Claim: A stereohedron, a convex polyhedron that fills space isohedrally, 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. Dodecahedrille Oblate octahedrille Oblate cubille Cubille Quarter cubille Quarter oblate octahedrille Half oblate octahedrille Pyramidille Square quarter pyramidille Half pyramidille Oblate tetrahedrille Triangular pyramidille Eighth pyramidille Tetrahedra Square pyramid Triangular bipyramid Cube Octahedron Rhombic dodecahedron Faces