Before revision:  This result is purely combinatorial. We also demonstrate that a minimum of 114 triangulations do correspond to hexahedron geometrical triangulations.Each hexahedron is valid for finite element computations (strictly positive Jacobian determinant) .
After revision:  We further show that exactly 171 of these subdivisions have a geometrical realization, i.e. there exist coordinates of the eight hexahedron vertices in a three-dimensional space such that the geometrical tetrahedral mesh is valid .