Thursday, September 1, 2011
Polyomnic Plyctals (Four Space Unfoldings)
Polyomnic Plyctals (Four Space Unfolding's)
When extended into four space these fold and cut concepts find many wonderful and new patterns and physical principles. Some of which I may post later or as an illustration of the original notes of last night.
Briefly, in the n-Phoenix physics (Phph) we have three areas which meet sometimes coincidentally at a singularity point of three kinds of singularities (for example a point itself in a structure may be considered a cut as also the count of edges and planes). We have the Polyomnic Structure (QsPh), the topological guage (QlPh) and the Physicality entity (QmPh) all part of the Omnium and roughly corresponding to quasic, qlassical and quantum physics.
The three forms of singularity, the singularity itself and the first pixel, the complex over all of quasic space and half of the infinity between, may meet in a point that expels one of eight cubes of the hypercube as unfolded.
These ideas may exist in the literature such as the proof for the twelve in closed packed sphere although here we by volumes can make use of the room for one more and a part of one more- a question to ask again of foundations. In any case the level of ideas here is found from the foundations up rather than from the topological common level down. There are disphenoids possible as a dual to these polynomic rhombidodecahedra just as in the natural dimensions we can think of analogs to the dihedron of zero volume and two faces- that is say for example zero hypervolume and two cube faces connected... and so on.
Such "conflangelation" (condenser flangelation) as superimposed doubling is equivalent to cutting as virtual guage alternative lattice is in effect a folding.
Of course if these principles were understood and accessible in general perhaps there would not be all the confusion, the scandal really, of what to do to describe the yang 6D manifolds and so on. Is there a uniqueness of primes (p-adic TGD-like) based on the general axiom of hyperspace where orthogons such as two branes may intersect a a point (two ditopes of many dimensions intersect at a singularity).