Tiling space and slabs with acute tetrahedra

2003/02/19 by David Eppstein, John M. Sullivan, Alper Üngör +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Materials and Mechanics #Cellular Automata and Applications #Computational Geometry and Mesh Generation #cs.CG #math.MG

paper · pdf · doi:10.1016/j.comgeo.2003.11.003

published as Computational Geometry Theory & Applications 27(3):237-255, 2004 · 20 pages; 17 figures; 1 table; see also http://www.cs.duke.edu/~ungor/abstracts/acute_tiling.html

arxiv created 2003/02/19 · openalex publication_date 2004/02/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

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 77.08^∘, and another which tiles a slab in space.

Citations

• Building Space-Time Meshes over Arbitrary Spatial Domains

Cited by

• Mathematical and numerical study of symmetry and positivity of the tensor-valued spring constant defined from P1-FEM for two- and three-dimensional linear elasticity

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