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Great disnub dirhombidodecahedron
In geometry, the great disnub dirhombidodecahedron, also called ''Skilling's figure'', is a uniform star polyhedron.
It was proven in 1970 that there are only 75 uniform polyhedra other than the infinite families of prisms and antiprisms. John Skilling discovered one more, by relaxing the condition that only two faces may meet at an edge. Some authors do not count it as a uniform polyhedron, because some pairs of edges coincide.
It has 120 edges with 2 faces and 120 edges with 4 faces. If the 4-face edges are counted twice, as two topologically disjoint edges, this figure can be considered to have 360 total edges, and the Euler characteristic becomes −88.
The vertex figure has 4 square faces passing through the center of the model.
It may be constructed as the exclusive or (blend) of the great dirhombicosidodecahedron and compound of twenty octahedra.
== Related polyhedra ==
It shares the same edge arrangement as the great dirhombicosidodecahedron, but has a different set of triangular faces. The vertices and edges are also shared with the uniform compounds of 20 octahedra or 20 tetrahemihexahedra. 180 of the edges are shared with the great snub dodecicosidodecahedron.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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