Small dodecicosahedron
In geometry, the small dodecicosahedron (or small dodekicosahedron) is a nonconvex uniform polyhedron, indexed as U50. It has 32 faces (20 hexagons and 12 decagons), 120 edges, and 60 vertices.[1] Its vertex figure is a crossed quadrilateral.
| Small dodecicosahedron | |
|---|---|
 | |
| Type | Uniform star polyhedron |
| Elements | F = 32, E = 120 V = 60 (χ = −28) |
| Faces by sides | 20{6}+12{10} |
| Wythoff symbol | 3 5 (3/2 5/4) | |
| Symmetry group | Ih, [5,3], *532 |
| Index references | U50, C64, W90 |
| Dual polyhedron | Small dodecicosacron |
| Vertex figure |  6.10.6/5.10/9 |
| Bowers acronym | Siddy |
3D model of a small dodecicosahedron
Related polyhedra
It shares its vertex arrangement with the great stellated truncated dodecahedron. It additionally shares its edges with the small icosicosidodecahedron (having the hexagonal faces in common) and the small ditrigonal dodecicosidodecahedron (having the decagonal faces in common).
 Great stellated truncated dodecahedron |
 Small icosicosidodecahedron |
 Small ditrigonal dodecicosidodecahedron |
Small dodecicosahedron |
gollark: Just go to a slime island or press honey or whatever though.
gollark: We do also have Forestry and the Forestry genetic engineering mod.
gollark: I agree. The pack developers explicitly let it make a few more things than usual.
gollark: I may actually make an arbitrarily good power source cuboid™ and IC² replicator setup. It lets you make a lot of things.
gollark: Somewhat.
References
- Maeder, Roman. "50: small dodecicosahedron". MathConsult.
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