Small rhombidodecahedron

Small rhombidodecahedron
Small rhombidodecahedron.png
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 Small rhombidodecahedron vertfig.png
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.

3D model of a small rhombidodecahedron

Related polyhedraEdit

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).

Small dodecicosidodecahedron
Small rhombidodecahedron
Small stellated truncated dodecahedron
Compound of six pentagrammic prisms
Compound of twelve pentagrammic prisms

Small rhombidodecacronEdit

Small rhombidodecacron
Type Star polyhedron
Elements F = 60, E = 120
V = 42 (χ = −18)
Symmetry group Ih, [5,3], *532
Index references DU39
dual polyhedron Small rhombidodecahedron
3D model of a small rhombidodecacron

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.


  1. ^ Maeder, Roman. "39: small rhombidodecahedron". MathConsult.

External linksEdit