First stellation of icosahedron
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| First stellation of icosahedron | |
|---|---|
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| Index | W26 |
| Stellation core | Icosahedron |
| Symmetry group | icosahedral (Ih) |
This polyhedron is the first stellation of the icosahedron, and given as Wenninger model index 26.
The stellation facets for construction are:
This stellation can be seen a construction of an icosahedron with short triangular pyramids added to all the faces. From of this interpretation, it can be given the name triakis icosahedron, however that name is also shared by a Catalan solid, the dual of the truncated dodecahedron. Both have the same surface topology but the other is convex with even shorter pyramids.
The nonconvex uniform polyhedra great stellated dodecahedron and great dodecahedron, as viewed as surface topologies, can also be constructed as icosahedron with pyramids, the first with much tall pyramids, and the second with inverted ones.
The stellated icosahedron is a popular subject for construction in modular origami, often made of thirty Sonobe units.
[edit] References
- Wenninger, Magnus (1974). Polyhedron Models. Cambridge University Press. ISBN 0-521-09859-9.
