Skilling's Figure
The list of uniform polyhedra was first published by H.S.M.Coxeter, M.S.Longuet-Higgins and J.C.P.Miller in "Uniform Polyhedra", published in Philosophical Transactions of the Royal Society of London, Series A Volume 246 pp 401-450 (1954). The list was shown to be complete by Skilling.J in "The Complete Set of Uniform Polyhedra", published in Philosophical Transactions of the Royal Society of London, Series A Volume 278 pp 111-135 (1975).. By relaxing one of the conditions for a valid polyhedron, namely the condition that only two faces may meet at an edge, Skilling was able to produce one further figure, his great disnub dirhombidodecahedron. Wythoff Symbol: | (3/2) 5/3 (3) 5/2. This figure has twelve polygons at each vertex, however there are only eight edges as a number of edges are 'double', connecting four faces at once. A single vertex with the double edges highlighted is linked here. These double edges make the figure partially degenerate and it is not always classified as a true polyhedron.