Principles of the Eighteen Faced Deltahedron

Principles of the Eighteen Faced Deltahedron and the Better Defining of Physical Dimensions as Constructable Models 

L. Edgar Otto    07 December 2012

The counting of things, taken as arrays of quasifinite points seems to have unexplainable exceptions to the topological laws used to describe them.  By the count alone we see the anomaly but more so in that we cannot imagine a symmetry to so describe a structure such as the gap in the sequence of the 18 faced deltahedron. 

The relationship of points and lines is not the simple one of an idea of projective duality in interactive dimensions and groups but covers also the more general idea of the linear and the more restricted idea of the so called non-linear.

By these considerations we may better define the idea of dimensions, not merely point out that idea still not shored up even by Cantor.  So too the idea of Dark Matter and Gravity, the nature of coherence in the breaking of this relation equally defined by systems based on strict points or lines of force. 

Outside the anomaly we may find what we distinguish as dark matter or matter in general and gravity as distinct and not necessarily connect although the shadows left by one may influence the other.  We can construct to a fine degree in a relaxed way what Fuller imagines of his Four Dimensional background of the tensegrity that holds things together from that perspective, again the relation between interacting adjacent dimensions on the same level although a dimension up or down.

If the points are relaxed this tensegrity may not hold in the specific cases where the laws are above the idea of what is loose or rigid in constructions or rotations where the quasifinite contiguity of the issue is one of the count.  We can imagine in a loose system of points with rigid lines between them as polyhedra of hexagons, squares and octagons which come near to being a convex shell structure but fail.  We can also imagine the reverse of a rigid system of points and a loose system of edges as in the ten faced deltahedron.  In that case the coherence fails to hold together in the main and the structure responds to or as if an outside force exists, that is the ill defined idea of Gravity.

But the counting has its valid geometrical analogies.  If these ideas were understood better it would be no surprise the physics of Bucky Balls nor the new idea of Graphite used in ways that we might call Bucky Branes, for it is as synergetics a lesser total theory, one that in space reaches the numerology of atomic numbers to uranium in the periodic table.

The more general law than Euler's topological one, and a less general topology of what seems the widest span of changes with some invariant would be to consider these powers where continuous as binary or binary plus something and so on (as Pitkanen discerns) as real squared, zero, or plus or minus one as inverse laws of such subsets as continua.

Statistical methods alone, although things like charges put in a field or on the surface of an object will average out cannot explain the anomaly of the 10faced deltahedron, it is rather foundational physics and not an artifact of our logical and symbol system.  Yet in the greater number of cases these methods do work to a very fine degree as part of the philosophic core landscape.

In a Bucky Brane we can imagine, intrinsic in the properties of space and counting numbers - for the zero aleph also relates interactively on a more general level to the aleph of the Cantor's continuum, that this not provable or unprovable an artifact of how we see dimensions defined in absolutes instead of another possibility of nonnecessary exceptions of coherence and merging in a more general space.  We can imagine the count in the even dimension two of such a constructed physical brane all the numbers that match, say four times 16 and only one, not two in the center for 81 but in four space zero in the center. In this respect with the  addition of 8 in the center evidently to be interpreted in the three space or vertical direction we find the 89 quasic pixels of which it is also an anomalous substraction itself of what would be the more sensible count of 90 objects.

What we gain here is an explanation and vindication for physics as primary, its constants having a more foundational grounding (Which Rowlands maintained as primary over the math while exploring foundations) for such laws as real, as R or 2^R space and R can be for example Mersenne merge at this fine singularity like structure of the quasifinite anomaly.  It is not just the idea of mass that grounds physics and reality nor the idea of the nature and distinguishing of inertia's.  But it also restricts the evolution of the world that constructable processes regardless of the geometry involve evolve over some intelligible measure of time, it continuous or hidden in its symmetries or not. 

We shore up also the relation independent of direction of entropy states so finely balanced like on the 10face deltahedron itself as that which selects out of endless landscapes an analogous singularity of all that is real implied in being or creative force from the nothingness (a sort of reverse Rowlands metaphysical axiom). Penrose also is less controversial in his proposal of the relation of stars and black-holes in the seesaw balance of their entropy roles across the Omnium, but this observation too may not be necessarily a universal law where anomalies and analogies are their own relaxed quasifinite exceptions of the rules that in a wider sense verifies or proves the rules, in geometric fact of that paradoxical saying.

There are other general, scalar like multiplications of the brane grids that make for intelligible counts- for one thing 8 or 18 times the 81 and the center pixel in a constant state of shift in equal probable directions that may be described in some representations as a half dihedron, one face and no volume.  But in the count as to what we imagine in some higher unified space as say a maximum symmetry we may still make a shift of one or imagine more than the maximum that in fact nature may express although rarely.  It will be quite the recreation and formal presentation for those willing to investigate and follow numbers in this light.

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