I wish to distinguish the golden ratio symbols tau (European) and phi (United States) for the kinds of these hyper deltatope symmetries. As in Sabine's intuition of Analog Duality and general proof that Poincare in reduction to a final approached abstract point in a manifold is not the last and most general word. Taudeltatopes are analogs to Kepler's 14 solids where the cubic rhombihedron can have the square and triangular faces across the diagonal rotated 90 degress (or not as there are two twisted or torsion and parallel analog varieties. This is the last face problem in construction of polyhedra, Tau as in tauon as if the sixth quark or 6th face exists as necessary over the 5 in these issues between infinite reflections between adjacent (even and odd) dimensions transitive globally over any particular node point but only realized at one point expressed linearly.
In this cube construction we have 4 hexagons ( directions Pitkanen-like xy parallels looped or stacked as one representation) 4 pentagons, and 4 rhomboids (diamond of four edges) all of which can be abstractly subdivided triangularly.
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