Summary
| Small rhombidodecahedron | |
|---|---|
| |
| Type | Uniform star polyhedron |
| Elements | F = 42, E = 120 V = 60 (χ = −18) |
| Faces by sides | 30{4}+12{10} |
| Coxeter diagram |      (with extra double-covered triangles) (with extra double-covered pentagons)
|
| Wythoff symbol | 2 5 (3/2 5/2) | |
| 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 |
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.
Related polyhedra edit
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 edit
| 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 edit
External links edit
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