![cover image](https://wikiwandv2-19431.kxcdn.com/_next/image?url=https://upload.wikimedia.org/wikipedia/commons/thumb/1/15/Rhombic_icosahedron.png/640px-Rhombic_icosahedron.png&w=640&q=50)
Rhombic icosahedron
From Wikipedia, the free encyclopedia
The rhombic icosahedron is a polyhedron shaped like an oblate sphere. Its 20 faces are congruent golden rhombi;[1] 3, 4, or 5 faces meet at each vertex. It has 5 faces (green on top figure) meeting at each of its 2 poles; these 2 vertices lie on its axis of 5-fold symmetry, which is perpendicular to 5 axes of 2-fold symmetry through the midpoints of opposite equatorial edges (example on top figure: most left-hand and most right-hand mid-edges). Its other 10 faces follow its equator, 5 above and 5 below it; each of these 10 rhombi has 2 of its 4 sides lying on this zig-zag skew decagon equator. The rhombic icosahedron has 22 vertices. It has D5d, [2+,10], (2*5) symmetry group, of order 20; thus it has a center of symmetry (since 5 is odd).
Rhombic icosahedron | |
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Type | Zonohedron |
Faces | 20 congruent golden rhombi |
Edges | 40 |
Vertices | 22 |
Symmetry group | D5d = D5v, [2+,10], (2*5) |
Dual polyhedron | irregular-faced pentagonal gyrobicupola |
Properties | convex |
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Rhombic_icosahedron.stl/640px-Rhombic_icosahedron.stl.png)
Even though all its faces are congruent, the rhombic icosahedron is not face-transitive, since one can distinguish whether a particular face is near the equator or near a pole by examining the types of vertices surrounding this face.