Face Type

These pages allow selection of polyhedra by their face types.

There are no polyhedra with more than three different face types. Other than the spherical polyhedra, the only other polyhedron containing a pentagon is one with five pentagons at a vertex. Only spherical polyhedra contain a decagon. The only polyhedra containing a polygon with 7, 9, 11 or 13 or more sides are the prisms or antiprisms.

Although there are no polyhedra with more than three different face types, there are polyhedra with more than three different transitivity classes. See the face count pages for polyhedra grouped by their face transitivity.

• {3} : triangular faces only
• {4} : square faces only
• {5} : pentagonal faces only
• {6} : hexagonal faces only
• {3}+{4} : triangular and square faces
• {3}+{4}+{6} : triangular, square and hexagonal faces
• {3}+{5} : triangular and pentagonal faces
• {3}+{6} : triangular and hexagonal faces
• {3}+{8} : triangular and octagonal faces
• {3}+{12} : triangular and dodecagonal faces
• {4}+{6} : square and hexagonal faces
• {4}+{6}+{8} : square, hexagonal and octagonal faces
• {4}+{6}+{12} : square, hexagonal and dodecagonal faces
• {4}+{8} : square and octagonal faces
• {4}+{12} : square and dodecagonal faces
• Other