1033.121 Click-stop 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 closest-packed, unit-radius 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 closest-packed spheres and the complex of isotropic vector matrixes required to accommodate the varying radii as well as their ultra- and inffapermeating: 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 always-and- only-co-occurring, non-tuned-in cosmic complementations of our only-from-moment-to-moment systematically tuned-in conceptionings. Synergetics’ always symmetrical, complementarity expanding and contracting intertransformings disclose a succession of “local way stations.” Progressive arrival at these convergent-divergent “way station” states discloses a succession of immediately neighboring, larger-to-smaller, 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 closingscissor-hinge-wise 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 contractingdepending 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, 20-tetravolume vector equilibrium of 12 vertices, 14 faces, and 24 vector edges shrinks its vertex- described spherical domain, it may receive one quantum of energy released entropically by some elsewhere-in-Universe 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 syn- tropically harvested by the 20-tetravolume vector equilibrium, and, constituting one quantum of energy, they will structurally stabilize the shrinking 20- tetravolume vector equilibrium >4-tetravolume 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 sixall the while the icosahedron’s ever-shrinking 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 edgesas well as the six compressed vector edgesnow appears as one; and each of the congruent pairs is now topologically countable only as onein this instance as the six vertices, eight faces, and 12 edges of the suddenly realized octahedron of tetra-volume 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 statethe octahedron, in its simplest and completely symmetrical conditionis what we mean by a “click-stop” or “way station” state.
1033.126 Assessing accurately the “click-stop” volumes of the inter- transformative hierarchy in terms of the volume of the tetrahedron equaling one, we find that the relative tetravolumes of these primitive polyhedrawhen divergent are successively, 1, 2l/z, 3, 22, 5, 6, 20, 24, and thenconvergingfrom 24, 20, 6, 5, 22, 3, 2l/z, 1 Change: fix eqn . These omnirational, wholenumber, “click-stop” volumes and their successive topological characteristic numbers elegantly introduceand give unique volumetric shape to each of all of the first four prime numbers of Universe: 1, 2, 3, 5. (Compare Sec. 100.3210
1033.127 These click-stop, whole-tetravolumed, 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 hierarchyit 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 “click-stop” states that the smooth intertransforming is four-dimensional, accommodated by local transformations around four axes of system symmetry. The systems’ vertices always remain spherically arrayed and describe a smooth, overall-spheric-continuum-contraction from the largest to the smallest tune-in-able- by-the-numbers system states occurring successively between the beyond-tune-in-able system ranges of the macronothingness and the beyond-tune-in- able micronothingness.