Cantic octagonal tiling explained
In geometry, the tritetratrigonal tiling or shieldotritetragonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t1,2(4,3,3). It can also be named as a cantic octagonal tiling, h2.
Related polyhedra and tiling
*n33 orbifold symmetries of cantic tilings: 3.6.n.6Symmetry
*n32
[1<sup>+</sup>,2n,3]
= [(n,3,3)] | Spherical | Euclidean | Compact Hyperbolic | Paracompact |
|---|
- 233
[1<sup>+</sup>,4,3]
= [3,3]
| - 333
[1<sup>+</sup>,6,3]
= [(3,3,3)]
| - 433
[1<sup>+</sup>,8,3]
= [(4,3,3)]
| - 533
[1<sup>+</sup>,10,3]
= [(5,3,3)]
| - 633...
[1<sup>+</sup>,12,3]
= [(6,3,3)]
| - ∞33
[1<sup>+</sup>,∞,3]
= [(∞,3,3)]
|
|---|
Coxeter
Schläfli | =
h2 | =
h2 | =
h2 | =
h2 | =
h2 | =
h2 |
|---|
Cantic
figure | | | | | | |
|---|
| Vertex | 3.6.2.6 | 3.6.3.6 | 3.6.4.6 | 3.6.5.6 | 3.6.6.6 | 3.6.∞.6 |
|---|
Domain | | | | | | |
|---|
| Wythoff | 2 3 3 | 3 3 3 | 4 3 3 | 5 3 3 | 6 3 3 | ∞ 3 3 |
|---|
Dual
figure | | | | | | |
|---|
| Face | V3.6.2.6 | V3.6.3.6 | V3.6.4.6 | V3.6.5.6 | V3.6.6.6 | V3.6.∞.6 | |
|---|
See also
References
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, (Chapter 19, The Hyperbolic Archimedean Tessellations)
- Book: The Beauty of Geometry: Twelve Essays. 1999. Dover Publications. 99035678. 0-486-40919-8. Chapter 10: Regular honeycombs in hyperbolic space.
External links
