Symmetries of 3-polytopes with fixed edge lengths
Metric Geometry
2020-11-24 v2 Combinatorics
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.
Keywords
Cite
@article{arxiv.1808.09495,
title = {Symmetries of 3-polytopes with fixed edge lengths},
author = {Egor Morozov},
journal= {arXiv preprint arXiv:1808.09495},
year = {2020}
}
Comments
6 pages, 3 figures, a minor gap in the proof of the former Lemma 1 (now Lemma 2) is filled, the proof of the former Lemma 2 (now Lemma 3) is simplified