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Small retrosnub icosicosidodecahedron
Uniform star polyhedron with 112 faces / From Wikipedia, the free encyclopedia
In geometry, the small retrosnub icosicosidodecahedron (also known as a retrosnub disicosidodecahedron, small inverted retrosnub icosicosidodecahedron, or retroholosnub icosahedron) is a nonconvex uniform polyhedron, indexed as U72. It has 112 faces (100 triangles and 12 pentagrams), 180 edges, and 60 vertices.[1] It is given a Schläfli symbol sr{⁵/₃,³/₂}.
Small retrosnub icosicosidodecahedron | |
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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 | | 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 |
![](http://upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Small_retrosnub_icosicosidodecahedron.stl/640px-Small_retrosnub_icosicosidodecahedron.stl.png)
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.
George Olshevsky nicknamed it the yog-sothoth (after the Cthulhu Mythos deity).[2][3]