Tetrahedral cages for unit discs

IF 0.5 4区数学 Q3 MATHEMATICS

Advances in Geometry Pub Date : 2021-07-01 DOI:10.1515/advgeom-2021-0016

Liping Yuan, T. Zamfirescu, Yanxue Zhang

引用次数: 0

Abstract

Abstract A cage is the 1-skeleton of a convex polytope in ℝ3. A cage is said to hold a set if the set cannot be continuously moved to a distant location, remaining congruent to itself and disjoint from the cage. In how many positions can (compact 2-dimensional) unit discs be held by a tetrahedral cage? We completely answer this question for all tetrahedra.

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单位圆盘用四面体笼

摘要笼是中凸多面体的1-骨架ℝ3.如果一个集合不能连续地移动到一个遥远的位置，保持与它本身一致并与笼子不相交，那么笼子就被称为容纳了这个集合。四面体笼可以保持（紧凑的二维）单位圆盘的多少个位置？我们完全回答了所有四面体的这个问题。

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

Advances in Geometry 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.