Related Tilings
This hyperbolic tiling is topologically related as a part of sequence of uniform truncated polyhedra with vertex configurations (n.6.6), and Coxeter group symmetry.
| Symmetry *n42 |
Spherical | Euclidean | 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 |
∞.6.6 |
| 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,∞} |
| Uniform dual figures | ||||||||
| n-kis figures |
V2.6.6 |
V3.6.6 |
V4.6.6 |
V5.6.6 |
V6.6.6 |
V7.6.6 |
V8.6.6 |
V∞.6.6 |
| Coxeter | ||||||||
From a Wythoff construction there are eight hyperbolic uniform tilings that can be based from the regular heptagonal tiling.
Drawing the tiles colored as red on the original faces, yellow at the original vertices, and blue along the original edges, there are 8 forms.
| Symmetry:, (*732) | +, (732) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| {7,3} | t0,1{7,3} | t1{7,3} | t1,2{7,3} | t2{7,3} | t0,2{7,3} | t0,1,2{7,3} | s{7,3} | |||
| Uniform duals | ||||||||||
| V73 | V3.14.14 | V3.7.3.7 | V6.6.7 | V37 | V3.4.7.4 | V4.6.14 | V3.3.3.3.7 | |||
Read more about this topic: Order-7 Truncated Triangular Tiling
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)