English

Computing symmetry groups of polyhedra

Combinatorics 2019-02-20 v3 Group Theory Metric Geometry

Abstract

Knowing the symmetries of a polyhedron can be very useful for the analysis of its structure as well as for practical polyhedral computations. In this note, we study symmetry groups preserving the linear, projective and combinatorial structure of a polyhedron. In each case we give algorithmic methods to compute the corresponding group and discuss some practical experiences. For practical purposes the linear symmetry group is the most important, as its computation can be directly translated into a graph automorphism problem. We indicate how to compute integral subgroups of the linear symmetry group that are used for instance in integer linear programming.

Keywords

Cite

@article{arxiv.1210.0206,
  title  = {Computing symmetry groups of polyhedra},
  author = {David Bremner and Mathieu Dutour Sikiric and Dmitrii V. Pasechnik and Thomas Rehn and Achill Schürmann},
  journal= {arXiv preprint arXiv:1210.0206},
  year   = {2019}
}

Comments

20 pages, 1 figure; containing a corrected and improved revision

R2 v1 2026-06-21T22:13:31.275Z