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Small snub icosicosidodecahedron 
Summary
| Small snub icosicosidodecahedron | |
|---|---|
| |
| Type | Uniform star polyhedron |
| Elements | F = 112, E = 180 V = 60 (χ = −8) |
| Faces by sides | (40+60){3}+12{5/2} |
| Coxeter diagram |    
|
| Wythoff symbol | | 5/2 3 3 |
| Symmetry group | Ih, [5,3], *532 |
| Index references | U32, C41, W110 |
| Dual polyhedron | Small hexagonal hexecontahedron |
| Vertex figure |  35.5/2 |
| Bowers acronym | Seside |
In geometry, the small snub icosicosidodecahedron or snub disicosidodecahedron is a uniform star polyhedron, indexed as U32. It has 112 faces (100 triangles and 12 pentagrams), 180 edges, and 60 vertices. Its stellation core is a truncated pentakis dodecahedron. It also called a holosnub icosahedron, ß{3,5}.
The 40 non-snub triangular faces form 20 coplanar pairs, forming star hexagons that are not quite regular. Unlike most snub polyhedra, it has reflection symmetries.
Convex hull edit
Its convex hull is a nonuniform truncated icosahedron.
 Truncated icosahedron (regular faces) |
 Convex hull (isogonal hexagons) |
 Small snub icosicosidodecahedron |
Cartesian coordinates edit
Cartesian coordinates for the vertices of a small snub icosicosidodecahedron are all the even permutations of
![{\displaystyle {\begin{array}{clllc}{\Bigl (}&\pm {\bigl [}1-\varphi +\alpha {\bigr ]},&\ \ \ \,0,&\pm {\bigl [}3+\varphi \alpha {\bigr ]}&{\Bigr )}\\{\Bigl (}&\pm {\bigl [}\varphi -1+\alpha {\bigr ]},&\pm \,2,&\pm {\bigl [}2\varphi -1+\varphi \alpha {\bigr ]}&{\Bigr )}\\{\Bigl (}&\pm {\bigl [}\varphi +1+\alpha {\bigr ]},&\pm \,2{\bigl [}\varphi -1{\bigr ]},&\pm {\bigl [}1+\varphi \alpha {\bigr ]}&{\Bigr )}\end{array}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/461ca721561f77e9bbb5e1da73526a52c1da9cbc)
where is the golden ratio and
See also edit
External links edit
- Weisstein, Eric W. "Small snub icosicosidodecahedron". MathWorld.
- Klitzing, Richard. "3D star small snub icosicosidodecahedron".