*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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