The 8T-LE partition applied to the obtuse triangulations of the 3D-cube

Abstract

Four of the six types of the regular triangulations of the 3D-cube, up to isomorphism, are obtuse. We study the eight-tetrahedra longest-edge partition (8T-LE) of the triangulations of the cube containing two regular right-type tetrahedra, two regular trirectangular tetrahedra and two quasi right-type tetrahedra. We prove that the iterative 8T-LE partition of these triangulations yields a sequence of triangulations where the number of similarity classes is bounded, and hence the non-degeneracy of the meshes is simply proved. It is also proved that asymptotically, most of the tetrahedra generated are regular right-type.