honeycomb t0,1{4,3,4}, has a square pyramid vertex figure, with truncated cube and octahedron cells. Here there are two types of edge figures. One is a square edge figure at the apex of the pyramid. This represents the four truncated cubes around an edge. The other four edge figures are isosceles triangles on the base vertices of the pyramid. These represent the arrangement of two truncated cubes and one octahedron around the other edges. See also Simplicial link - an abstract concept related to vertex figure. List of regular polytopes References Notes Bibliography H. S. M. Coxeter, Regular Polytopes, Hbk (1948), ppbk (1973). H.S.M. Coxeter (et al.), Uniform Polyhedra, Phil. Trans. 246 A (1954) pp. 401–450. P. Cromwell, Polyhedra, CUP pbk. (1999). H.M. Cundy and A.P. Rollett, Mathematical Models, Oxford Univ. Press (1961). J. Skilling, The Complete Set of Uniform Polyhedra, Phil. Trans. 278 A (1975) pp. 111–135. M. Wenninger, Dual Models, CUP hbk (1983) ppbk (2003). The Symmetries of Things 2008, John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, (p289 Vertex figures) External links Vertex Figures Consistent Vertex Descriptions Polyhedra Polytopes