Symmetries of 3-polytopes with fixed edge lengths

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Symmetries of 3-polytopes with fixed edge lengths

Siberian Electronic Mathematical Reports. 2020. Vol. 17. No. n/a. P. 1580–1587.

E. A. Morozov

We consider an interesting class of combinatorial symmetries of polytopes which we call 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 sucient 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.

Research target: Mathematics

Language: English

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