| Great icosihemidodecahedron | |
|---|---|
 | |
| Type | Uniform star polyhedron |
| Elements | F = 26, E = 60 V = 30 (χ = −4) |
| Faces by sides | 20{3}+6{10/3} |
| Coxeter diagram |     |
| 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 |
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.
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 |