Related Polyhedra
The truncated octahedron is one of a family of uniform polyhedra related to the cube and regular octahedron.
| {4,3} | t0,1{4,3} | t1{4,3} | t0,1{3,4} | {3,4} | t0,2{4,3} | t0,1,2{4,3} | s{4,3} | h0{4,3} | h1,2{4,3} |
|---|---|---|---|---|---|---|---|---|---|
It also exists as the omnitruncate of the tetrahedron family:
| {3,3} | t0,1{3,3} | t1{3,3} | t1,2{3,3} | t2{3,3} | t0,2{3,3} | t0,1,2{3,3} | s{3,3} |
|---|---|---|---|---|---|---|---|
| Symmetry | Spherical | planar | Hyperbolic | |||||
|---|---|---|---|---|---|---|---|---|
| *232 D3h |
*332 Td |
*432 Oh |
*532 Ih |
*632 P6m |
*732 |
*832 |
*∞32 |
|
| Order | 12 | 24 | 48 | 120 | ∞ | |||
| Omnitruncated figure |
4.6.4 |
4.6.6 |
4.6.8 |
4.6.10 |
4.6.12 |
4.6.14 |
4.6.16 |
4.6.∞ |
| Coxeter Schläfli |
t0,1,2{2,3} |
t0,1,2{3,3} |
t0,1,2{4,3} |
t0,1,2{5,3} |
t0,1,2{6,3} |
t0,1,2{7,3} |
t0,1,2{8,3} |
t0,1,2{∞,3} |
| Omnitruncated duals |
V4.6.4 |
V4.6.6 |
V4.6.8 |
V4.6.10 |
V4.6.12 |
V4.6.14 |
V4.6.16 | V4.6.∞ |
| Coxeter | ||||||||
This polyhedron can be considered a member of a sequence of uniform patterns with vertex figure (4.6.2p) and Coxeter-Dynkin diagram . For p < 6, the members of the sequence are omnitruncated polyhedra (zonohedra), shown below as spherical tilings. For p > 6, they are tilings of the hyperbolic plane, starting with the truncated triheptagonal tiling.
| Symmetry | Spherical | Planar | Hyperbolic... | |||||
|---|---|---|---|---|---|---|---|---|
| *232 D3h |
*332 Td |
*432 Oh |
*532 Ih |
*632 P6m |
*732 |
*832 ... |
*∞32 |
|
| Order | 12 | 24 | 48 | 120 | ∞ | |||
| Truncated figures |
2.6.6 |
3.6.6 |
4.6.6 |
5.6.6 |
6.6.6 |
7.6.6 |
8.6.6 |
3.4.∞.4 |
| Coxeter Schläfli |
t0,1{3,2} |
t0,1{3,3} |
t0,1{3,4} |
t0,1{3,5} |
t0,1{3,6} |
t0,1{3,7} |
t0,1{3,8} |
t0,1{3,∞} |
| n-kis figures |
V2.6.6 |
V3.6.6 |
V4.6.6 |
V5.6.6 |
V6.6.6 |
V7.6.6 |
||
| Coxeter | ||||||||
Read more about this topic: Truncated Octahedron
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