Tiling space and slabs with acute tetrahedra

Authors:
David Eppstein;John M. Sullivan;Alper Üngör
Affiliations:
Department of Information and Computer Science, Univ. of California at Irvine;Department of Mathematics, Univ. of Illinois at Urbana-Champaign and Institut für Mathematik, Technische Universität Berlin, Berlin, Germany;Department of Computer Science, Duke Univ.
Venue:
Computational Geometry: Theory and Applications
Year:
2004

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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 74.21°, and another which tiles a slab in space.