986.770 Shell Growth Rate Predicts Proton and Neutron Population of the Elements 
986.772
If we look at Fig.
222.01
(Synergetics 1), which shows
the three successive
layers of closestpacked spheres around the prime nuclear
sphere, we find the successive
layer counts to be 12, 42, 92 . . . that is, they are
"frequency to the second power times 10
plus 2." While we have been aware for 40 years that
the outermost layer of these
concentric layers is 92, and that its first three layers
add to

986.773 Recently, however, a scientist who had been studying synergetics and attending my lectures called my attention to the fact that the first closestpacked layer 12 around the nuclear sphere and the second embracing closestpacked layer of 42 follow the same neutron count, combining with the outer layer number of protons^{__}as in the 92 uraniumlayer case^{__}to provide a physically conceptual model of magnesium and molybdenum. (See Table 419.21.) 
986.800 Behavioral Proclivities of Spheric Experience 
986.810 Discard of Abstract Dimensions 
986.813 Because they cannot qualify as laws if any exceptions to them are found, the generalizable laws of Universe are inherently eternaltimelesssizeless. Sizing requires time. Time is a cosmically designed consequence of humanity's having been endowed with innate slowness of apprehension and comprehension, which lags induce timelapsealtered concepts. (Compare Sec. 529.09.) 
Fig. 986.816 
986.816 In conventional geometry the linear characteristics and the relative sizes of lines dominate the conceptioning and its nomenclatureas, for instance, using the term "equiangular" triangle because only lengths or sizes of lines vary in time. Lines are unlimited in size and can be infinitely extended, whereas angles are discrete fractions of a discrete whole circle. Angles are angles independently of the lengths of their edges. (See Sec. 515.10.) Lengths are always special timesize cases: angles are eternally generalized.... We can say with scientific accuracy: "identical equiangular triangles." (See Fig. 986.816.) 
986.819 Synergetics procedure is always from a given whole to the particular fractional angles of the whole system considered. Synergetics employs multiplication only by division.... only by division of finite but nonunitarilyconceptual Scenario Universe, subdivided into initially whole primitive systems that divide whole Universe into all the Universe outside the system, all the Universe inside the system, and the little bit of Universe that provides the relevant set of special case stars of experience that illuminatingly define the vertexes of the considered primitive generalized system of consideration. (See Sec. 509.) Conventional geometry "abstracts" by employment of nonexistent^{__}ergo, nondemonstrable^{__}parts, and it compounds a plurality of those nonexistents to arrive at supposedly real objects. 
986.821 Synergetics identifies all of its primitive hierarchy and their holistic subdivisions only by their timelesssizeless relative angular fractional subdivisions of six equiangular triangles surrounding a point, which hexagonal array equals 360 degrees, if we assume that the three angles of the equiangular triangle always add up to 180 degrees. Synergetics conducts all of its calculations by spherical trigonometry and deals always with the central and surface angles of the primitive hierarchy of pretimesize relationships of the symmetrically concentric systems around any nucleus of Universe^{__}and their seven greatcircle symmetries of the 25 and 31 greatcircle systems (Sec. 1040). The foldability of the four greatcircle planes demonstrates the four sets of hexagons omnisurrounding the cosmic nucleus in omni60degree angular symmetry. This we call the VE. (See Sec. 840.) Angular identities may be operationally assumed to be identical: There is only one equiangular triangle, all of its angles being 60 degrees. The 60ness comes from the 60 positive and 60 negative, maximum number of surface triangles or T Quanta Modules per cosmic system into which convergentdivergent nuclear unity may be subdivided. The triangle, as physically demonstrated by the tube necklace polygons (Sec. 608), is the only selfstabilizing structure, and the equiangular triangle is the most stable of all triangular structures. Equiangular triangles may be calculatingly employed on an "identical" basis. 
986.830 Unrealizability of Primitive Sphere 
986.831 As is shown elsewhere (Sec. 1022.11), synergetics finds that the abstract Greek "sphere" does not exist; nor does the quasisphere^{__}the sensereported "spheric" experiencings of humans^{__}exist at the primitive stage in company with the initial cosmic hierarchy of timelesssizeless symmetric polyhedra as defined by the six positive and six negative cosmic degrees of freedom and their potential force vectors for adequately coping with all the conditions essential to maintain the individual integrity of minmax primitive, structural, presubdivision systems of Universe. 
986.833 The volume of a static quasisphere of unit vector length (radius = l) is 4.188. Each quasisphere is subexistent because it is not as yet spun and there is as yet no time in which to spin it. Seeking to determine anticipatorily the volumetric value of the asyet onlypotential sphere's asyettobespun domain (as recounted in Secs. 986.206214), I converted my synergetics constant 1.0198255 to its ninth power, as already recounted and as intuitively motivated to accommodate the energetic factors involved, which gave me the number 1.192 (see Sec. 982.55), and with this ninthpowered constant multiplied the incipient sphere's alreadythirdpowered volume of 4.188, which produced the twelfth powered value 4.99206, which seems to tell us that synergetics' experimentally evidenceable onlybyhighfrequencyspinning polyhedral sphere has an unattainable but evermorecloselyapproached limit tetravolume5.000 (alpha) with however a physically imperceptible 0.007904 volumetric shortfall of tetravolume5, the limit 4.99206 being the maximum attainable twelfthpowered dynamism^{__}being a sphericity far more perfect than that of any of the planets or fruits or any other of nature's myriads of quasispheres, which shortfallers are the rule and not the exceptions. The primitively nonconceptual, only incipient sphere's onlypotentiallytobedemonstrated domain, like the square root of minus one, is therefore a useful, approximatemagnitude, estimating tool, but it is not structurally demonstrable. The difference in magnitude is close to that of the T and E Quanta Modules. 
986.834 Since structure means an interselfstabilized complexofevents patterning (Sec. 600.01), the "spheric" phenomenon is conceptually^{__}sensorially^{__}experienceable only as a timesize highfrequency recurrence of events, an onlybydynamic sweepout domain, whose complex of involved factors is describable only at the twelfthpower stage. Being nonstructural and involving a greater volumetric sweepout domain than that of their unrevolved structural polyhedral domains, all quasispheres are compressible. 
986.840 Primitive Hierarchy as Physical and Metaphysical 
986.850 Powerings as Systemicintegrity Factors 
986.857
Not including the

986.860 Rhombic Dodecahedron 6 Minus Polyhedron 5 Equals Unity 
986.861 Highfrequency, triangulated unitradiusvertexed, geodesically interchorded, spherical polyhedral apparencies are also structural developments in timesize. There are therefore two kinds of spherics: the highfrequencyeventstabilized, geodesic, structural polyhedron and the dynamically spun, only superficially "apparent" spheres. The static, structural, multifaceted, polyhedral, geodesic sphere's vertexes are uniformly radiused only by the generalized vector, whereas the only superficially spun and only apparently profiled spheres have a plurality of vertexial distances outward from their systemic center, some of which distances are greater than unit vector radius while some of the vertexes are at less than unit vector radius distance. (See Fig. 986.861.) 
986.862 Among the symmetrical polyhedra having a tetravolume of 5 and also having radii a little more or a little less than that of unit vector radius, are the icosahedron and the enenicontahedron whose mean radii of spherical profiling are less than four percent vectoraberrant. There is, however, one symmetrical primitive polyhedron with two sets of its vertexes at greater than unit radius distance outwardly from their system's nucleic center; that is the rhombic dodecahedron, having, however, a tetravolume of 6. The rhombic dodecahedron's tetravolume of 6 may account for the minimum intersystemness in pure principle, being the space between omniclosestpacked unitradius spheres and the spheres themselves. And then there is one symmetric primitive polyhedron having a volume of exactly tetravolume 5 and an interpattern radius of 0.9995 of one unit vector; this is the T Quanta Module phase rhombic triacontahedron. There is also an additional rhombic triacontahedron of exact vector radius and a tetravolume of 5.007758031, which is just too much encroachment upon the rhombic dodecahedron 6 minus the triacontahedron 5 6  5 = 1, or one volumetric unit of unassigned cosmic "failsafe space": BANG^{__}radiationentropy and eventual turnaround precessional fallin to syntropic photosynthetic transformation into one of matter's four states: plasmic, gaseous, liquid, crystalline. 
986.863 All the hierarchy of primitive polyhedra were developed by progressive greatcirclespun hemispherical halvings of halvings and trisectings of halvings and quintasectings (see Sec. 100.1041) of halvings of the initial primitive tetrahedron itself. That the rhombic triacontahedron of contactfacet radius of unit vector length had a trigonometrically calculated volume of 4.998 proved in due course not to be a residual error but the "critical difference" between matter and radiation. This gives us delight in the truth whatever it may be, recalling that all the discoveries of this chronicle chapter were consequent only to just such faith in the truth, no matter how initially disturbing to misinformed and misconditioned reflexes it may be. 
986.870 Nuclear and Nonnuclear Module Orientations 
986.871 The rhombic triacontahedron may be fashioned of 120 trivalently bonded T Quanta Module tetrahedra, or of either 60 bivalently interbonded positive T Modules or of 60 bivalently interbonded negative T Modules. In the rhombic triacontahedron we have only radiantly arrayed basic energy modules, arrayed around a single spheric nuclear inadequate volumetric domain with their acute "corners" pointed inwardly toward the system's volumetric center, and their centers of mass arrayed outwardly of the system^{__}ergo, prone to escape from the system. 
986.872 In the tetrahedron constructed exclusively of 24 A Modules, and in the octahedron constructed of 48 A and 48 B Modules, the asymmetric tetrahedral modules are in radical groups, with their acute points arrayed outwardly of the system and their centers of mass arrayed inwardly of the system^{__}ergo, prone to maintain their critical mass interattractive integrity. The outer sharp points of the A and B Modules are located at the centers of the four or six corner spheres defining the tetrahedron and octahedron, respectively. The fact that the tetrahedron's and octahedron's A and B Modules have their massive centers of volume pointing inwardly of the system all jointly interarrayed in the concentric layers of the VE, whereas in the rhombic triacontahedron (and even more so in the halfCouplers of the rhombic dodecahedron) we have the opposite condition^{__}which facts powerfully suggest that the triacontahedron, like its congruent icosahedron's nonnuclear closestpossiblepacked omniarray, presents the exclusively radiational aspect of a "one" or of a "no" nuclearspherecentered and isolated most "spheric" polyhedral system to be uniquely identified with the nonnuclear bubble, the onemoleculedeep, kineticallyescapeprone, gasmoleculescontaining bubble. 
986.8721 In the case of the rhombic dodecahedra we find that the centers of volume of their halfCouplers' A and B Modules occur almost congruently with their respective closestpacked, unitradius sphere's outward ends and thereby concentrate their energies at several sphericalradius levels in respect to a common nuclearvolumeadequate center^{__}all of which suggests some significant relationship of this condition with the various sphericalradius levels of the electron "shells." 
986.873 The tetrahedron and octahedron present the "gravitational" model of self andotherness interattractive systems which inherently provide witnessable evidence of the systems' combined massive considerations or constellations of their interbindings. 
986.874 The highly varied alternate A and B Module groupings permitted within the same primitive rhombic dodecahedron, vector equilibrium, and in the Couplers, permit us to consider a wide spectrum of complexedly reorientable potentials and realizations of intermodular behavioral proclivities Lying in proximity to one another between the extreme radiational or gravitational proclivities, and all the reorientabilities operative within the same superficially observed space (Sec. 954). All these large numbers of potential alternatives of behavioral proclivities may be circumferentially, embracingly arrayed entirely within the same superficially observed isotropic field. 
Next Section: 987.00 