论文标题
紧密的手性多面体
Tight Chiral Polytopes
论文作者
论文摘要
带有schläfli符号$ \ {p_1，\ ldots，p_ {n-1} \} $的手性polytope至少具有$ 2p_1 \ cdots p_ {n-1} $ flags，并且如果符合此较低限制的标志，则称为\ emph {citter}。紧密手性多面体的Schläfli符号被归类为较早的论文，另一篇论文证明，没有$ n \ geq 6 $的紧密手性$ n $ polytopes。在这里，我们证明没有紧张的手性$ 5 $ - 多层型，描述11个紧密手性的家庭$ 4 $ - 多层型，并表明每一种紧张的手性$ 4 $ - Polytope覆盖了其中一个家庭的多层人士。
A chiral polytope with Schläfli symbol $\{p_1, \ldots, p_{n-1}\}$ has at least $2p_1 \cdots p_{n-1}$ flags, and it is called \emph{tight} if the number of flags meets this lower bound. The Schläfli symbols of tight chiral polyhedra were classified in an earlier paper, and another paper proved that there are no tight chiral $n$-polytopes with $n \geq 6$. Here we prove that there are no tight chiral $5$-polytopes, describe 11 families of tight chiral $4$-polytopes, and show that every tight chiral $4$-polytope covers a polytope from one of those families.
