Snub icosidodecadodecahedron
In geometry, the snub icosidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U46. It has 104 faces (80 triangles, 12 pentagons, and 12 pentagrams), 180 edges, and 60 vertices. As the name indicates, it belongs to the family of snub polyhedra.
| Snub icosidodecadodecahedron | |
|---|---|
| Type | Uniform star polyhedron |
| Elements | F = 104, E = 180 V = 60 (χ = −16) |
| Faces by sides | (20+60){3}+12{5}+12{5/2} |
| Coxeter diagram | |
| Wythoff symbol | | 5/3 3 5 |
| Symmetry group | I, [5,3]+, 532 |
| Index references | U46, C58, W112 |
| Dual polyhedron | Medial hexagonal hexecontahedron |
| Vertex figure | 3.3.3.5.3.5/3 |
| Bowers acronym | Sided |
The circumradius of the snub icosidodecadodecahedron with unit edge length is
where ρ is the plastic constant, or the unique real root of ρ3 = ρ + 1.
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