Small dodecahemicosahedron
From Wikipedia, the free encyclopedia
| Small dodecahemicosahedron | |
|---|---|
 |
|
| Type | Uniform polyhedron |
| Elements | F = 22, E = 60 V = 30 (χ = -8) |
| Faces by sides | 12{5/2}+10{6} |
| Wythoff symbol | 5/35/2 | 3 |
| Symmetry group | Ih |
| Index references | U62, C78, W100 |
 6.5/2.6.5/3 (Vertex figure) |
 Small dodecahemicosacron (dual polyhedron) |
In geometry, the small dodecahemicosahedron is a nonconvex uniform polyhedron, indexed as U62.
The Small dodecahemicosahedron has 30 vertices, 60 edges, and 22 faces (12{5/2}+10{6}). The vertex configuration is 6.5/2.6.5/3. Its symmetry group is Ih, its Wythoff symbol is 5/35/2 | 3, and its Euler characteristic is χ=-8.
Its uniform index number is U62, its Kaleido index is K67, its number in Wenninger's Polyhedron Models is 100, and it was given the number 78 in Coxeter's 1954 paper, which first gave the complete list of the uniform polyhedra.
It shares the same edge arrangement, along with its 12 pentagrammic faces, with the convex dodecadodecahedron.
[edit] See also
[edit] External links
The Dodecahemicosahedron can be distinguished in the design of some Football Balls.
