- Face configuration
There is no single standard accepted representation, but one common notation prefixes the description with a "V" and separates the vertices by a period (".") or a comma (",").
For example, V18.104.22.168 represents the
rhombic dodecahedronwhich is face-transitive: every face is a rhombus, and alternating vertices of the rhombus contain 3 or 4 faces each.
Another form of this notation, used in "Tilings and Patterns", has brackets around the symbol, for instance [22.214.171.124] .
Face-transitive polyhedra are generally the polyhedral duals of the
vertex-transitivepolyhedra, which are described by a parallel vertex configurationnotation. That notation omits the "V" prefix and represents sequentially the number of edges of the faces around a vertex. For example, 126.96.36.199 is the cuboctahedronwith alternating triangular and square faces around each vertex. Polyhedra have the same representation in face configuration notation (with the addition of the "V") that their duals have in vertex configuration notation. The rhombic dodecahedron (V188.8.131.52) and the cubocahedron (184.108.40.206) above are dual polyhedra.
Platonic solids: five regular polyhedra that are either self-dual or whose dual is another Platonic solid.
Catalan solids: thirteen polyhedra that are dual to the Archimedean solids
Bipyramids: an infinite set of duals of prisms
Trapezohedrons: an infinite set of duals of antiprisms
List of uniform planar tilings
Branko Grünbaumand G. C. Shephard"Tilings and Patterns". New York: W. H. Freeman & Co., 1987. ISBN 0-7167-1193-1.
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