Claim: A stereohedron has six types of faces and 13 unique honeycomb designs.
Evidence: In geometry and crystallography, a stereohedron is a convex polyhedron that fills space isohedrally, meaning that the symmetries of the tiling take any copy of the stereohedron to any other copy. Faces Tetrahedra Square pyramid Triangular bipyramid Cube Octahedron Rhombic dodecahedron Eighth pyramidille Triangular pyramidille Oblate tetrahedrille Half pyramidille Square quarter pyramidille Pyramidille Half oblate octahedrille Quarter oblate octahedrille Quarter cubille Cubille Oblate cubille Oblate octahedrille Dodecahedrille