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.