Triakis icosahedron
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| Triakis icosahedron | |
|---|---|
 (Click here for rotating model) |
|
| Type | Catalan solid |
| Face type | isosceles triangle |
| Faces | 60 |
| Edges | 90 |
| Vertices | 32 |
| Vertices by type | 20{3}+12{10} |
| Face configuration | V3.10.10 |
| Symmetry group | Ih |
| Dihedral angle | 160°36'45" |
| Dual | Truncated dodecahedron |
| Properties | convex, face-transitive |
 Net |
|
A triakis icosahedron is an Archimedean dual solid, or a Catalan solid. Its dual is the truncated dodecahedron.
It can be seen as an icosahedron with triangular pyramids augmented to each face. This interpretation is expressed in the name.
This interpretation can also associated with other similar nonconvex polyhedra with pyramids of different heights:
First stellation of icosahedron (Sometimes called a triakis icosahedron)
Great stellated dodecahedron (With very tall pyramids)
Great dodecahedron (With inverted pyramids)
[edit] See also
- Triakis triangular tiling for other "triakis" polyhedral forms.
[edit] References
- Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X. (Section 3-9)
- Wenninger, Magnus (1974). Polyhedron Models. Cambridge University Press. ISBN 0-521-09859-9.
[edit] External links
- Eric W. Weisstein, Triakis icosahedron (Catalan solid) at MathWorld.
- Triakis Icosahedron -- Interactive Polyhedron Model
