Related Polyhedra and Tilings
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 (zonohedrons), 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 | ∞ | |||
| 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 | ||||||||
Read more about this topic: Hexagonal Prism
Famous quotes containing the word related:
“The near explains the far. The drop is a small ocean. A man is related to all nature. This perception of the worth of the vulgar is fruitful in discoveries. Goethe, in this very thing the most modern of the moderns, has shown us, as none ever did, the genius of the ancients.”
—Ralph Waldo Emerson (1803–1882)
Related Phrases
Related Words