The eight-tetrahedra longest-edge partition and Kuhn triangulations

The Kuhn triangulation of a cube is obtained by subdividing the cube into six right-type tetrahedra once a couple of opposite vertices have been chosen. In this paper, we explicitly define the eight-tetrahedra longest-edge (8T-LE) partition of right-type tetrahedra and prove that for any regular right-type tetrahedron tt, the iterative 8T-LE partition of tt yields a sequence of tetrahedra similar to the former one. Furthermore, based on the Kuhn-type triangulations, the 8T-LE partition commutes with certain refinements based on the canonical boxel partition of a cube and its Kuhn triangulation.