tetrahedra being covaryingly and ever-progressively-disparately altered with the sixth edge alone of each and all stages of the transformation remaining unaltered in frequency and wavelength magnitude. The concurrent constant-volume-and-wavelength transformings, and system rotating around and angular tilting of the constant, unaltered-in-length, sixth edge’s axial altitude in respect to the all-other-in-Universe experiences’ omniinterangular orientations, altogether both permit and accommodate any two other points X and Y in Universe being interconnected not only with one another, but also with the two points A and B that define the unaltered sixth edge AB of the constant-volume and constant-/lB-edge-length, omni-Universe-interconnecting tetrahedron ABXY; all of which permits the constant sixth edge AB length to serve as the anywhere and anywhen in Universe to be established transceiver’s wave-length-defining and frequency-selecting and tuning interconnecting any given two points in Universe with any two other points in Universe; ergo, with all other points in Universe, granted only sufficient elapsed time for rotational realization of the frequency of repetition of the wavelength vector’s velocity factor to reach any given loci in Universe with a given volumetric-unit quantum of energy. (This is the significance of Fig. 923.10.)

image

Fig. 986.726 Constant-iinit-volume Progressions of Asymmetric Tetrahedra: In this progression of ever-more-asymmetric tetrahedra, only the sixth edge remains constant. Tetrahedral wavelength and tuning permits any two points in Universe to connect with any other two points in Universe.

986.727 Fifth, I recall as recounted in Sec. 961.40 that the more elongated the unit-volume tetrahedron of only one-edge-length-constancy (the sixth edge), the less becomes the unit-volume tetrahedron’s least-altitude aspect as related to its other interdimensional aspects, wherefore there is attained a condition wherein the controlling sixth edge’s wavelength is greater than half the tetrahedron’s least-altitude aspectat which condition the tetrahedron spontaneously turns itself inside-out, ergo, turns itself outnot out of Universe, but out of tune-in-able range. Prior to this spontaneous tuning-out range we have a vast range of now-partially-tuned-in-and-now-tuned-out, which altogether propagates finitely packaged, tuned-in energy information occurring in packages yet recurring in constant, contained wavelength intervals that introduce what has hitherto been considered to be the paradoxical aspect of electromagnetic phenomena, of which it has been misassumed that as of any one moment we can consider our electromagnetic phenomena as being continuous-wave phenomena or as discontinuous-particle phenomenaboth simultaneous. We thus learn that no such paradox exists. (Compare Secs. 541.30, 961.46-48, 973.30, and 1072.32.)

986.728 Sixth, we recall that there are no solids or absolute continuums; ergo, there are no physically demonstrable faces or sides of hedra; ergo, we reidentify the system-conceptioning experiences heretofore spoken of as polyhedra, by the name polyvertexia, the simplest of which is the tetravertex, or “four-fix” system.

986.729 Seventh, we recall that the tetravertex is not only the simplest limit casei.e., the topologically most economically definable polyvertex system casebut also the simplest spheric-system experience case. (See Secs. 1024.10-25, 1053.40-62, 1054. 1054.30, and Fig. 1054.40.)

986.730 The Spheric Experience: We now scientifically redefine the spheric experience as an aggregate of vertex-direction-pointed-to (fixed) subtune-in-able microevent centers surrounding a system center at equal-radius distances from the system center. Four such surrounding, vertex-convergence-indicated, microevent fixes are redemonstrably proven to be the minimum number of such a microcenter-surrounding aggregate geometrically adequate to constitute systemic subdivision of Universe into macrocosm and microcosm by convergent envelopment, which inherently excludes the thus-constituted system’s macrocosm and inherently includes the thus-constituted system’s microcosm, in which spheric experiencing the greater the population of equi-radiused-from-system-center microevent fixes, the more spheric the experience, and the earliest and simplest beyond the tetrahedron being the hierarchy of concentric, symmetric, primitive polyhedra.