Tiling 3D Euclidean space with acute tetrahedra

To appear in Proc. of the Canadian Conference on Computational Geometry, August 2001.

Abstract:

We show that it is possible to tile the three dimensional space using only acute dihedral angle tetrahedra. Several constructions to achieve this objective are presented. Some necessary and/or sufficient conditions for acuteness of a tetrahedron are given. We also show that an acute angle triangulation is a Delaunay triangulation in two dimensions but not necessarily in three dimensions.