User:Double sharp/List of uniform tilings

The source for this page is this complete list by Hironori Sakamoto of the known convex and nonconvex Euclidean uniform tilings, including Coxeter's 39 and his own 13. The current total is 52 known uniform tilings. This page includes every tiling in that list, sorted by the Wythoff symbol in the same way as that page, but without pictures or any layout other than simple bullets here.

This page is secondary to User:Double sharp/List of uniform tilings by Schwarz triangle, and is mainly a source of info for that page that is easier to search through than the original page by Sakamoto.

p | 2 q

6 | 2 3 (triangular tiling, trat) 3⁶
3 | 3/2 ∞ (ditrigonal trihemiapeirogonal tiling, ditatha) (3.∞)³/2
3 | 2 6 (hexagonal tiling, hexat) 6³
4 | 2 4 (square tiling, squat) 4⁴
4 4/3 | ∞ (squarihemiapeirogonal tiling, sha) 4.∞.4/3.∞
2 | 2 ∞ (apeirogonal tiling, azat) ∞²

p | q r

2 | 3 6 (trihexagonal tiling, that) (3.6)²
3 3/2 | ∞ (trihemiapeirogonal tiling, tha) 3.∞.3/2.∞
6 6/5 | ∞ (hexahemiapeirogonal tiling, hoha) 6.∞.6/5.∞

2 p | q

2 3 | 6 (truncated hexagonal tiling, toxat) 3.12²
2 3 | 6/5 (quasitruncated hexagonal tiling, quitoxat) 3.12/5²
2 4 | 4 (truncated square tiling, tosquat) 4.8²
2 4 | 4/3 (quasitruncated square tiling, quitosquat) 4.8/3²
2 ∞ | 2 (apeirogonal prism, azip) 4².∞

p q | r

3 6 | 2 (rhombitrihexagonal tiling, rothat) 3.4.6.4
3/2 6 | 2 (quasirhombitrihexagonal tiling, qrothat) 3/2.4.6.4
3/2 6 | 6 (small hexatrihexagonal tiling, shothat) 3/2.12.6.12
3 6 | 6/5 (great hexatrihexagonal tiling, gahothat) 3.12/5.6.12/5
2 6 (3/2 6/2) | (small rhombihexagonal tiling, sarxat) 4.12.4/3.12/11
2 6/5 (3/2 6/2) | (great rhombihexagonal tiling, garxat) 4.12/5.4/3.12/7
6 ∞ | 6/5 (great hexahemihexagonal tiling, gaxahexat) 6.12/5.∞.12/5
4 ∞ | 4/3 (great squarihemisquare tiling, gashast) 4.8/3.∞.8/3
6/5 ∞ | 6 (small hexahemihexagonal tiling, saxahexat) 6/5.12.∞.12
4/3 ∞ | 4 (small squarihemisquare tiling, sashast) 4/3.8.∞.8
6 6/5 (6/2 ∞/2) | (blendic hexahexagonal tiling, blexaxat) 12.12/5.12/11.12/7
4 4/3 (4/2 ∞/2) | (blendic squarisquare tiling, blasasquat) 8.8/3.8/7.8/5

p q r |

2 3 6 | (truncated trihexagonal tiling, othat) 4.6.12
2 3 6/5 | (quasitruncated trihexagonal tiling, quothat) 4.6.12/5
2 4 4/3 | (quasiomnitruncated square tiling, quosquat) 4.8.8/3
3 6 6/5 | (trihexatruncated trihexagonal tiling, thatothat) 6.12.12/5
6 6/5 ∞ | (truncated hexahemiapeirogonal tiling, thoha) 12.12/5.∞
4 4/3 ∞ | (truncated squarihemiapeirogonal tiling, tisha) 8.8/3.∞

| p q r

| 2 3 6 (snub hexagonal tiling, snathat) 3⁴.6
| 2 4 4 (snub square tiling, snasquat) 3.4.3².4
| 2 4/3 4/3 (retrosnub square tiling, rassquat) 3.4/3.3².4/3
| 2 2 ∞ (apeirogonal antiprism, azap) 3³.∞
| 4 4/3 ∞ (snub squarihemiapeirogonal tiling, snasha) 3.4.3.4/3.3.∞

Non-Wythoffians

3³.4² (elongated triangular tiling, etrat)
3³.4/3² (retroelongated triangular tiling, retrat)
(3/2.∞)².3/2.4² (hemiretroelongated triangular tiling, haretrat)
(3/2.∞)².3/2.4/3² (hemielongated triangular tiling, hetrat)
(3/2.∞)².3/2.12/5.6.12/5 (hemiretroelongated great hexatrihexagonal tiling, hareghath)
(3/2.∞)².3/2.12/7.6/5.12/7 (hemielongated great hexatrihexagonal tiling, heghath)
(3/2.∞)².3/2.12.6/5.12 (hemiretroelongated small hexatrihexagonal tiling, hareshath)
(3/2.∞)².3/2.12/11.6.12/11 (hemielongated small hexatrihexagonal tiling, heshath)
3/2.∞.(3/2.4/3²)² (sisdirint?)
3/2.∞.(3/2.4²)² (gisdirint?)
3/2.∞.3/2.4².3/2.4/3² (irsint?)
4.∞.4/3.8/3.4.8/3 (irstobsint?)
4.∞.4/3.8.4/3.8 (irocsint?)
4.∞.4/3.8/3.8 (sirostobint?)
4.∞.4/3.8.8/3 (girostobint?)

(These are my names, instead of Sakamoto's, except for those with a question mark, which are Sakamoto's.)