Packing, Tiling, and Covering with Tetrahedra

• Published in: Proceedings of the National Academy of Sciences - PNAS Vol. 103; no. 28; pp. 10612 - 10617
• Main Authors: Conway, J. H., Torquato, S.
• Format: Journal Article
• Language: English
• Published: United States National Academy of Sciences 11.07.2006; National Acad Sciences
• Subjects: Bubbles; Coordinate systems; Density; Euclidean space; Icosahedrons; Mathematical lattices; Octahedrons; Packing density; Physical Sciences; Studies; Symmetry; Tessellations; Tetrahedra; Tetrahedrons; Vertices

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...