Great Dirhombicosidodecahedron

In geometry, the great dirhombicosidodecahedron is a nonconvex uniform polyhedron, indexed last as U₇₅.

This is the only uniform polyhedron with more than six faces meeting at a vertex. Each vertex has 4 squares which pass through the vertex central axis (and thus through the centre of the figure), alternating with two triangles and two pentagrams.

This is also the only uniform polyhedron that cannot be made by Wythoff construction. It has a special Wythoff symbol | 3/₂ 5/₃ 3 5/₂.

It has been nicknamed "Miller's monster" (after J. C. P. Miller, who with H. S. M. Coxeter and M. S. Longuet-Higgins enumerated the uniform polyhedra in 1954).