Great Disnub Dirhombidodecahedron
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 J. Skilling 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. 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.