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 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 .
Face-transitive polyhedra are generally the polyhedral duals of the vertex-transitive polyhedra, which are described by a parallel vertex 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 the cuboctahedron 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.
Famous quotes containing the word face:
“Our life is a faint tracing on the surface of mystery, like the idle, curved tunnels of leaf miners on the face of a leaf. We must somehow take a wider view, look at the whole landscape, really see it, and describe what’s going on here. Then we can at least wail the right question into the swaddling band of darkness, or, if it comes to that, choir the proper praise.”
—Annie Dillard (b. 1945)