- Face configuration
In geometry, a "face configuration" is notational description of a

face-transitive polyhedron . It represents a sequential count of the number of faces that exist at each vertex around a face.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, V3.4.3.4 represents the

rhombic dodecahedron which is face-transitive: every face is arhombus , 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 [3.4.3.4] .

Face-transitive polyhedra are generally the polyhedral duals of the

vertex-transitive polyhedra, which are described by a parallelvertex configuration notation. That notation omits the "V" prefix and represents sequentially the number of edges of the faces around a vertex. For example, 3.4.3.4 is thecuboctahedron with 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 (V3.4.3.4) and the cubocahedron (3.4.3.4) above are dual polyhedra.**See also***

Platonic solid s: five regular polyhedra that are either self-dual or whose dual is another Platonic solid.

*Catalan solid s: thirteen polyhedra that are dual to theArchimedean solid s

*Bipyramid s: an infinite set of duals of prisms

*Trapezohedron s: an infinite set of duals ofantiprism s

*List of uniform planar tilings **References***

*Branko Grünbaum andG. C. Shephard "Tilings and Patterns". New York: W. H. Freeman & Co., 1987. ISBN 0-7167-1193-1.

*Wikimedia Foundation.
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