| Great dodecicosahedron | |
|---|---|
| Type | Uniform star polyhedron |
| Elements | F = 32, E = 120 V = 60 (χ = −28) |
| Faces by sides | 20{6}+12{10/3} |
| Wythoff symbol | 3 5/3 (3/2 5/2) | |
| Symmetry group | Ih, [5,3], *532 |
| Index references | U63, C79, W101 |
| Bowers acronym | Giddy |
6.10/3.6/5.10/7 (Vertex figure) |
Great dodecicosacron (dual polyhedron) |
In geometry, the great dodecicosahedron is a nonconvex uniform polyhedron, indexed as U63. Its vertex figure is a crossed quadrilateral.
It has a composite Wythoff symbol, 3 5/3 (3/2 5/2) |, requiring two different Schwarz triangles to generate it: (3 5/3 3/2) and (3 5/3 5/2).
Its vertex figure 6.10/3.6/5.10/7 is also ambiguous, having two clockwise and two counterclockwise faces around each vertex.
It shares its vertex arrangement with the truncated dodecahedron. It additionally shares its edge arrangement with the great icosicosidodecahedron (having the hexagonal faces in common) and the great ditrigonal dodecicosidodecahedron (having the decagrammic faces in common).
Truncated dodecahedron |
Great icosicosidodecahedron |
Great ditrigonal dodecicosidodecahedron |
Great dodecicosahedron |