623.00 Coordinate Symmetry
623.10 Cheese Tetrahedron: If we take a symmetrical polyhedron of cheese, such as a cube, and slice parallel to one of its faces, what is left over is no longer symmetrical; it is no longer a cube. Slice one face of a cheese octahedron, and what is left over is no longer symmetrical; it is no longer an octahedron. If you try slicing parallel to one of the faces of all the symmetrical geometries, i.e., all the Platonic and Archimedean “solids,” each made of cheese, what is left after the parallel slice is removed is no longer the same symmetrical polyhedron but with one exception, the tetrahedron.
623.11 Let us take a foam rubber tetrahedron and compress on one of its four faces inward toward its opposite vertex instead of slicing it away. It remains symmetrical, but smaller. If we pull out on a second face at the same rate that we push in on the first face, the tetrahedron will remain the same size. It is still symmetrical, but the pushing of the first face made it get a little smaller, while the pulling of the second face made it get a little larger. By pushing and pulling at the same rate, it remains the same size, but its center of gravity has to move because the whole tetrahedron seems to move. As it moves, it receives one positive alteration and one negative alteration. But in moving it we have acted on only two of the tetrahedron’s four faces. We could push in on the third face at a rate different from the first couple, which is already operating; and we could pull out the fourth face at the same rate we are pushing in on the third face. We are introducing two completely different rates of change: one being very fast and the other slow; one being very hard and the other soft. We are introducing two completely different rates of change in physical energy or change in abstract metaphysical conceptuality. These completely different rates are coupled so that the tetrahedron as a medium of exchange remains both symmetrical and the same size, but it has to change its position to accommodate two alterations of the center of gravity positioning but not in the same plane or the same line. So it will be moving in a semihelix. This is another manifestation of precessional resultants.
623.12 The tetrahedron’s four faces may be identified as A, B, C, andZ). Any two of these four faces can be coupled and can be paired with the other two to provide the dissimilar energy rate-of-exchange accommodation.
-. There are six possible couples: AB, AC, AD, BC, BD, CD, and
these six couples may be mterpaired in-ways; therefore, -= 15;
which 15 ways are:
(1) AB-AC (6) AC-AD (11) AD-BD
(2) AB-AD (7) AC-BC (12) AD-CD
(3) AB-BC (8) AC-BD (13) BC-BD
(4) AB-BD (9) AC-CD (14) BD-CD
(5) AB-CD (10) AD-BC (15) BD-CD
Thus any one tetrahedron can accommodate 15 different amplitude (A) and, or frequency (F) of interexchanging without altering the tetrahedron’s size while, however, always changing the tetrahedron’s apparent occurrence locale; therefore the number of possible alternative exchanges are three; i.e., AA, AF, FF; therefore, 3 x 15 = 45 different combinations of interface couplings and message contents can be accommodated by the same apparent unit-size tetrahedron, the only resultants of which are the 15 relocations of the tetrahedrons and the 45 different message accommodations.
623.13 Tetrahedron has the extraordinary capability of remaining symmetrically coordinate and entertaining 15 pairs of completely disparate rates of change of three different classes of energy behaviors in respect to the rest of Universe and not changing its size. As such, it becomes a universal joint to couple disparate actions in Universe. So we should not be surprised at all to find nature using such a facility and moving around Universe to accommodate all kinds of local transactions, such as coordination in the organic chemistry or in the metals. The symmetry, the fifteen ess, the sixness, the fourness, and the threeness are all constants. This induced “motion,” or position displacement, may explain all apparent motion of Universe. The fifteenness is unique to the icosahedron and probably valves the 15 great circles of the icosahedron.
623.14 A tetrahedron has the strange property of coordinate symmetry, which permits local alteration without affecting the symmetrical coordination of the whole. This means it is possible to receive changes in respect to one part or direction of Universe and not in the direction of the others and still have the symmetry of the whole. In contradistinction to any other Platonic or Archimedean symmetrical “solid,” only the tetrahedron can accommodate local asymmetrical addition or subtraction without losing its cosmic symmetry. Thus the tetrahedron becomes the only exchange agent of Universe that is not itself altered by the exchange accommodation.
623.20 Size Comes to Zero: There are three different aspects of size linear, areal, and volumetricand each aspect has a different velocity. As you move one of the tetrahedron’s faces toward its opposite vertex, it gets smaller and smaller, with the three different velocities operative. But it always remains a tetrahedron with six edges, four vertexes, and four faces. So the symmetry is not lost and the fundamental topological aspectits 60-degreeness never changes. As the faces move in, they finally become congruent to the opposite vertex as all three velocities come to zero at the same time. The 60-degreeness, the six edges, the four faces, and the symmetry were never altered because they were not variables. The only variable was size. Size alone can come to zero. The conceptuality of the other aspects never changes.