1033.50 Quanta Loss by Congruence
1033.51 Euler’s Uncored Polyhedral Formula:
$`V + F = E + 2`$
Vector Equilibrium
Octahedron
Tetrahedron
1033.52 Although superficially the tetrahedron seems to have only six vector edges, it has in fact 24. The sizeless, primitive tetrahedron—conceptual independent of size—is quadrivalent, inherently having eight potential alternate ways of turning itself inside out—four passive and four active—meaning that four positive and four negative tetrahedra are congruent. (See Secs. 460 and 461.)
1033.53 The vector equilibrium jitterbug provides the articulative model for demonstrating the always omnisymmetrical, divergently expanding or convergently contracting intertransformability of the entire primitive polyhedral hierarchy, structuring as you go in an omnitriangularly oriented evolution.
1033.54 As we explore the interbonding (valencing) of the evolving structural components, we soon discover that the universal interjointing of systems—and their foldability—permit their angularly hinged convergence into congruence of vertexes (single bonding), vectors (double bonding), faces (triple bonding), and volumetric congruence (quadri-bonding). Each of these multicongruences appears only as one vertex or one edge or one face aspect. The Eulerean topological accounting as presently practiced—innocent of the inherent synergetical hierarchy of intertransformability—accounts each of these multicongruent topological aspects as consisting of only one of such aspects. This misaccounting has prevented the physicists and chemists from conceptual identification of their data with synergetics’ disclosure of nature’s comprehensively rational, intercoordinate mathematical system.
1033.55 Only the topological analysis of synergetics can account for all the multicongruent—doubled, tripled, fourfolded—topological aspects by accounting for the initial tetravolume inventories of the comprehensive rhombic dodecahedron and vector equilibrium. The comprehensive rhombic dodecahedron has an initial tetravolume of 48; the vector equilibrium has an inherent tetravolume of 20; their respective initial or primitive inventories of vertexes, vectors, and faces are always present—though often imperceptibly so—at all stages in nature’s comprehensive 48 convergence transformation.
1033.56 Only by recognizing the deceptiveness of Eulerean topology can synergetics account for the primitive total inventories of all aspects and thus conceptually demonstrate and prove the validity of Boltzmann’s concepts as well as those of all quantum phenomena. Synergetics’ mathematical accounting conceptually interlinks the operational data of physics and chemistry and their complex associabilities manifest in geology, biology, and other disciplines.