Prescribing symmetries and automorphisms for polytopes
Prescribing symmetries and automorphisms for polytopes
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规定多胞体的对称性和自同构
DOI：
10.1090/conm/764/15359
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Williams, Gordon Ian
中科院分区：
文献类型：
--
作者：
Egon, Schulge;Soberón, Pablo;Williams, Gordon Ian
我们研究的有限群出现的组合自同构群或几何对称群的凸多面体。当Γ是凸d-多胞形的组合自同构群的子群，d≥ 3时，存在一个与原多胞形相关的凸d-多胞形，其组合自同构群恰为Γ.当Γ是凸d-多胞形的几何对称群的子群，d≥ 3时，存在与原多胞形相关的凸d-多胞形，其几何对称群和组合自同构群恰为Γ.然后应用这些破缺的结果证明了：对于任意偶数阶阿贝尔群Γ和Γ的任意对合σ，存在一个具有几何对称群Γ的中心对称凸多面体，使得σ对应于中心对称.
We study finite groups that occur as combinatorial automorphism groups or geometric symmetry groups of convex polytopes. When Γ is a subgroup of the combinatorial automorphism group of a convex d-polytope, d≥ 3, then there exists a convex d-polytope related to the original polytope with combinatorial automorphism group exactly Γ. When Γ is a subgroup of the geometric symmetry group of a convex d-polytope, d≥ 3, then there exists a convex d-polytope related to the original polytope with both geometric symmetry group and combinatorial automorphism group exactly Γ. These symmetrybreaking results then are applied to show that for every abelian group Γ of even order and every involution σ of Γ, there is a centrally symmetric convex polytope with geometric symmetry group Γ such that σ corresponds to the central symmetry.