In geometry, a face configuration is notational description of a face-uniform polyhedron. It represents a sequential count of the number of faces that exist at each vertices around a face.

There is no single standard accepted representation, but one standard, by author Williams, prefixes the notation with a V and separates vertices by a period (.). (Sometimes commas (,) are used instead.)

For example V3.4.3.4 represents the rhombic dodecahedron which is face-uniform, where every face is a rhombus, and alternating vertices contain 3 or 4 faces each.

It is most useful to describe face-uniform polyhedra, which generally are the polyhedral duals of the vertex-uniform polyhedra.

The vertex-uniform polyhedra are described by vertex configuration notation. The notation exists in parallel as the same sequence, but without the V prefix. It represents the sequential face types around a vertex. For example, 3.4.3.4 is the Cuboctahedron with alternating triangles and squares around each vertex.

See also

• Catalan solids: 13 Archimedean duals
• Bipyramids: infinite set of prism duals
• Trapezohedrons: infinite set of antiprism duals
• List of uniform planar tilings

Reference

Polyhedra | Mathematical notation