Packing, tiling, and covering with tetrahedra

被引：115

作者：

Conway, J. H.

Torquato, S. ^{[1
]}

机构：

[1] Princeton Univ, PRISM, Program Appl & Computat Math, Dept Chem, Princeton, NJ 08544 USA

[2] PRISM, Program Appl & Computat Math, Dept Math, Princeton, NJ 08544 USA

[3] Princeton Univ, Ctr Theoret Phys, Princeton, NJ 08544 USA

来源：

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA | 2006年 / 103卷 / 28期

关键词：

tessellations; polyhedra;

D O I：

10.1073/pnas.0601389103

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

It is well known that three-dimensional Euclidean space cannot be tiled by regular tetrahedra. But how well can we do? In this work, we give several constructions that may answer the various senses of this question. in so doing, we provide some solutions to packing, tiling, and covering problems of tetrahedra. Our results suggest that the regular tetrahedron may not be able to pack as densely as the sphere, which would contradict a conjecture of Ulam. The regular tetrahedron might even be the convex body having the smallest possible packing density.

引用

页码：10612 / 10617

页数：6

共 19 条

[1]

[Anonymous], APPL GEOMETRY DISCRE

[2] Densest lattice packings of 3-polytopes [J].