Theoretical analysis demonstrates full polytopal realization for all two-vertex premaniplexes in rank at least three, upgrading existing finite-maniplex realization theorems.
For every rank r>=3, there are 2^r-1 connected two-vertex premaniplexes. We prove that every one of them is the full symmetry type graph of a finite abstract polytope. The main argument localizes the support of the recursive regular-polytopal voltage construction, treats arbitrary sets of internal link colors simultaneously, and establishes the remaining path-intersection identity. Two exceptional rank-four base types are handled by exact finite computation. This upgrades the known finite-maniplex realization theorem to a finite-polytopal realization theorem in every rank at least three. Status: Public Beta; internally verified candidate proof; external mathematical review pending.
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