Small rhombidodecahedron
In geometry, the small rhombidodecahedron is a nonconvex uniform polyhedron, indexed as U39. It has 42 faces (30 squares and 12 decagons), 120 edges, and 60 vertices.[1] Its vertex figure is a crossed quadrilateral.
| Small rhombidodecahedron | |
|---|---|
 | |
| Type | Uniform star polyhedron |
| Elements | F = 42, E = 120 V = 60 (χ = −18) |
| Faces by sides | 30{4}+12{10} |
| Wythoff symbol | |
| Symmetry group | Ih, [5,3], *532 |
| Index references | U39, C46, W74 |
| Dual polyhedron | Small rhombidodecacron |
| Vertex figure |  4.10.4/3.10/9 |
| Bowers acronym | Sird |
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 square faces in common), and with the small dodecicosidodecahedron (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 rhombidodecacron
| Small rhombidodecacron | |
|---|---|
 | |
| Type | Star polyhedron |
| Face |  |
| Elements | F = 60, E = 120 V = 42 (χ = −18) |
| Symmetry group | Ih, [5,3], *532 |
| Index references | DU39 |
| dual polyhedron | Small rhombidodecahedron |
The small rhombidodecacron (or small dipteral ditriacontahedron) is a nonconvex isohedral polyhedron. It is the dual of the small rhombidodecahedron. It is visually identical to the Small dodecacronic hexecontahedron. It has 60 intersecting antiparallelogram faces.
References
- Maeder, Roman. "39: small rhombidodecahedron". MathConsult.
- Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208
External links
- Weisstein, Eric W. "Small rhombidodecahedron". MathWorld.
- Weisstein, Eric W. "Small rhombidodecacron". MathWorld.
- Uniform polyhedra and duals