Regular square tilings of the torus have traditional subscripted labels with the format "(a,b)". The number of squares in a tiling is a2+b2.
| Name | Schläfli | V / F / E | mV, mF | notes | C&D no. | images |
|---|---|---|---|---|---|---|
| {4,4}(1,0) | {4,4}2 | 1 / 1 / 2 | 4,4 | β° κ° | R1.s1-0 | 1 |
| {4,4}(1,1) | {4,4}2 | 2 / 2 / 4 | 4,4 | γ° ζ'° ζ'°' μ° | R1.s1-1 | 6 |
| {4,4}(2,0) | {4,4}4 | 4 / 4 / 8 | 2,2 | θ θ' θ° λ λ' λ° | R1.s2-0 | 4 |
| {4,4}(2,1) | {4,4}10 | 5 / 5 / 10 | 1,1 | | C1.s2-1 | 1 |
| {4,4}(2,2) | {4,4}4 | 8 / 8 / 16 | 1,1 | μ μ' μ° | R1.s2-2 | 2 |
| {4,4}(3,0) | {4,4}6 | 9 / 9 / 18 | 1,1 | κ° | R1.s3-0 | 1 |
| {4,4}(3,1) | {4,4}10 | 10 / 10 / 20 | 1,1 | | C1.s3-1 | 2 |
| {4,4}(3,2) | {4,4}26 | 13 / 13 / 26 | 1,1 | | C1.s3-2 | 1 |
| {4,4}(4,0) | {4,4}8 | 16 / 16 / 32 | 1,1 | λ° | R1.s4-0 | 1 |
| {4,4}(4,1) | {4,4}34 | 17 / 17 / 34 | 1,1 | | C1.s4-1 | 1 |
| {4,4}(3,3) | {4,4}6 | 18 / 18 / 36 | 1,1 | μ° | R1.s3-3 | 1 |
| {4,4}(4,2) | {4,4}20 | 20 / 20 / 40 | 1,1 | | C1.s4-2 | 1 |
| {4,4}(5,0) | {4,4}10 | 25 / 25 / 50 | 1,1 | κ° | R1.s5-0 | 1 |
| {4,4}(4,3) | {4,4}50 | 25 / 25 / 50 | 1,1 | | C1.s4-3 | 1 |
| {4,4}(5,1) | {4,4}26 | 26 / 26 / 52 | 1,1 | | C1.s5-1 | 1 |
| {4,4}(5,2) | {4,4}58 | 29 / 29 / 58 | 1,1 | | C1.s5-2 | 1 |
| {4,4}(4,4) | {4,4}8 | 32 / 32 / 64 | 1,1 | μ° | R1.s4-4 | 1 |
| {4,4}(5,3) | {4,4}34 | 34 / 34 / 68 | 1,1 | | C1.s5-3 | 1 |
| {4,4}(6,0) | {4,4}12 | 36 / 36 / 72 | 1,1 | λ° | R1.s6-0 | 1 |
| {4,4}(6,1) | {4,4}74 | 37 / 37 / 74 | 1,1 | | C1.s6-1 | 1 |
| {4,4}(6,2) | {4,4}20 | 40 / 40 / 80 | 1,1 | | C1.s6-2 | 1 |
| {4,4}(5,4) | {4,4}82 | 41 / 41 / 82 | 1,1 | | C1.s5-4 | 1 |
| {4,4}(6,3) | {4,4}30 | 45 / 45 / 90 | 1,1 | | C1.s6-3 | 1 |
| {4,4}(7,0) | {4,4}14 | 49 / 49 / 98 | 1,1 | κ° | R1.s7-0 | 1 |
| {4,4}(5,5) | {4,4}10 | 50 / 50 / 100 | 1,1 | μ° | R1.s5-5 | 1 |
| {4,4}(7,1) | {4,4}50 | 50 / 50 / 100 | 1,1 | | C1.s7-1 | 1 |
| {4,4}(8,0) | {4,4}16 | 64 / 64 / 128 | 1,1 | λ° | R1.s8-0 | 0 |
| {4,4}(6,6) | {4,4}12 | 72 / 72 / 144 | 1,1 | μ° | R1.s6-6 | 0 |
| {4,4}(9,0) | {4,4}18 | 81 / 81 / 162 | 1,1 | κ° | R1.s9-0 | 0 |
| {4,4}(7,7) | {4,4}14 | 98 / 98 / 196 | 1,1 | μ° | R1.s7-7 | 0 |
| {4,4}(10,0) | {4,4}20 | 100 / 100 / 200 | 1,1 | λ° | R1.s10-0 | 0 |
| {4,4}(11,0) | {4,4}22 | 121 / 121 / 242 | 1,1 | κ° | R1.s11-0 | 0 |
| {4,4}(8,8) | {4,4}16 | 128 / 128 / 256 | 1,1 | μ° | R1.s8-8 | 0 |
| {4,4}(12,0) | {4,4}24 | 144 / 144 / 288 | 1,1 | λ° | R1.s12-0 | 0 |
| {4,4}(9,9) | {4,4}18 | 162 / 162 / 324 | 1,1 | μ° | R1.s9-9 | 0 |
| {4,4}(13,0) | {4,4}26 | 169 / 169 / 338 | 1,1 | κ° | R1.s13-0 | 0 |
| {4,4}(14,0) | {4,4}28 | 196 / 196 / 392 | 1,1 | λ° | R1.s14-0 | 0 |
| {4,4}(10,10) | {4,4}20 | 200 / 200 / 400 | 1,1 | μ° | R1.s10-10 | 0 |
| {4,4}(15,0) | {4,4}30 | 225 / 225 / 450 | 1,1 | κ° | R1.s15-0 | 0 |
| {4,4}(11,11) | {4,4}22 | 242 / 242 / 484 | 1,1 | μ° | R1.s11-11 | 0 |
| {4,4}(16,16) | {4,4}32 | 256 / 256 / 512 | 1,1 | μ° | R1.s16-16 | 0 |
| {4,4}(16,0) | {4,4}32 | 256 / 256 / 512 | 1,1 | λ° | R1.s16-0 | 0 |
| {4,4}(12,12) | {4,4}24 | 288 / 288 / 576 | 1,1 | μ° | R1.s12-12 | 0 |
| {4,4}(17,0) | {4,4}34 | 289 / 289 / 578 | 1,1 | κ° | R1.s17-0 | 0 |
| {4,4}(18,0) | {4,4}36 | 324 / 324 / 648 | 1,1 | λ° | R1.s18-0 | 0 |
| {4,4}(13,13) | {4,4}26 | 338 / 338 / 676 | 1,1 | μ° | R1.s13-13 | 0 |
| {4,4}(19,0) | {4,4}38 | 361 / 361 / 722 | 1,1 | κ° | R1.s19-0 | 0 |
| {4,4}(14,14) | {4,4}28 | 392 / 392 / 784 | 1,1 | μ° | R1.s14-14 | 0 |
| {4,4}(20,0) | {4,4}40 | 400 / 400 / 800 | 1,1 | λ° | R1.s20-0 | 0 |
| {4,4}(21,0) | {4,4}42 | 441 / 441 / 882 | 1,1 | κ° | R1.s21-0 | 0 |
| {4,4}(15,15) | {4,4}30 | 450 / 450 / 900 | 1,1 | μ° | R1.s15-15 | 0 |
| {4,4}(22,0) | {4,4}44 | 484 / 484 / 968 | 1,1 | λ° | R1.s22-0 | 0 |
A {4,4} with label (a,b) has Petrie polygons with 2(a2+b2) / gcd(a+b, a-b) edges.
There are separate pages for other regular maps of genus 1 showing hexagons only and triangles only.
| Orientable | |
| Non-orientable |