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Polyhedron with 42 faces From Wikipedia, the free encyclopedia
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.
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 |
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 | |
---|---|
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.
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