关于多面体手征扩张的Schläfli符号
On the Schläfli symbol of chiral extensions of polytopes
摘要：
给定一个抽象$n$ -多面体$\mathcal{K}$，如果$\mathcal{P}$的所有刻面都同构于$\mathcal{K}$，则抽象$(n+1)$ -多面体$\mathcal{P}$是$\mathcal{K}$的扩展.手征多面体是具有不允许任何反射的最大旋转对称性的多面体。如果$\mathcal{P}$是$\mathcal{K}$的手性延伸，则除了$\mathcal{P}$的Schläfli符号的最后一个条目之外的所有条目都被确定。本文给出了某些手征多胞形的手征扩张$\mathcal{P}$的构造，使得$\mathcal{P}$的Schläfli符号的最后一项是任意大的.
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
