Tiling space and slabs with acute tetrahedra

David Eppstein; John M. Sullivan; Alper Ungor

doi:10.1016/j.comgeo.2003.11.003

paper

Tiling space and slabs with acute tetrahedra

arXiv:cs/0302027 · doi:10.1016/j.comgeo.2003.11.003

Abstract

We show it is possible to tile three-dimensional space using only tetrahedra with acute dihedral angles. We present several constructions to achieve this, including one in which all dihedral angles are less than $77.0 8^{\circ}$ , and another which tiles a slab in space.

20 pages; 17 figures; 1 table; see also http://www.cs.duke.edu/~ungor/abstracts/acute_tiling.html