Small rhombidodecahedron

Small rhombidodecahedron
File:Small rhombidodecahedron.png
Type	Uniform star polyhedron
Elements	F = 42, E = 120 V = 60 (χ = −18)
Faces by sides	30{4}+12{10}
Coxeter diagram	Template:CDD (with extra double-covered triangles) Template:CDD (with extra double-covered pentagons)
Wythoff symbol
Symmetry group	I_h, [5,3], *532
Index references	U₃₉, C₄₆, W₇₄
Dual polyhedron	Small rhombidodecacron
Vertex figure	File:Small rhombidodecahedron vertfig.png 4.10.4/3.10/9
Bowers acronym	Sird

3D model of a 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.

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).

File:Small rhombicosidodecahedron.png Rhombicosidodecahedron	File:Small dodecicosidodecahedron.png Small dodecicosidodecahedron	File:Small rhombidodecahedron.png Small rhombidodecahedron
File:Small stellated truncated dodecahedron.png Small stellated truncated dodecahedron	File:UC36-6 pentagrammic prisms.png Compound of six pentagrammic prisms	File:UC37-12 pentagrammic prisms.png Compound of twelve pentagrammic prisms

Small rhombidodecacron
File:DU39 small rhombidodecacron.png
Type	Star polyhedron
Face	File:DU39 facets.png
Elements	F = 60, E = 120 V = 42 (χ = −18)
Symmetry group	I_h, [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.

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