Great icosihemidodecahedron
In geometry, the great icosihemidodecahedron (or great icosahemidodecahedron) is a nonconvex uniform polyhedron, indexed as U71. It has 26 faces (20 triangles and 6 decagrams), 60 edges, and 30 vertices.[1] Its vertex figure is a crossed quadrilateral.
| Great icosihemidodecahedron | |
|---|---|
 | |
| Type | Uniform star polyhedron |
| Elements | F = 26, E = 60 V = 30 (χ = −4) |
| Faces by sides | 20{3}+6{10/3} |
| Wythoff symbol | 3/2 3 | 5/3 |
| Symmetry group | Ih, [5,3], *532 |
| Index references | U71, C85, W106 |
| Dual polyhedron | Great icosihemidodecacron |
| Vertex figure |  3.10/3.3/2.10/3 |
| Bowers acronym | Geihid |
3D model of a great icosihemidodecahedron
It is a hemipolyhedron with 6 decagrammic faces passing through the model center.
Related polyhedra
Its convex hull is the icosidodecahedron. It also shares its edge arrangement with the great icosidodecahedron (having the triangular faces in common), and with the great dodecahemidodecahedron (having the decagrammic faces in common).
 Great icosidodecahedron |
 Great dodecahemidodecahedron |
Great icosihemidodecahedron |
 Icosidodecahedron (convex hull) |
Gallery
Traditional filling |
 Modulo-2 filling |
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See also
References
- Maeder, Roman. "71: great icosihemidodecahedron". MathConsult.
External links
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