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arXiv · 1808.09495

Symmetries of 3-polytopes with fixed edge lengths

Egor Morozov
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Abstract

We consider an interesting class of combinatorial symmetries of polytopes which we call \emph{edge-length preserving combinatorial symmetries}. These symmetries not only preserve the combinatorial structure of a polytope but also map each edge of the polytope to an edge of the same length. We prove a simple sufficient condition for a polytope to realize all edge-length preserving combinatorial symmetries by isometries of ambient space. The proof of this condition uses Cauchy's rigidity theorem in an unusual way.

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Egor Morozov. 2020-11-23. Symmetries of 3-polytopes with fixed edge lengths. https://doi.org/10.33048/semi.2020.17.110

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