Packing, tiling, and covering with tetrahedra

J. H. Conway, S. Torquato

Research output: Contribution to journalArticle

89 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)10612-10617
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Volume103
Issue number28
DOIs
StatePublished - Jul 11 2006

All Science Journal Classification (ASJC) codes

  • General

Keywords

  • Polyhedra
  • Tessellations

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