Before revision:  The subset of tetrahedra of triangulating each potential hexahedron is determined once its eight vertices are computed. The new algorithm computes around 3 millions potential hexahedra in 10 seconds and ensures that each potential hexahedron is computed only once.
After revision:  The subset of tetrahedra of triangulating each potential hexahedron is then determined. Quality checks allow to early discard poor quality hexahedra and to dramatically improve the efficiency of the method. Each potential hexahedron is computed only once.