# Small rhombidodecahedron

Small rhombidodecahedron Type Uniform star polyhedron
Elements F = 42, E = 120
V = 60 (χ = −18)
Faces by sides 30{4}+12{10}
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. 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 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.