Fig. 1032.30 |
1032.30 Complementary Allspace Filling of Octahedra and Vector Equilibria: The closest packing of concave octahedra, concave vector equilibria, and spherical vector equilibria corresponds exactly to the allspace filling of planar octahedra and planar vector equilibria (see Sec. 470). Approximately half of the planar vector equilibria become concave, and the other half become spherical. All of the planar octahedra become concave (see Illus. 1032.30). |
Fig. 1032.31 |
1032.31 Concave octahedra and concave vector equilibria close-pack together to define the voids of an array of closest-packed spheres which, in conjunction with the spherical vector equilibria, fill allspace. This array suggests how energy trajectories may be routed over great-circle geodesic arcs from one sphere to another, always passing only through the vertexes of the array^{__}which are the 12 external vertexes of the vector equilibria and the only points where the closest-packed, uniradius spheres touch each other (see Illus. 1032.31). |
1033.00 Intertransformability Models and Limits
[1033.00-1033.92 Involvement Field Scenario]
1033.010 Generation of the Involvement Field in Which Synergetics Integrates Topology, Electromagnetics, Chemistry and Cosmology |
1033.011 Commencing with the experimentally demonstrated proof that the tetrahedron is the minimum structural system of Universe (i.e., the vectorially and angularly self-stabilizing minimum polyhedron consisting of four minimum polygons in omnisymmetrical array), we then discover that each of the four vertices of the tetrahedron is subtended by four "faces," or empty triangular windows. The four vertices have proven to be only whole-range tunable and point-to-able noise or "darkness" centers^{__}which are primitive (i.e., as yet frequency-blurred), systemic somethings (see Secs. 505.65, 527.711, and 1012.33) having six unique angularly intersightable lines of interrelationship whose both-ends-interconnected six lines produce four triangular windows, out through which each of the four system-defining somethings gains four separate views of the same omninothingness of as-yet-untuned-in Universe. As subtunable systems, points are substances, somethings ergo, we have in the tetrahedron four somethings symmetrically arrayed against four nothingnesses. (Four INS versus four OUTS.) |
1033.017 We have elsewhere reviewed the progressive tangential agglomeration of other "spherical" somethings with the otherness observer's spherical something (Secs. 411.01-08) and their four-dimensional symmetry's systemic intermotion blocking and resultant system's interlockage, which locking and blocking imposes total system integrity and permits whole-system-integrated rotation, orbiting, and interlinkage with other system integrities. |
1033.018
Since we learned by experimental proof that our four-dimensional
symmetry
accommodates three axial freedoms of rotation motion
(see the Triangular-cammed, In-
out-and-around, Jitterbug Model, Sec.
465), while also
permitting us to restrain^{3} one of
the four axes of perpendicularity to the four planes,
i.e., of the INS most economically^{__}
or perpendicularly^{__}approaching the tensor relationship's
angularly planed and framed
views through to the nothingness, we find that we may
make a realistic model of the
omniinvolvement field of all eight phases of the tetrahedron's
self-intertransformability.
(Footnote 3: "Restrain" does not mean motionless or "cosmically at rest." Restrain does mean "with the axis locked into congruent motion of another system." Compare a system holding in relative restraint one axis of a four-axis wheel model.) |
Fig. 1033.019 |
1033.019
The involvement field also manifests the exclusively
unique and inviolable
fourfold symmetry of the tetrahedron (see Cheese Tetrahedron,
Sec.
623), which permits
us always to move symmetrically and convergently each^{__}and
inadvertently any or all^{__}of
the four triangular window frames perpendicularly toward
their four subtending
somethingness-converging-point-to-able IN foci, until
all four planes pass through the
same threshold between INness and OUTness, producing
one congruent, zerovolume
tetrahedron. The four inherent planes of the four tensegrity
triangles of Anthony Pugh's
model^{4}* demonstrate the nothingness of their four planes,
permitting their timeless^{__}i.e.,
untuned^{__}nothingness congruence. (See Fig.
1033.019.)
The tuned-in, somethingness
lines of the mathematician, with their inherent self-interferences,
would never permit a
plurality of such lines to pass through the same somethingness
points at the same time (see
Sec.
517).
(Footnote 4: This is what Pugh calls his "circlit pattern tensegrity," described on pages 19-22 of his An Introduction to Tensegrity (Berkeley: University of California Press, 1976.) |
1033.020 Four-triangular-circuits Tensegrity: The four-triangular-circuits tensegrity relates to the four great circles of the vector equilibrium. The four great circles of the vector equilibrium are generated by the four axes of vector equilibrium's eight triangular faces. Each of the four interlocking triangles is inscribed within a hexagonal circuit of vectors^{__}of four intersecting hexagonal planes of the vector equilibrium. These tensegrity circuits relate to the empty tetrahedron at its center. (See Secs. 441.021, 938.12, and 1053.804.) |
1033.022 The involvement field also identifies the unique cosmically inviolate environment domain of convergent-divergent symmetrical nuclear systems, i.e., the vector equilibrium's unique domain provided by one "external" octahedron (see Sec. 415.17), which may be modeled most symmetrically by the 4-tetravolume octahedron's symmetrical subdivision into its eight similar asymmetric tetrahedra consisting of three 90-degree angles, three 60-degree angles, and six 45-degree angles, whose 60-degree triangular faces have been addressed to each of the vector equilibrium's eight outermost triangular windows of each of the eight tetrahedra of the 20-tetravolume vector equilibrium. |
Next Section: 1033.030 |