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 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).

If the definition of a uniform polyhedron is relaxed to allow an even number of faces adjacent to an edge then this polyhedron gives rise to one further polyhedron the Great disnub dirhombidodecahedron which has the same vertices and edges but with a different arrangement of triangular faces.

External links

• http://www.mathconsult.ch/showroom/unipoly/75.html
• http://home.aanet.com.au/robertw/MillersMonster.html

Uniform polyhedra

大二重斜方二十・十二面体