Computing symmetry groups of polyhedra
Computing symmetry groups of polyhedra
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DOI：
10.1112/s1461157014000400
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发表时间：
2014-01-01
影响因子：
--
通讯作者：
Schuermann, Achill
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文献类型：
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作者：
Bremner, David;Sikiric, Mathieu Dutour;Schuermann, Achill
了解多面体的对称性对于分析多面体的结构以及实际的多面体计算都是非常有用的。本文研究了保持多面体线性、射影和组合结构的对称群。在每种情况下，我们给出了算法方法来计算相应的组，并讨论了一些实际经验。对于实际的目的，线性对称群是最重要的，因为它的计算可以直接转化为一个图自同构问题。我们指出如何计算整数分组的线性对称群，例如，在整数线性规划。
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.