Tetrahedral Decompositions of Hexahedral Meshes

Europ. J. Combinatorics, Academic Press, Vol 10, pp.435-443, 1989

MESHING
RESEARCH
CORNER

Abstract
A hexahedral mesh is a partition of a region in 3-space R3 into (not necessarily regular) hexahedra, which fit together face to face. We are concerned here with the question of how the hexahedra may be decomposed into tetrahedra without introducing any new vertices. We consider two possible decompositions, in which each hexahedron breaks into five or six tetrahedra in a prescribed fashion. In both cases, we obtain simple verifiable criteria for the existence of a decomposition, by making use of elementary facts of graph theory and algebraic topology.