986.720 Absolute Constancy: Cheese Polyhedra

986.721 My first o bservation of the polyhedral hierarchy was introduced in Sec. 223.64, Table 224.2 0, and Fig. 400.30. That hierarchy may be considered as cheese polyhedra in which there is an experimental redemonstrability of absolute constancy of areal, volume tric, topological, and symmetry characteristics, which constancy is exclusively u nique to triangles and tetrahedra and is maintained despite any and all asymmetri cal aberrations of those triangles and tetrahedra, as caused by per s pective distortion; by interproportional variations of relative len g ths and angles as manifest in isosceles, scalene, acute, or obtuse system aspect s (see quadrangular versus triangular accounting in Figs. 990.01 and *100.301 .),*by truncatings parallel to triangle edges or para llel to tetrahedron faces; or by frequency modulations, in contradi s tinction to complete loss of symmetry and topological constancy of all polygons o ther than the triangle and of all polyhedra other than the tetrahedron as cause d by any special-case, time-size alterations or changes of the perspective point fr om which the observations of those systems are taken.

986.722 In connectio n with this same cheese tetrahedron recall we remember (1) that we could push in on the faceAof the tetrahedron at a given rate of radial contraction of the sys te m, while pulling out face# at a matching rate of radial expansion of the syste m , which “couple” of local alterations of the system left the tetrahedron unalt ered 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; an d we remember (2) that we could also push in on the same tetrahedron’s faceCand pull out on face/) at a coupled rate other than the coupled rate of radial expans ion and contraction of the A-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 alter ing 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 no ted, however, that because of the generalized nonsimultaneity of cosmic events , there exists an inherent lag between the pushing in of faceAand the pulling o u t of faceB, which induces an inherent interim wave-depression or a wave-breaki ng pulsating of the coupling functionings of the tetrahedron’s accommodation of t ransmission of two disparately frequenced energetic communications.

986.724 S econd, 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 t he single-tuned-length axis of the edge-axis- rotatable tetrahedro n’s two nonaxi s polar vertexes may be deployed to connect up with any two other p oints in Univ erse without altering the tetrahedron s unit volume or its tuned-axi s length. (S ee Sec. 961.30.)

986.726 Fourth, I recall that the tetrahedron’ s 24AModule s 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 relabeli ng of Fig. 923.10B) together with theTandEModules provid e transformative sig nificance of being the constant-unit-volume progression of ev er-more-asymmetrica lly-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 consta nt-volume tetrahedra being covaryingly and ever-progressively-d isparately altere dwith the sixth edge alone of each and all stages of the transformati on remaining unaltered in frequency and wavelength magnitude. The concurrent constant-volume-and-wavelength transformings, and system rotating aro und and angular tilting of the constant, unaltered-in-length, sixth edge’s axial altitude in respect to the all-other-in-Universe experiences’ omniinterangular or ientations, altogether both permit and accommodate any two oth er points X andYi n Universe being interconnected not only with one another, but also with the two pointsAandBthat define the unaltered sixth edgeA Bof the c onstant-volume an d constant-/lB-edge-length, omni-Universe-interconnecting tetrah edron *ABXY ;*all of which permits the constant sixth edgeABlength to serve as the anywhere and anywhen in Universe to be established transceiver’s wave-leng th-defining and frequency-selecting and tuning interconnecting any given two poin ts in Universe with any two other points in Universe; ergo, with all other points in Universe, g ranted only sufficient elapsed time for rotational realization of t he frequency of repetition of the wavelength vector’s velocity factor to reach an y given loci in Universe with a given volumetric-unit quantum of energy. (This is the signific ance of Fig. 923.10.) image Fig. *986.726 Constant-iinit-volume Progressions of Asymmetric Tetrahedra:*I n this progression of ever-more-asymmetric tetrahedra, only the sixth edge remain s 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 a s recounted in Sec. 961.40 that the more elongated the unit-volume tetrahedron o f only one-edge-length-constancy (the sixth edge), the less becomes the unit-vol um e tetrahedron’s least-altitude aspect as related to its other interdimensional as pects, wherefore there is attained a condition wherein the controlling sixth e dg e’s wavelength is greater than half the tetrahedron’s least-altitude aspect at 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 n ow-partially -tuned-in-and-now-tuned-out, which altogether propagates finitely pa ckaged, tune d-in energy information occurring in packages yet recurring in const ant, contain ed wavelength intervals that introduce what has hitherto been consid ered to be t he paradoxical aspect of electromagnetic phenomena, of which it has been misassum ed that as of any one moment we can consider our electromagnetic ph enomena as be ing continuous-wave phenomena or as discontinuous-particle phenomen aboth simultaneous. We thus learn that no such paradox exists. (Comp are Secs. 541 .30, 961.46-48, 973.30, and 1072.32.) 986.728 Sixth, we r ecall that th ere are no solids or absolute continuums; ergo, there are no physic ally demonstr able faces or sides of *hedra;*ergo, we reidentify the system- conceptioning experiences heretofore spoken of as polyhedra, by the name *polyvertexia,*t he simplest of which is the *tetravertex,*or “four-fix” sy stem.

986.729 Seventh, we recall that the tetravertex is not only the simple st limit casei.e., the topologically most economically definable poly vertex system casebut also the simplest spheric-system experience cas e. (See Secs. 1024.10-25, 105 3.40-62, 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.