Small retrosnub icosicosidodecahedron
| 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 | |3/2 3/2 5/2 |
| Symmetry group | Ih, [5,3], *532 |
| Index references | U72, C91, W118 |
| Dual polyhedron | Small hexagrammic hexecontahedron |
| Vertex figure |  (35.5/3)/2 |
| Bowers acronym | Sirsid |
In geometry, the small retrosnub icosicosidodecahedron or small inverted retrosnub icosicosidodecahedron is a nonconvex uniform polyhedron, indexed as U72. It is also called a retroholosnub icosahedron, ß{3/2,5}. Unlike most snub polyhedra, it has reflection symmetries.
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
- (±(1-ϕ−α), 0, ±(3−ϕα))
- (±(ϕ-1−α), ±2, ±(2ϕ-1−ϕα))
- (±(ϕ+1−α), ±2(ϕ-1), ±(1−ϕα))
where ϕ = (1+√5)/2 is the golden ratio and α = √(3ϕ−2).
See also
External links
- Klitzing, Richard. "3D star small retrosnub icosicosidodecahedron".
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