Small retrosnub icosicosidodecahedron
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| Small retrosnub icosicosidodecahedron | |
|---|---|
 | |
| Type | Uniform star polyhedron |
| Elements | F = 112, E = 180 V = 60 (χ = −8) |
| Faces by sides | (40+60){3}+12{5/2} |
| Wythoff symbol(s) | |3/2 3/2 5/2 |
| Symmetry group | Ih, [5,3], *532 |
| Index references | U72, C91, W118 |
| Bowers acronym | Sirsid |
 (35.5/3)/2 (Vertex figure) |
 Small hexagrammic hexecontahedron (dual polyhedron) |
In geometry, the small retrosnub icosicosidodecahedron is a nonconvex uniform polyhedron, indexed as U72.
Convex hull
Its convex hull is a nonuniform truncated dodecahedron.
 truncated dodecahedron |
 Convex hull |
Small retrosnub icosicosidodecahedron |
Cartesian coordinates
Cartesian coordinates for the vertices of a small retrosnub icosicosidodecahedron are all the even permutations of
- (±½(−1/τ−√(3τ−2)), 0, ±½(3−τ√(3τ−2)))
- (±½(1/τ−√(3τ−2)), ±1, ±½(1+2/τ−τ√(3τ−2)))
- (±½(τ2−√(3τ−2)), ±1/τ, ±½(1−τ√(3τ−2)))
where τ = (1+√5)/2 is the golden ratio (sometimes written φ).
See also
External links
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