Computing symmetry groups of polyhedra. Issue Volume 17:Issue A(2014) (October 2014)

• Record Type: Journal Article
• Authors: Bremner, David; Dutour Sikirić, Mathieu; Pasechnik, Dmitrii V.; Rehn, Thomas; Schürmann, Achill
• Is Part Of: LMS journal of computation and mathematics. Volume 17:Issue A(2014)
• Page Start: 565
• Page End: 581
• Publication Date: 2014-10
• Subjects: 20B25, -- 52B15 (primary)
• DOI: 10.1112/S1461157014000400
• Languages: English
• ISSNs: 1461-1570

Abstract

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.