论文标题
在schläfli的手性延伸的符号上
On the Schläfli symbol of chiral extensions of polytopes
论文作者
论文摘要
给定一个抽象的$ n $ -polytope $ \ MATHCAL {K} $，一个抽象$（n+1）$ - Polytope $ \ Mathcal {p} $是$ \ Mathcal {K {K} $的扩展，如果所有$ \ Mathcal {p} $的所有方面对$ \ nmathcal ismorphic is osomorphic is osomorphic is iasomorphic is iasomorphic is Mathcal ismorphic is iasomorphic is iasomorphic is Mathcal}。手性多层人士是具有最大旋转对称性的多层，不接受任何反射。如果$ \ mathcal {p} $是$ \ mathcal {k} $的手性扩展，则确定$ \ Mathcal {p} $的Schläfli符号的最后一项。在本文中，我们介绍了某些手性多面体的手性扩展的一些构建$ \ Mathcal {p} $，以至于$ \ Mathcal {p} $的Schläfli符号的最后一个条目是任意的。
Given an abstract $n$-polytope $\mathcal{K}$, an abstract $(n+1)$-polytope $\mathcal{P}$ is an extension of $\mathcal{K}$ if all the facets of $\mathcal{P}$ are isomorphic to $\mathcal{K}$. A chiral polytope is a polytope with maximal rotational symmetry that does not admit any reflections. If $\mathcal{P}$ is a chiral extension of $\mathcal{K}$, then all but the last entry of the Schläfli symbol of $\mathcal{P}$ are determined. In this paper we introduce some constructions of chiral extensions $\mathcal{P}$ of certain chiral polytopes in such a way that the last entry of the Schläfli symbol of $\mathcal{P}$ is arbitrarily large.
