Small rhombidodecahedron

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.

3D model of a small rhombidodecahedron
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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

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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
 
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.

References

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