Essential hyperbolic Coxeter polytopes
Essential hyperbolic Coxeter polytopes
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本质双曲 Coxeter 多面体
DOI：
10.1007/s11856-013-0046-3
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发表时间：
2009
影响因子：
1
通讯作者：
P. Tumarkin
中科院分区：
文献类型：
--
作者：
A. Felikson;P. Tumarkin
我们引入了基本双曲 Coxeter 多面体的概念，作为符合某些极小条件的多面体。双曲反射群的分类问题可以很容易地简化为基本 Coxeter 多面体的分类。我们确定了一个潜在的大多面体组合类，其中特别包含已知必需的维数至少为 6 的所有紧凑双曲 Coxeter 多面体，并证明该类仅包含有限多个多面体。我们还构建了一种有效的多胞形分类算法，在四维情况下实现，并提出了基本多胞形数量有限性的猜想。
We introduce a notion of an essential hyperbolic Coxeter polytope as a polytope which fits some minimality conditions. The problem of classification of hyperbolic reflection groups can be easily reduced to classification of essential Coxeter polytopes. We determine a potentially large combinatorial class of polytopes containing, in particular, all the compact hyperbolic Coxeter polytopes of dimension at least 6 which are known to be essential, and prove that this class contains finitely many polytopes only. We also construct an effective algorithm of classifying polytopes from this class, realize it in the four-dimensional case, and formulate a conjecture on finiteness of the number of essential polytopes.