Vertex Configuration

Archimedean Solid - Classification
... Here the vertex configuration refers to the type of regular polygons that meet at any given vertex ... For example, a vertex configuration of (4,6,8) means that a square, hexagon, and octagon meet at a vertex (with the order taken to be clockwise around the vertex) ... Name (Vertex configuration) Transparent Solid Net Faces Edges Vertices Point group truncated tetrahedron (3.6.6) 4 ... triangles 4 hexagons 12 ... Td ...

Quasiregular Polyhedron - The Convex Quasiregular Polyhedra
... There are two convex quasiregular polyhedra The cuboctahedron, vertex configuration 3.4.3.4, Coxeter-Dynkin diagram The icosidodecahedron, vertex configuration 3.5.3.5, Coxeter-Dynkin diagram ... The remaining convex regular polyhedra have an odd number of faces at each vertex so cannot be colored in a way that preserves edge transitivity ... Regular Dual regular Quasiregular Vertex figure Tetrahedron {3,3} 3

Quasiregular Polyhedron
... two kinds of regular faces, which alternate around each vertex ... step closer to regularity than the semiregular which are merely vertex-transitive ... A quasiregular polyhedron with this symbol will have a vertex configuration p.q.p.q (or (p.q)2) ...