Chiral Extensions of Regular Toroids

IF 1 2区数学 Q1 MATHEMATICS Combinatorica Pub Date : 2024-12-29 DOI:10.1007/s00493-024-00132-0

Antonio Montero, Micael Toledo

引用次数: 0

Abstract

Abstract polytopes are combinatorial objects that generalise geometric objects such as convex polytopes, maps on surfaces and tilings of the space. Chiral polytopes are those abstract polytopes that admit full combinatorial rotational symmetry but do not admit reflections. In this paper we build chiral polytopes whose facets (maximal faces) are isomorphic to a prescribed regular cubic tessellation of the n-dimensional torus (\(n \geqslant 2\)). As a consequence, we prove that for every \(d \geqslant 3\) there exist infinitely many chiral d-polytopes.

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正则环面的手性扩展

抽象多面体是一种组合对象，它概括了几何对象，如凸多面体、表面上的地图和空间的平铺。手性多面体是那些承认完全组合旋转对称但不承认反射的抽象多面体。在本文中，我们建立了手性多面体，其面（最大面）与n维环面的规定规则立方镶嵌同构（\(n \geqslant 2\)）。因此，我们证明了对于每一个\(d \geqslant 3\)存在无限多个手性d-多面体。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Combinatorica 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： COMBINATORICA publishes research papers in English in a variety of areas of combinatorics and the theory of computing, with particular emphasis on general techniques and unifying principles. Typical but not exclusive topics covered by COMBINATORICA are - Combinatorial structures (graphs, hypergraphs, matroids, designs, permutation groups). - Combinatorial optimization. - Combinatorial aspects of geometry and number theory. - Algorithms in combinatorics and related fields. - Computational complexity theory. - Randomization and explicit construction in combinatorics and algorithms.

期刊最新文献

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