标题： 关于双曲空间中的ADEG-多面体 显示英文标题

标题： On ADEG-polyhedra in hyperbolic spaces

摘要： 在本文中，我们证明了高维双曲Coxeter多面体的非零二面角不会任意小。具体来说，在维度$n\geq 32$时，它们的形式为$\frac{\pi}{m}$，其中$m\leq 6$。此外，这一性质在所有维度$n\geq 7$的Coxeter多面体中成立，这些多面体的面相互相交。然后，我们开发了一种针对具有指定二面角的Coxeter多面体的构造性过程，由此我们得出了ADEG-多面体的完整分类，这些多面体的特点是没有一对不相交的面，且二面角仅为$\frac{\pi}{2}, \frac{\pi}{3}$和$\frac{\pi}{6}$。 除了某些著名的单形和棱锥外，还有三个特殊的多面体，其中一个是新的多面体$P_{\star}\subset \mathbb H^9$，具有$14$个面。 显示英文摘要

摘要： In this paper, we establish that the non-zero dihedral angles of hyperbolic Coxeter polyhedra of large dimensions are not arbitrarily small. Namely, for dimensions $n\geq 32$, they are of the form $\frac{\pi}{m}$ with $m\leq 6$. Moreover, this property holds in all dimensions $n\geq 7$ for Coxeter polyhedra with mutually intersecting facets. Then, we develop a constructive procedure tailored to Coxeter polyhedra with prescribed dihedral angles, from which we derive the complete classification of ADEG-polyhedra, characterized by having no pair of disjoint facets and dihedral angles $\frac{\pi}{2}, \frac{\pi}{3}$ and $\frac{\pi}{6}$, only. Besides some well-known simplices and pyramids, there are three exceptional polyhedra, one of which is a new polyhedron $P_{\star}\subset \mathbb H^9$ with $14$ facets.