Small dodecicosidodecahedron
| Small dodecicosidodecahedron | |
|---|---|
 | |
| Type | Uniform star polyhedron |
| Elements | F = 44, E = 120 V = 60 (χ = −16) |
| Faces by sides | 20{3}+12{5}+12{10} |
| Wythoff symbol | 3/2 5 | 5 3 5/4 | 5 |
| Symmetry group | Ih, [5,3], *532 |
| Index references | U33, C42, W72 |
| Dual polyhedron | Small dodecacronic hexecontahedron |
| Vertex figure |  5.10.3/2.10 |
| Bowers acronym | Saddid |
In geometry, the small dodecicosidodecahedron is a nonconvex uniform polyhedron, indexed as U33. Its vertex figure is a crossed quadrilateral.
Related polyhedra
It shares its vertex arrangement with the small stellated truncated dodecahedron and the uniform compounds of 6 or 12 pentagrammic prisms. It additionally shares its edge arrangement with the rhombicosidodecahedron (having the triangular and pentagonal faces in common), and with the small rhombidodecahedron (having the decagonal faces in common).
 Rhombicosidodecahedron |
Small dodecicosidodecahedron |
 Small rhombidodecahedron |
 Small stellated truncated dodecahedron |
 Compound of six pentagrammic prisms |
 Compound of twelve pentagrammic prisms |
Small dodecacronic hexecontahedron
| Small dodecacronic hexecontahedron | |
|---|---|
 | |
| Type | Star polyhedron |
| Face |  |
| Elements | F = 60, E = 120 V = 44 (χ = −16) |
| Symmetry group | Ih, [5,3], *532 |
| Index references | DU33 |
| dual polyhedron | Small dodecicosidodecahedron |
The dual polyhedron to the small dodecicosidodecahedron is called a small dodecacronic hexecontahedron is the dual of the small dodecicosidodecahedron. It is visually identical to the small rhombidodecacron.
References
- Coxeter, H. S. M. (May 13, 1954). "Uniform Polyhedra". Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences 246 (916): 401–450. doi:10.1098/rsta.1954.0003.
- Wenninger, Magnus (1974). Polyhedron Models. Cambridge University Press. ISBN 0-521-09859-9. OCLC 1738087.
- Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 730208