ON d-DIMENSIONAL COMPACT HYPERBOLICCOXETER POLYTOPES WITH d + 4 FACETS

PAVEL TUMARKIN; ANNA FELIKSON

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ON d-DIMENSIONAL COMPACT HYPERBOLICCOXETER POLYTOPES WITH d + 4 FACETS

机译：d + 4面的d维紧实双曲线双多边形

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摘要

We prove that there are no compact Coxeter polytopes with di- 4 facetsin a hyperbolic space of dimension d > 7. This estimate is sharp: examples of suchpolytopes in dimensions d < 7 were found by V. O. Bugaenko in 1984. We also showthat in dimension 7 there is a unique polytope with 11 facets.

机译：我们证明在尺寸为d> 7的双曲空间中，没有紧凑的Coxeter多面体为di-4面。这一估计很明确：VO Bugaenko在1984年发现了尺寸为7的多面体实例。有一个具有11个方面的独特多面体。

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《Transactions of the Moscow Mathematical Society for the year ...》 |2008年第null期|共47页
作者
PAVEL TUMARKIN; ANNA FELIKSON;
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正文语种 eng
中图分类数学;
关键词
dimension; hyperbolic space; polytope;

机译：尺寸;双曲空间;多面体;

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1. 复射影空间和四元数射影空间中紧致实极小超曲面的谱几何 [J] . 瞿成勤, 欧阳崇珍东北数学：英文版 . 1998,第003期
2. ON d-DIMENSIONAL COMPACT HYPERBOLICCOXETER POLYTOPES WITH d + 4 FACETS [J] . PAVEL TUMARKIN, ANNA FELIKSON Transactions of the Moscow Mathematical Society for the year ... . 2008,第Null期

机译：d + 4面的d维紧实双曲线双多边形
3. THE CLASSIFICATION OF COMPACT HYPERBOLIC COXETER D-POLYTOPES WITH D+2 FACETS [J] . Esselmann F. Commentarii Mathematici Helvetici . 1996,第2期

机译：具有D + 2面的紧凑型双曲面Coxeter D-Polypokes的分类
4. Volume, Facets and Dual Polytopes of Twinned Chain Polytopes [J] . Tsuchiya Akiyoshi Annals of combinatorics . 2018,第4期

机译：孪晶链多粒子的体积，刻面和双多面孔
5. On the Complexity of Some Facet-Defining Inequalities of the QAP-Polytope [C] . Pawan Aurora, Hans Raj Tiwary International Conference on Combinatorial Optimization and Applications . 2020

机译：关于QAP-Polytope的一些刻面不等式的复杂性
6. Finding optimized bounding boxes of polytopes in d-dimensional space and their properties in k-dimensional projections. [D] . Shahid, Salman. 2014

机译：在d维空间中找到优化的多面体边界框及其在k维投影中的属性。
7. Linear and Fisher Separability of Random Points in the d-Dimensional Spherical Layer and Inside the d-Dimensional Cube [O] . Sergey Sidorov, Nikolai Zolotykh 2020

机译：线性和FISHER在D尺寸球形层中的随机点和D维立方体内的可分动性
8. On compact hyperbolic Coxeter d-polytopes with d+4 facets [O] . Felikson, Anna, Tumarkin, Pavel 2007

机译：关于具有d + 4面的紧致双曲线Coxeter d-polytopes

ON d-DIMENSIONAL COMPACT HYPERBOLICCOXETER POLYTOPES WITH d + 4 FACETS

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