Hypertope is a generalization of the concept of polytope, which in turn generalizes the concept of a map and hypermap, to higher rank objects. Regular hypertopes with spherical residues, which we call regular locally spherical hypertopes, must be either of spherical, euclidean, or hyperbolic type. That is, the type-preserving automorphism group of a locally spherical regular hypertope is a quotient of a finite irreducible, infinite irreducible, or compact hyperbolic Coxeter group. We classify the locally spherical regular hypertopes of spherical and euclidean type and investigate finite hypertopes of hyperbolic type, giving new examples and summarizing some known results.

中文翻译：

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局部球面规则超表的探索

Hypertope 是 polytope 概念的推广，它反过来将映射和超映射的概念推广到更高级别的对象。具有球形残基的规则超曲面，我们称之为规则局部球形超曲面，必须是球形、欧几里得或双曲线类型。也就是说，局部球面正则双曲面的类型保留自同构群是有限不可约、无限不可约或紧双曲 Coxeter 群的商。我们对球型和欧几里得型的局部球面规则超曲面进行分类，研究双曲型的有限超曲面，给出新的例子并总结了一些已知的结果。