Great disnub dirhombidodecahedron
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| Great disnub dirhombidodecahedron | |
|---|---|
 |
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| Type | Uniform polyhedron |
| Elements | F=204, E=240, V=60 (χ=32) |
| Faces by sides | 120{3}+60{4}+24{5/2} |
| Wythoff symbol | | (3/2) 5/3 (3) 5/2 |
| Symmetry group | Ih |
| Index references | U-, C-, W- |
 (5/2.4.3.3.3.4. 5/3.4.3/2.3/2.3/2.4)/2 (Vertex figure) |
 Great disnub dirhombidodecacron (dual polyhedron) |
In geometry, the Great disnub dirhombidodecahedron, also called Skilling's figure, is a nonconvex uniform polyhedron.
John Skilling discovered this one further uniform polyhedron, 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.
It shares the same vertices and edges 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 tetrahemihexahedra. 180 of the edges are shared with the great snub dodecicosidodecahedron.
The vertex figure has 4 square faces passing through the center of the model.
[edit] See also
[edit] References
- John Skilling, The complete set of uniform polyhedra. Philosophical Transactions of the Royal Society, Ser. A, 278, pp. 111-135, 1975
