论文标题
所有多面体都是固定的几何形状：表征K-轨道抽象多型的自动形态群体
All polytopes are coset geometries: characterizing automorphism groups of k-orbit abstract polytopes
论文作者
论文摘要
摘要多面体将凸多属的经典概念推广到更通用的组合结构。研究最多的是常规和手性多面体，众所周知，它们可以从其自动形态群中构造为固定的几何形状。对于2和3轨道3-派系，也已知这是正确的。在本文中，我们表明，每个抽象的$ n $ - 多重台面都可以构造为固定几何形状。这种结构是通过在发电机，关系和交点条件下，由给定的对称类型图的$ K $ -Orbit Polytope的自动形态组的表征来完成。此外，我们使用这些结果表明，对于所有$ k \ neq 2 $，存在$ k $ -orbit $ n $ n $ - 带有布尔汽车组的$ n $ polytopes，对于所有$ n \ geq 3 $。
Abstract polytopes generalize the classical notion of convex polytopes to more general combinatorial structures. The most studied ones are regular and chiral polytopes, as it is well-known, they can be constructed as coset geometries from their automorphism groups. This is also known to be true for 2- and 3- orbit 3-polytopes. In this paper we show that every abstract $n$-polytope can be constructed as a coset geometry. This construction is done by giving a characterization, in terms of generators, relations and intersection conditions, of the automorphism group of a $k$-orbit polytope with given symmetry type graph. Furthermore, we use these results to show that for all $k\neq 2$, there exist $k$-orbit $n$-polytopes with Boolean automorphism groups, for all $n\geq 3$.
