1033.030 Untenable Equilibrium Compulsion 
1033.031 In the 20tetravolume vector equilibrium we have four passive and four active tetrahedra vertexially interconnected. The eight tetrahedra have a total of 32 vertexes. In the 20tetravolume vector equilibrium each tetrahedron has three of its vertexial somethings outwardly arrayed and one vertexial something inwardly arrayed. Their 24 externally arrayed vertexes are congruently paired to form the 12 vertexes of the vector equilibrium, and their eight interior vertexial somethings are nuclear congruent; ergo, fourforcedlymorevectorinterconstrained than any of their externally paired vertexial something sets: an untenable equilibrium compulsion (UEC). (Compare Secs. 1012.11 and 1224.13.) 
1033.10 Octave System of Polyhedral Transformations 
1033.101 The systematic outsideness is the macrountuned: the ultratunable. The systemic insideness is the micrountuned: the infratunable. The system is the discretely tunedin conceptuality. 
1033.102
The closestpacked spheres are simply the frequencies
that are activated, that
get into closest proximity as a continuum of the outsideness:

1033.103 If there were a geometric outsideness and insideness, we would have a static geometrical Universe. But since the insideness and outsideness are the asyetuntunedin or nolongertunedin wavelengths and their frequencies, they require only Scenario Universe, its past and future. Only the NOW conceptualizing constitutes a geometry^{__}the immediate conceptual, specialcase, systemic episode in a scenario of nonunitarily conceptual, nonsimultaneous, and only partially overlapping, differently enduring, differently magnituded, specialcase, systemic episodes, each in itself a constellation of constellations within constellations of infra or ultratunably frequenced, special case frequenced systems (Compare Sec. 321.05.) 
1033.104 The isotropicvectormatrixfield has an infinite range of electromagnetic tunings that are always multiplying frequency by division of the a priori vector equilibrium and its contained cosmic hierarchy of timelesssizeless primitive systems' unfrequenced state. At maximum their primitive comprehensive domain is that of the sixtetravolume, 24AandBquantamoduled, unfrequenced rhombic dodecahedron, the long axis of whose 12 diamond faces is also the prime vector length of the isotropic vector matrix. At primitive minimum the unfrequenced state is that of the sixAandBquantamoduled Syte. Both the maximum and minimum, primitive, greatest and least primitive common divisors of Universe may be replicatively employed or convergently composited to produce the isotropic vector matrix field of selectable frequency tunability, whose key wavelength is that of the relative length of the uniform vector of the isotropic vector matrix as initially selected in respect to the diameter of the nucleus of the atom. 
Fig. 1033.11 
1033.11 Every electromagnetic wave propagation generates its own cosmic field. This field is a fourdimensional isotropic vector matrix that can be readily conceptualized as an aggregation of multilayered, closestpacked, unitradius spheres. (See Fig. 1033.111A.) Unitradius spheres pack tangentially together most closely in 60degree intertriangulations. Atoms closepack in this manner. The continuum of inherent outsideness of all systems enters every external opening of all closestpacked, unitradius sphere aggregates, permeating and omnisurrounding every closestpacked sphere within the total aggregate. Between the closestpacked, unitradius spheres the intervening voids constitute a uniform series of unique, symmetrical, curvilinear, geometrical shapes, and the successive centers of volumes of those uniform phase voids are uniformly interspaced^{__} the distance between them being always the same as the uniform distances between adjacent closestpacked spheres. 
Fig. 1033.111A Fig. 1033.111B 
1033.111 Each of the closestpacked, unitradius spheres is itself a geodesic sphere, a spherical sieve with triangular openings: a tetra, octa, or icosasphere of some frequency of modular subdivision. (Compare the fallacy of the Greek sphere as described at Secs. 981.19, 1022.1113, 1106.22, and 1107.21.) Wherefore, each of the closestpacked spheres is permeable by higherfrequency, shorterwavelength, electromagnetic propagations; ergo, appropriately frequenced fields may pass through the isotropic vector matrix's electromagnetic field of any given wavelengths without interference. Not only does each closestpacked sphere consist of a plurality of varifrequenced vertices interconnected by chords that define the triangular sieve, but also these vertexial somethings are massinterattractively positioned and have their own boundary layer (trampoline) cushions; ergo, they are never in absolute tangency. 
1033.112 The isotropic vector matrix grid illustrates that frequency multiplication may be accomplished only by division. The unitradius spheres of the isotropic vector matrix electromagnetic fields closepack in four planes of symmetry, permitting fourdimensional electromagnetic wavebands. The threeway, spherical, electromagnetic, basketry interweaving is illustrated at Fig. 1033.111B. There are six greatcircle equators of the six axes formed by the 12 vertices of the spherical icosahedron. The centers of area of the spherical triangles thus formed describe the terminals of the electromagnetic waveband widths. The widths of the bands of frequency tunability are determined by the truncatability of the spherical icosahedron's six bands as they run between the centers of area of the adjacent triangles. 
1033.113 Note that the centers of area of the adjacent spherical triangles are alternately staggered so as to define a broad path within which the electromagnetic waveband is generated. 
1033.120 Clickstop Subdivisioning 
1033.121 In synergetic geometry we witness the transformation of all spheres into their local complementary intervoid domains as the local intervoid domains transform into closestpacked, unitradius spheres. (See Fig. 1032.31.) The multifrequenced tetrahedral, octahedral, and icosahedral geodesic subdivisioning of spherical projections of the primitive polyhedral systems describes how the complex interbonding of substances occurs; it is further described by the varying radii of the closestpacked spheres and the complex of isotropic vector matrixes required to accommodate the varying radii as well as their ultra and infrapermeating: this elucidates the resonance of substances as well as the unique electromagnetic frequencies of chemical elements. Here is the grand synergetic nexus integrating electromagnetics, chemistry, and topology. 
1033.122 Synergetics arouses human awareness of the alwaysandonlycooccurring, nontunedin cosmic complementations of our onlyfrommomenttomoment systematically tunedin conceptionings. Synergetics' always symmetrical, complementarily expanding and contracting intertransformings disclose a succession of "local way stations." Progressive arrival at these convergentdivergent "way station" states discloses a succession of immediately neighboring, largertosmaller, symmetrical polyhedra of diminishingly numbered topological characteristics, which all together constitute a cosmic hierarchy of symmetrical, rationally volumed, most primitive, patternstabilization states. Superficially the states are recognizable as the family of Platonic polyhedra. 
1033.123 Throughout the convergent phase of the transformation continuum, all the vertices of these successive Platonic forms and their intertransformative phases are always diminishingly equidistant from the same volumetric center. The omnisymmetrical contraction is accommodated by the angular closing^{__}scissorhingewise^{__}of immediately adjacent edges of the polyhedra. The vertices of each of these intertransforming symmetric states, as well as their intermediate transforms, are always positioned in a sphere that is progressively expanding or contracting^{__}depending on whether we are reading the cosmic hierarchy as energetic volumes from 1 to 24 or from 24 to 1. 
1033.124 As the originally omnisymmetrical, 20tetravolume vector equilibrium of 12 vertices, 14 faces, and 24 vector edges shrinks its vertexdescribed spherical domain, it may receive one quantum of energy released entropically by some elsewhereinUniverse entropic radiation, as most frequently occurring when octahedra of matter are precessed and the octahedron's tetravolume 4 is reduced to tetravolume 3 (see Octahedron as Conservation and Annihilation Model, Sec. 935), the tetrahedron thus annihilated being one quantum lost entropically without any alteration of the Eulerean topological characteristics as an octahedron. Since each quantum consists of six vector edges that can now be entropically dispersed, they may be syntropically harvested by the 20tetravolume vector equilibrium, and, constituting one quantum of energy, they will structurally stabilize the shrinking 20tetravolume vector equilibrium 4tetravolume octahedron system in the intermediate symmetrical form of the icosahedron. As the icosahedron of 12 vertices, 20 faces, and 30 edges (24 + 6) shrinks its spherical domain, it can do so only by compressing the one energy quantum of six syntropically captured vector edges into the six vertical somethings of the octahedron, thereby allowing 12 faces to unite as six^{__}all the while the icosahedron's evershrinking spherical surface pattern alters uniformly, despite which its topological inventory of 12 vertices, 14 faces, and 24 edges remains constant until the simultaneous moment of vertex, face, and edge congruence occurs. Simultaneously each of the paired vertices and edges^{__}as well as the six compressed vector edges^{__}now appears as one; and each of the congruent pairs is now topologically countable only as one in this instance as the six vertices, eight faces, and 12 edges of the suddenly realized octahedron of tetravolume 4. 
1033.125 The simultaneous vanishing of the previously shuttling and lingering topological characteristics from the previously stable icosahedral state, and the instant appearance of the next neighboring state^{__}the octahedron, in its simplest and completely symmetrical condition^{__}is what we mean by a "clickstop" or "way station" state. 
1033.126 Assessing accurately the "clickstop" volumes of the intertransformative hierarchy in terms of the volume of the tetrahedron equaling one, we find that the relative tetravolumes of these primitive polyhedra^{__}when divergent^{__}are successively, 1, 2 1/2, 3, 2^{2}, 5, 6, 20, 24, and then^{__}converging^{__}from 24, 20, 6, 5, 2^{2}, 3, 2 l/2, 1. These omnirational, wholenumber, "clickstop" volumes and their successive topological characteristic numbers elegantly introduce^{__}and give unique volumetric shape to^{__}each of all of the first four prime numbers of Universe: 1, 2, 3, 5. (Compare Sec. 100.321.) 
1033.127 These clickstop, wholetetravolumed, symmetrical geometries have common centers of volume, and all are concentrically and intersymmetrically arrayed within the rhombic dodecahedron. In this concentric symmetric array they constitute what we call the cosmic hierarchy of primitive conceptuality of thought and comprehension. Intuitively hypersensitive and seeking to explain the solar system's interplanetary behaviors, Johannes Kepler evolved a concentric model of some of the Platonic geometries but, apparently frustrated by the identification of volumetric unity exclusively with the cube, failed to discover the rational cosmic hierarchy^{__}it became the extraordinary experience of synergetics to reveal this in its first written disclosure of 1944. 
1033.128 It is visually manifest both between and at the "clickstop" states that the smooth intertransforming is fourdimensional, accommodated by local transformations around four axes of system symmetry. The systems' vertices always remain spherically arrayed and describe a smooth, overallsphericcontinuumcontraction from the largest to the smallest tuneinablebythenumbers system states occurring successively between the beyondtuneinable system ranges of the macronothingness and the beyondtuneinable micronothingness. 
Next Section: 1033.180 