Small rhombidodecahedron
Small rhombidodecahedron | |
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![]() | |
Type | Uniform star polyhedron |
Elements | F = 42, E = 120 V = 60 (χ = −18) |
Faces by sides | 30{4}+12{10} |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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 |
![](http://upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Small_rhombidodecahedron.stl/220px-Small_rhombidodecahedron.stl.png)
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).
![]() Rhombicosidodecahedron | ![]() Small dodecicosidodecahedron | ![]() Small rhombidodecahedron |
![]() Small stellated truncated dodecahedron | ![]() Compound of six pentagrammic prisms | ![]() Compound of twelve pentagrammic prisms |
Small rhombidodecacron
Small rhombidodecacron | |
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![]() | |
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 |
![](http://upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Small_rhombidodecacron.stl/220px-Small_rhombidodecacron.stl.png)
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
- ^ Maeder, Roman. "39: small rhombidodecahedron". MathConsult.
- Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208
External links
- Weisstein, Eric W. "Small rhombidodecahedron". MathWorld.
- Weisstein, Eric W. "Small rhombidodecacron". MathWorld.
- Uniform polyhedra and duals
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polyhedra (nonconvex
regular polyhedra)
of Kepler-Poinsot
polyhedra
hemipolyhedra
uniform polyhedra
- medial rhombic triacontahedron
- small stellapentakis dodecahedron
- medial deltoidal hexecontahedron
- small rhombidodecacron
- medial pentagonal hexecontahedron
- medial disdyakis triacontahedron
- great rhombic triacontahedron
- great stellapentakis dodecahedron
- great deltoidal hexecontahedron
- great disdyakis triacontahedron
- great pentagonal hexecontahedron
uniform polyhedra with
infinite stellations
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