Before revision:  A recent observation at least one more pattern exists raise the question of the actual number of subdivisions  of the hexahedron into tetrahedra.
After revision:  A recent observation at least one more pattern exists raise the question of the actual number of subdivisions . Recent hexahedral dominant meshing methods try to take these configurations into account for combining tetrahedra into hexahedra, but fail to enumerate them all: they use only a set of 10 subdivisions among the 174 we found in this article. The enumeration of these 174 subdivisions of the hexahedron into tetrahedra.