Related Figures
This interpretation can also apply to other similar nonconvex polyhedra with pyramids of different heights:
- First stellation of icosahedron, or small triambic icosahedron (sometimes called a triakis icosahedron)
- Great stellated dodecahedron (with very tall pyramids)
- Great dodecahedron (with inverted pyramids)
The triakis icosahedron has numerous stellations, one of which is pictured at left.
The triakis icosahedron is a part of a sequence of polyhedra and tilings, extending into the hyperbolic plane. These face-transitive figures have (*n32) reflectional symmetry.
| Symmetry | Spherical | Planar | Hyperbolic... | |||||
|---|---|---|---|---|---|---|---|---|
| *232 D3h |
*332 Td |
*432 Oh |
*532 Ih |
*632 P6m |
*732 |
*832 ... |
*∞32 |
|
| Order | 12 | 24 | 48 | 120 | ∞ | |||
| Truncated figures |
3.4.4 |
3.6.6 |
3.8.8 |
3.10.10 |
3.12.12 |
3.14.14 |
3.16.16 |
3.∞.∞ |
| Coxeter Schläfli |
t0,1{2,3} |
t0,1{3,3} |
t0,1{4,3} |
t0,1{5,3} |
t0,1{6,3} |
t0,1{7,3} |
t0,1{8,3} |
t0,1{∞,3} |
| Triakis figures |
V3.4.4 |
V3.6.6 |
V3.8.8 |
V3.10.10 |
V3.12.12 |
V3.14.14 |
||
| Coxeter | ||||||||
Read more about this topic: Triakis Icosahedron
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