User:Tomruen/uniform tilings

Summary

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1-uniform tilings include 3 regular tilings, and 8 semiregular ones, with 2 or more types of regular polygon faces. There are 20 2-uniform tilings. 3-uniform tilings include 22 2-Archimedean tilings and 39 3-Archimedean ones. The 3 regular tilings have regular dual tilings. In general n-isogonal tilings have n-isohedral dual tilings.

k-uniform, m-Archimedean tiling counts
m
k 1 2 3 4 5 6 Total
1 11 0 0 0 0 0 11
2 0 20 0 0 0 0 20
3 0 22 39 0 0 0 61
4 0 33 85 33 0 0 151
5 0 74 149 94 15 0 332
6 0 100 284 187 92 10 673

Vertex figures and dual faces

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Valance 3 Valance 4
6.6.6 4.6.12 4.8.8 3.12.12 4.4.4.4 3.6.3.6 3.3.6.6
Valance 4 Valance 5 Valance 6
3.4.4.6 3.4.6.4 3.4.3.12 3.3.4.12 3.3.4.3.4 3.3.3.4.4 3.3.3.3.6 3.3.3.3.3.3
Conway's codes

H

Q

Δ

Semiregular and duals (1-8)

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There are 8 semiregular tilings, and 8 duals.

1-uniform tilings and duals, rectangular symmetry, (1 of 8)
cmm, 2*22

33.42, Δ:e
Elongated triangular tiling

V33.42, dΔ:e
Prismatic pentagonal tiling
1-uniform tilings and duals, square symmetry, (2 of 8)
p4m, *442 p4, 442

4.82, tQ
Truncated square tiling

V4.82, dtQ
Tetrakis square tiling

32.4.3.4, sQ
Snub square tiling

V32.4.3.4, dsQ
Cairo pentagonal tiling
1-uniform tilings and duals, hexagonal symmetry, (5 of 8)
p6m, *632 p6, 632

3.122, tH
Truncated hexagonal tiling

(3.6)2, aH
Trihexagonal tiling

3.4.6.4, eH
Rhombitrihexagonal tiling

4.6.12, taH
Truncated trihexagonal tiling

34.6, sH
Snub hexagonal tiling

V3.122, dtH
Triakis triangular tiling

V(3.6)2, daH
Rhombille tiling

V3.4.6.4, deH
Deltoidal trihexagonal tiling

V4.6.12, dtaH
Kisrhombille tiling

V34.6, dsH
Floret pentagonal tiling

2-uniform and duals (1-20)

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There are 20 2-uniform tilings, and 20 duals:

2-uniform tilings, rectangular symmetry (9 of 20)
cmm, 2*22 cmm, 2*22 pmm, *2222 cmm, 2*22 cmm, 2*22

(44; 33.42)1, Δ:e2
(t=2, e=4)

(44; 33.42)2, Δ:e3
(t=3, e=5)

(36; 33.42)1, Δ:e/2
(t=3, e=4)

(36; 33.42)2, Δ:e/3
(t=4, e=5)

(3.42.6; (3.6)2)2, aH:e
(t=3, e=4)

(V44; V33.42)1

(V44; V33.42)2

(V36; V33.42)1

(V36; V33.42)2

(V3.42.6; V(3.6)2)2
pmm, *2222 pmm, *2222 cmm, 2*22 pgg, 2×

(3.42.6; (3.6)2)1
(t=4, e=4)

((3.6)2; 32.62)
(t=2, e=3)

(32.62; 34.6)
(t=2, e=4)

(33.42; 32.4.3.4)2
(t=6, e=6)

(V3.42.6; V(3.6)2)1

(V(3.6)2; V32.62)

(V32.62; V34.6)

(V33.42; V32.4.3.4)2
2-uniform tilings, square symmetry (2 of 20)
p4m, *442 p4g, 4*2

(3.12.12; 3.4.3.12)
(t=3, e=3)

(33.42; 32.4.3.4)1
(t=4, e=5)

(V3.12.12; V3.4.3.12)

(V33.42; V32.4.3.4)1
2-uniform tilings, hexagonal symmetry (9 of 20)
p6m, *632 p6m, *632 p6m, *632 p6, 632

(36; 32.62)
(t=2, e=3)

(36; 32.4.3.4)
(t=3, e=3)

(36; 34.6)1
(t=3, e=3)

(36; 34.6)2
(t=5, e=7)

(V36; V32.62)

(V36; V32.4.3.4)

(V36; V34.6)1

(V36; V34.6)2
p6m, *632

(3.4.6.4; 32.4.3.4)
(t=4, e=4)

(3.4.6.4; 33.42)
(t=4, e=4)

(3.4.6.4; 3.42.6)
(t=5, e=5)

(4.6.12; 3.4.6.4)
(t=4, e=4)

(36; 32.4.12)
(t=4, e=4)

(V3.4.6.4; V32.4.3.4)

(V3.4.6.4; V33.42)

(V3.4.6.4; V3.42.6)

(V4.6.12; V3.4.6.4)

(V36; V32.4.12)

3-uniform and duals

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There are 61 3-uniform tilings, and 61 duals:

3-uniform tilings and duals (1-30)

p6m
(t=4, e=5)

cmm
(t=2, e=4)

pmg
(t=2, e=5)

p6m
(t=2, e=3)

p6m
(t=6, e=7)

p3m1
(t=5, e=6)

p6m
(t=5, e=6)

p6m
(t=5, e=6)

cmm
(t=5, e=7)

cmm
(t=4, e=7)

cmm
(t=5, e=7)

pmm
(t=6, e=7)

pmm
(t=5, e=7)

pmm
(t=4, e=6)

cmm
(t=5, e=7)

cmm
(t=3, e=6)

cmm
(t=4, e=5)

pmm
(t=5, e=6)

pmm
(t=4, e=6)

pmm
(t=3, e=5)

cmm
(t=4, e=6)

p4g
(t=3, e=4)

p4
(t=4, e=6)

p6m
(t=5, e=6)

cmm
(t=4, e=6)

p6m
(t=6, e=6)

cmm
(t=5, e=8)

cmm
(t=6, e=8)

cmm
(t=4, e=7)

pmg
(t=4, e=6)

3-uniform and duals (31-61)

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3-uniform tilings and duals (31-61)

pmm
(t=5, e=7)

cmm
(t=5, e=6)

pmm
(t=5, e=7)

p6m
(t=5, e=6)

p6m
(t=6, e=8)

p6m
(t=6, e=6)

p6m
(t=6, e=6)

pmg
(t=5, e=8)

cmm
(t=3, e=5)

pmm
(t=3, e=5)

cmm
(t=3, e=6)

p6m
(t=4, e=4)

p6m
(t=3, e=3)

cmm
(t=5, e=6)

pmg
(t=4, e=7)

p2
(t=4, e=7)

p6m
(t=6, e=7)

p6m
(t=5, e=6)

pmm
(t=5, e=6)

cmm
(t=6, e=7)

cmm
(t=4, e=6)

pmg
(t=5, e=7)

pgg
(t=5, e=8)

p6m
(t=4, e=5)

p2
(t=6, e=9)

p6m
(t=5, e=6)

p6m
(t=8, e=5)

p6m
(t=3, e=4)

p6m
(t=5, e=5)

p6
(t=7, e=9)

cmm
(t=4, e=6)

4-uniform and duals

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There are 151 4-uniform tilings, and 151 duals:

4-uniform and duals (1-25)

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4-uniform tilings and duals (1-25)

p6m, *632

p6m, *632

cmm, 2*22

cmm, 2*22

cmm, 2*22

p6m, *632

p6m, *632

p6m, *632

p6, 632

p6, 632

cmm, 2*22

cmm, 2*22

cmm, 2*22

p6m, *632

pmm, *2222

pmm, *2222

p6, 632

pmm, *2222

pmm, *2222

pmm, *2222

pmm, *2222

p6m, *632

p6, 632

p6, 632

p6m, *632

4-uniform and duals (26-50)

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4-uniform tilings and duals (26-50)

4-uniform and duals (51-75)

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4-uniform tilings and duals (51-100)

4-uniform and duals (76-100)

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4-uniform tilings and duals (76-100)

4-uniform and duals (101-125)

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4-uniform tilings and duals (101-125)

4-uniform and duals (125-151)

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4-uniform tilings and duals (125-151)

5-uniform tilings and duals (1-332)

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5-uniform tilings

[3342; 3262; 3446; (63)2]

[36; (3262)2; (63)2]

[36; 346; 3262; (63)2]

[3262; 3636; (63)3]

[346; 3262; (63)3]

[3342; 3262; 3446; (63)2]

[36; (3262)2; (63)2]

[36; 346; 3262; (63)2]

[3262; 3636; (63)3]

[346; 3262; (63)3]

[36; (3262)3; 63]

[36; 346; (3262)2; 63]

[346; (3262)2; 3636; 63]

[(3262)2; (3636)2; 63]

[(346)2; 3262; 3636; 63]

[36; (3262)3; 63]

[36; 346; (3262)2; 63]

[346; (3262)2; 3636; 63]

[(3262)2; (3636)2; 63]

[(346)2; 3262; 3636; 63]

[(36)2; 346; 3262; 63]

[36; (346)2; 3262; 63]

[(346)2; (3262)2; 63]

[(36)2; 346; 3262; 63]

[(36)2; 346; 3262; 63]

[(36)2; 346; 3262; 63]

[36; (346)2; 3262; 63]

[(346)2; (3262)2; 63]

[(36)2; 346; 3262; 63]

[(36)2; 346; 3262; 63]

[3342; 3262; 3446; (63)2]

[36; (3262)2; (63)2]

[36; 346; 3262; (63)2]

[(3262)2; 3636; (63)2]

[36; 346; 3262; (63)2]

[3342; 3262; 3446; (63)2]

[36; (3262)2; (63)2]

[36; 346; 3262; (63)2]

[(3262)2; 3636; (63)2]

[36; 346; 3262; (63)2]

[36; 346; 3262; (63)2]

[36; (3262)3; 63]

[36; 346; (3262)2; 63]

[346; (3262)2; 3636; 63]

[3262; (3636)3; 63]

[36; 346; 3262; (63)2]

[36; (3262)3; 63]

[36; 346; (3262)2; 63]

[346; (3262)2; 3636; 63]

[3262; (3636)3; 63]

[346; (3262)2; 3636; 63]

[346; (3262)2; 3636; 63]

[346; 3262; 3636; (63)2]

[33434; 3262; 3464; 3446; 63]

[36; 346; 3262; 3636; 63]

[346; (3262)2; 3636; 63]

[346; (3262)2; 3636; 63]

[346; 3262; 3636; (63)2]

[33434; 3262; 3464; 3446; 63]

[36; 346; 3262; 3636; 63]

[346; (3262)2; 3636; 63]

[36; 334.12; (46.12)3]

[36; 33434; (3446)2; 46.12]

[(3446)2; (3636)2; 46.12]

[36; 346; 3342; 3446; 46.12]

[346; (3262)2; 3636; 63]

[36; 334.12; (46.12)3]

[36; 33434; (3446)2; 46.12]

[(3446)2; (3636)2; 46.12]

[36; 346; 3342; 3446; 46.12]

[(3464)4; 46.12]

[36; 33434; 3446; (46.12)2]

[36; 33434; 3464; (46.12)2]

[(3464)2; (46.12)3]

[3464; 3446; (46.12)3]

[(3464)4; 46.12]

[36; 33434; 3446; (46.12)2]

[36; 33434; 3464; (46.12)2]

[(3464)2; (46.12)3]

[3464; 3446; (46.12)3]

[(3464)2; (46.12)3]

[36; (334.12)3; 46.12]

[33434; 334.12; 3464; 3.12.12; 46.12]

[343.12; (3.12.12)4]

[334.12; 343.12; (3.12.12)3]

[(3464)2; (46.12)3]

[36; (334.12)3; 46.12]

[33434; 334.12; 3464; 3.12.12; 46.12]

[343.12; (3.12.12)4]

[334.12; 343.12; (3.12.12)3]

[36; 33434; 334.12; (3.12.12)2]

[36; 33434; 343.12; (3.12.12)2]

[(3342)2; 334.12; 343.12; 3.12.12]

[(3342)2; 334.12; 343.12; 3.12.12]

[3342; (44)4]

[36; 33434; 334.12; (3.12.12)2]

[36; 33434; 343.12; (3.12.12)2]

[(3342)2; 334.12; 343.12; 3.12.12]

[(3342)2; 334.12; 343.12; 3.12.12]

[3342; (44)4]

[3446; 3636; (44)3]

[3446; 3636; (44)3]

[(3342)2; (44)3]

[36; 3342; (44)3]

[36; 3342; (44)3]

[3446; 3636; (44)3]

[3446; 3636; (44)3]

[(3342)2; (44)3]

[36; 3342; (44)3]

[36; 3342; (44)3]

[(3446)2; 3636; (44)2]

[(3446)2; 3636; (44)2]

[3262; 3446; 3636; (44)2]

[3446; (3636)2; (44)2]

[(3446)2; 3636; (44)2]

[(3446)2; 3636; (44)2]

[(3446)2; 3636; (44)2]

[3262; 3446; 3636; (44)2]

[3446; (3636)2; (44)2]

[(3446)2; 3636; (44)2]

[(3446)2; 3636; (44)2]

[3262; 3446; 3636; (44)2]

[3446; (3636)2; (44)2]

[(3342)2; (44)3]

[(3342)2; (44)3]

[(3446)2; 3636; (44)2]

[3262; 3446; 3636; (44)2]

[3446; (3636)2; (44)2]

[(3342)2; (44)3]

[(3342)2; (44)3]

[(3342)3; (44)2]

[36; (3342)2; (44)2]

[(36)2; 3342; (44)2]

[(36)2; 3342; (44)2]

[(3446)2; 3636; (44)2]

[(3342)3; (44)2]

[36; (3342)2; (44)2]

[(36)2; 3342; (44)2]

[(36)2; 3342; (44)2]

[(3446)2; 3636; (44)2]

[(3446)2; 3636; (44)2]

[(3446)2; 3636; (44)2]

[3262; 3446; (3636)2; 44]

[3446; (3636)3; 44]

[36; 346; 3446; 3636; 44]

[(3446)2; 3636; (44)2]

[(3446)2; 3636; (44)2]

[3262; 3446; (3636)2; 44]

[3446; (3636)3; 44]

[36; 346; 3446; 3636; 44]

[(3446)2; 3636; (44)2]

[(3446)2; 3636; (44)2]

[3262; 3446; (3636)2; 44]

[3446; (3636)3; 44]

[36; 346; 3446; 3636; 44]

[(3446)2; 3636; (44)2]

[(3446)2; 3636; (44)2]

[3262; 3446; (3636)2; 44]

[3446; (3636)3; 44]

[36; 346; 3446; 3636; 44]

[(3342)2; (44)3]

[(3342)3; (44)2]

[(3342)4; 44]

[36; (3342)3; 44]

[36; (3342)3; 44]

[(3342)2; (44)3]

[(3342)3; (44)2]

[(3342)4; 44]

[36; (3342)3; 44]

[36; (3342)3; 44]

[36; (3342)2; (44)2]

[36; (3342)3; 44]

[(36)2; (3342)2; 44]

[(36)3; 3342; 44]

[(36)3; 3342; 44]

[36; (3342)2; (44)2]

[36; (3342)3; 44]

[(36)2; (3342)2; 44]

[(36)3; 3342; 44]

[(36)3; 3342; 44]

[3342; 3262; 3446; (44)2]

[346; 3342; 3446; (44)2]

[33434; 3262; (3446)2; 44]

[(3342)2; 334.12; 343.12; 44]

[3342; (44)4]

[3342; 3262; 3446; (44)2]

[346; 3342; 3446; (44)2]

[33434; 3262; (3446)2; 44]

[(3342)2; 334.12; 343.12; 44]

[3342; (44)4]

[3446; 3636; (44)3]

[3446; 3636; (44)3]

[(3342)2; (44)3]

[36; 3342; (44)3]

[36; 3342; (44)3]

[3446; 3636; (44)3]

[3446; 3636; (44)3]

[(3342)2; (44)3]

[36; 3342; (44)3]

[36; 3342; (44)3]

[(3446)2; 3636; (44)2]

[(3446)2; 3636; (44)2]

[3262; 3446; 3636; (44)2]

[3446; (3636)2; (44)2]

[(3446)2; 3636; (44)2]

[(3446)2; 3636; (44)2]

[(3446)2; 3636; (44)2]

[3262; 3446; 3636; (44)2]

[3446; (3636)2; (44)2]

[(3446)2; 3636; (44)2]

[(3446)2; 3636; (44)2]

[3262; 3446; 3636; (44)2]

[3446; (3636)2; (44)2]

[(3342)2; (44)3]

[(3342)3; (44)2]

[(3446)2; 3636; (44)2]

[3262; 3446; 3636; (44)2]

[3446; (3636)2; (44)2]

[(3342)2; (44)3]

[(3342)3; (44)2]

[36; (3342)2; (44)2]

[(36)2; 3342; (44)2]

[(36)2; 3342; (44)2]

[(3342)3; (44)2]

[36; (3342)2; (44)2]

[36; (3342)2; (44)2]

[(36)2; 3342; (44)2]

[(36)2; 3342; (44)2]

[(3342)3; (44)2]

[36; (3342)2; (44)2]

[36; (3342)2; (44)2]

[(3446)2; 3636; (44)2]

[3262; 3446; (3636)2; 44]

[3446; (3636)3; 44]

[36; 346; 3446; 3636; 44]

[36; (3342)2; (44)2]

[(3446)2; 3636; (44)2]

[3262; 3446; (3636)2; 44]

[3446; (3636)3; 44]

[36; 346; 3446; 3636; 44]

[3262; 3446; (3636)2; 44]

[3446; (3636)3; 44]

[36; 346; 3446; 3636; 44]

[36; 3342; 3446; 3636; 44]

[36; 346; 3342; 3446; 44]

[3262; 3446; (3636)2; 44]

[3446; (3636)3; 44]

[36; 346; 3446; 3636; 44]

[36; 3342; 3446; 3636; 44]

[36; 346; 3342; 3446; 44]

[3342; 3262; 3446; (44)2]

[346; 3342; 3446; (44)2]

[346; 3342; 33434; 3446; 44]

[(3342)4; 44]

[36; (3342)3; 44]

[3342; 3262; 3446; (44)2]

[346; 3342; 3446; (44)2]

[346; 3342; 33434; 3446; 44]

[(3342)4; 44]

[36; (3342)3; 44]

[36; (3342)3; 44]

[36; (3342)3; 44]

[(36)2; (3342)2; 44]

[(36)3; 3342; 44]

[(36)3; 3342; 44]

[36; (3342)3; 44]

[36; (3342)3; 44]

[(36)2; (3342)2; 44]

[(36)3; 3342; 44]

[(36)3; 3342; 44]

[(3342)4; 44]

[36; (3342)3; 44]

[(36)2; (3342)2; 44]

[(36)2; (3342)2; 44]

[36; (3342)3; 44]

[(3342)4; 44]

[36; (3342)3; 44]

[(36)2; (3342)2; 44]

[(36)2; (3342)2; 44]

[36; (3342)3; 44]

[36; (3342)3; 44]

[(36)2; (3342)2; 44]

[346; (3342)2; 3636; 44]

[36; (3342)2; 33434; 44]

[346; (3342)2; 33434; 44]

[36; (3342)3; 44]

[(36)2; (3342)2; 44]

[346; (3342)2; 3636; 44]

[36; (3342)2; 33434; 44]

[346; (3342)2; 33434; 44]

[36; 3342; (3464)2; 3446]

[3342; 3262; 3464; (3446)2]

[33434; 3262; 3464; (3446)2]

[36; 33434; (3446)2; 3636]

[(33434)2; 3262; (3446)2]

[36; 3342; (3464)2; 3446]

[3342; 3262; 3464; (3446)2]

[33434; 3262; 3464; (3446)2]

[36; 33434; (3446)2; 3636]

[(33434)2; 3262; (3446)2]

[(3464)3; (3446)2]

[3342; 33434; 3464; (3446)2]

[36; 33434; (3262)2; 3446]

[(3342)3; 3262; 3446]

[3342; (3262)2; (3446)2]

[(3464)3; (3446)2]

[3342; 33434; 3464; (3446)2]

[36; 33434; (3262)2; 3446]

[(3342)3; 3262; 3446]

[3342; (3262)2; (3446)2]

[3342; (3262)2; (3446)2]

[3342; 3262; (3464)2; 3446]

[33434; 3262; (3464)2; 3446]

[(3446)3; (3636)2]

[36; 3342; (3446)2; 3636]

[3342; (3262)2; (3446)2]

[3342; 3262; (3464)2; 3446]

[33434; 3262; (3464)2; 3446]

[(3446)3; (3636)2]

[36; 3342; (3446)2; 3636]

[3262; (3446)2; (3636)2]

[(3262)2; 3446; (3636)2]

[3262; 3446; (3636)3]

[(3446)2; (3636)3]

[3262; 3446; (3636)3]

[3262; (3446)2; (3636)2]

[(3262)2; 3446; (3636)2]

[3262; 3446; (3636)3]

[(3446)2; (3636)3]

[3262; 3446; (3636)3]

[3446; (3636)4]

[346; (3342)2; 3446; 3636]

[346; (3342)2; 3446; 3636]

[(36)2; 346; 3446; 3636]

[(3446)3; (3636)2]

[3446; (3636)4]

[346; (3342)2; 3446; 3636]

[346; (3342)2; 3446; 3636]

[(36)2; 346; 3446; 3636]

[(3446)3; (3636)2]

[36; 3342; (3446)2; 3636]

[(3262)2; 3446; (3636)2]

[3262; 3446; (3636)3]

[3262; 3446; (3636)3]

[3446; (3636)4]

[36; 3342; (3446)2; 3636]

[(3262)2; 3446; (3636)2]

[3262; 3446; (3636)3]

[3262; 3446; (3636)3]

[3446; (3636)4]

[346; (3342)2; 3446; 3636]

[346; (3342)2; 3446; 3636]

[(36)2; 346; 3446; 3636]

[(3464)2; (3446)2; 3636]

[3262; (3446)2; (3636)2]

[346; (3342)2; 3446; 3636]

[346; (3342)2; 3446; 3636]

[(36)2; 346; 3446; 3636]

[(3464)2; (3446)2; 3636]

[3262; (3446)2; (3636)2]

[(3446)2; (3636)3]

[3262; (3446)2; (3636)2]

[(3446)2; (3636)3]

[(3342)3; 3446; 3636]

[(3342)3; 3446; 3636]

[(3446)2; (3636)3]

[3262; (3446)2; (3636)2]

[(3446)2; (3636)3]

[(3342)3; 3446; 3636]

[(3342)3; 3446; 3636]

[(36)2; 3342; 3446; 3636]

[36; 3342; 3262; 3446; 3636]

[36; 3342; 3446; (3636)2]

[(346)2; (3446)2; 3636]

[346; 3342; (3446)2; 3636]

[(36)2; 3342; 3446; 3636]

[36; 3342; 3262; 3446; 3636]

[36; 3342; 3446; (3636)2]

[(346)2; (3446)2; 3636]

[346; 3342; (3446)2; 3636]

[(346)2; (3446)2; 3636]

[(346)2; (3446)2; 3636]

[(346)2; (3446)2; 3636]

[(3342)2; (3446)2; 3636]

[(3342)2; (3446)2; 3636]

[(346)2; (3446)2; 3636]

[(346)2; (3446)2; 3636]

[(346)2; (3446)2; 3636]

[(3342)2; (3446)2; 3636]

[(3342)2; (3446)2; 3636]

[36; 33434; 3464; 3446; 3636]

[36; 346; 3464; 3446; 3636]

[36; 346; (3342)2; 3446]

[36; 346; 3342; 3262; 3446]

[36; (346)2; 3342; 3446]

[36; 33434; 3464; 3446; 3636]

[36; 346; 3464; 3446; 3636]

[36; 346; (3342)2; 3446]

[36; 346; 3342; 3262; 3446]

[36; (346)2; 3342; 3446]

[(346)2; (3342)2; 3446]

[36; (346)2; 3342; 3446]

[36; (346)2; 3342; 3446]

[346; (3342)3; 3446]

[(346)2; 3342; (3446)2]

[(346)2; (3342)2; 3446]

[36; (346)2; 3342; 3446]

[36; (346)2; 3342; 3446]

[346; (3342)3; 3446]

[(346)2; 3342; (3446)2]

[346; 3342; (3464)2; 3446]

[36; 3342; (334.12)2; 3464]

[(36)2; (3342)2; 3464]

[36; (3342)2; 33434; 3464]

[36; (3342)2; 33434; 3464]

[346; 3342; (3464)2; 3446]

[36; 3342; (334.12)2; 3464]

[(36)2; (3342)2; 3464]

[36; (3342)2; 33434; 3464]

[36; (3342)2; 33434; 3464]

[36; (3342)2; 334.12; 3464]

[36; 3342; (33434)2; 3464]

[36; 33434; (334.12)2; 3464]

[(36)2; 3342; 33434; 3464]

[36; 3342; (33434)2; 3464]

[36; (3342)2; 334.12; 3464]

[36; 3342; (33434)2; 3464]

[36; 33434; (334.12)2; 3464]

[(36)2; 3342; 33434; 3464]

[36; 3342; (33434)2; 3464]

[(33434)2; (3464)3]

[(3342)2; 334.12; (3464)2]

[36; (33434)2; (3464)2]

[(33434)3; (3464)2]

[3342; (33434)2; (3464)2]

[(33434)2; (3464)3]

[(3342)2; 334.12; (3464)2]

[36; (33434)2; (3464)2]

[(33434)3; (3464)2]

[3342; (33434)2; (3464)2]

[3342; (33434)2; (3464)2]

[3342; (33434)2; (3464)2]

[(33434)2; 343.12; (3464)2]

[36; 346; (3342)2; 3262]

[(36)3; 346; 3262]

[3342; (33434)2; (3464)2]

[3342; (33434)2; (3464)2]

[(33434)2; 343.12; (3464)2]

[36; 346; (3342)2; 3262]

[(36)3; 346; 3262]

[(36)3; 346; 3262]

[(36)3; 346; 3262]

[(36)2; 346; 3262; 3636]

[(36)2; (346)2; 3262]

[36; 346; (3262)2; 3636]

[(36)3; 346; 3262]

[(36)3; 346; 3262]

[(36)2; 346; 3262; 3636]

[(36)2; (346)2; 3262]

[36; 346; (3262)2; 3636]

[36; (346)2; (3262)2]

[(36)2; 346; (3262)2]

[346; (3262)3; 3636]

[36; (346)2; (3262)2]

[346; (3262)2; (3636)2]

[36; (346)2; (3262)2]

[(36)2; 346; (3262)2]

[346; (3262)3; 3636]

[36; (346)2; (3262)2]

[346; (3262)2; (3636)2]

[(346)2; (3262)2; 3636]

[36; (346)2; (3262)2]

[(3262)2; (3636)3]

[3262; (3636)4]

[346; (3342)2; 3262; 3636]

[(346)2; (3262)2; 3636]

[36; (346)2; (3262)2]

[(3262)2; (3636)3]

[3262; (3636)4]

[346; (3342)2; 3262; 3636]

[346; (3342)2; 3262; 3636]

[(36)2; 346; 3262; 3636]

[346; (3262)3; 3636]

[3262; (3636)4]

[36; 346; 3262; (3636)2]

[346; (3342)2; 3262; 3636]

[(36)2; 346; 3262; 3636]

[346; (3262)3; 3636]

[3262; (3636)4]

[36; 346; 3262; (3636)2]

[36; (346)2; 3262; 3636]

[36; (346)2; 3262; 3636]

[36; (346)2; 3262; 3636]

[(346)3; 3262; 3636]

[(346)2; 3262; (3636)2]

[36; (346)2; 3262; 3636]

[36; (346)2; 3262; 3636]

[36; (346)2; 3262; 3636]

[(346)3; 3262; 3636]

[(346)2; 3262; (3636)2]

[(346)3; 3262; 3636]

[36; (346)2; 3262; 3636]

[36; 346; (3262)2; 3636]

[36; 346; (3262)2; 3636]

[(346)2; (3262)2; 3636]

[(346)3; 3262; 3636]

[36; (346)2; 3262; 3636]

[36; 346; (3262)2; 3636]

[36; 346; (3262)2; 3636]

[(346)2; (3262)2; 3636]

[(36)3; 346; 3262]

[(36)3; 346; 3262]

[(36)2; (346)2; 3262]

[(36)2; (346)2; 3262]

[(36)2; (346)2; 3262]

[(36)3; 346; 3262]

[(36)3; 346; 3262]

[(36)2; (346)2; 3262]

[(36)2; (346)2; 3262]

[(36)2; (346)2; 3262]

[(346)3; 3262; 3636]

[(346)4; 3262]

[(346)4; 3262]

[36; (346)2; (3262)2]

[36; (346)2; (3262)2]

[(346)3; 3262; 3636]

[(346)4; 3262]

[(346)4; 3262]

[36; (346)2; (3262)2]

[36; (346)2; (3262)2]

[36; 346; (3636)3]

[(346)3; (3636)2]

[36; 346; (3636)3]

[346; (3342)2; (3636)2]

[346; (3342)2; (3636)2]

[36; 346; (3636)3]

[(346)3; (3636)2]

[36; 346; (3636)3]

[346; (3342)2; (3636)2]

[346; (3342)2; (3636)2]

[(36)2; 346; (3636)2]

[36; 346; (3636)3]

[36; 346; (3636)3]

[(36)2; (346)2; 3636]

[(346)3; (3636)2]

[(36)2; 346; (3636)2]

[36; 346; (3636)3]

[36; 346; (3636)3]

[(36)2; (346)2; 3636]

[(346)3; (3636)2]

[(346)2; (3636)3]

[(36)2; 346; 3342; 3636]

[(36)2; 346; 3342; 3636]

[(36)3; 346; 3636]

[(36)3; 346; 3636]

[(346)2; (3636)3]

[(36)2; 346; 3342; 3636]

[(36)2; 346; 3342; 3636]

[(36)3; 346; 3636]

[(36)3; 346; 3636]

[36; (346)3; 3636]

[(346)4; 3636]

[(36)2; (346)2; 3636]

[(36)2; (346)2; 3636]

[36; 346; (3342)2; 334.12]

[36; (346)3; 3636]

[(346)4; 3636]

[(36)2; (346)2; 3636]

[(36)2; (346)2; 3636]

[36; 346; (3342)2; 334.12]

[(36)2; 3342; 33434; 334.12]

[36; 33434; (334.12)2; 343.12]

[36; (33434)3; 343.12]

[36; (3342)4]

[(36)2; (3342)3]

[(36)2; 3342; 33434; 334.12]

[36; 33434; (334.12)2; 343.12]

[36; (33434)3; 343.12]

[36; (3342)4]

[(36)2; (3342)3]

[(36)2; (3342)3]

[(36)2; (3342)3]

[(36)2; (3342)3]

[(36)4; 3342]

[(36)4; 3342]

[(36)2; (3342)3]

[(36)2; (3342)3]

[(36)2; (3342)3]

[(36)4; 3342]

[(36)4; 3342]

[36; (346)2; (3342)2]

[(36)2; 346; 3342; 33434]

[(36)2; 3342; (33434)2]

[36; (3342)4]

[36; (3342)4]

[36; (346)2; (3342)2]

[(36)2; 346; 3342; 33434]

[(36)2; 3342; (33434)2]

[36; (3342)4]

[36; (3342)4]

[(36)3; (3342)2]

[(36)3; (3342)2]

[(36)3; (3342)2]

[(36)3; (3342)2]

[(36)3; (3342)2]

[(36)3; (3342)2]

[(36)3; (3342)2]

[(36)3; (3342)2]

[(36)3; (3342)2]

[(36)3; (3342)2]

[(36)3; (3342)2]

[(36)2; (3342)2; 33434]

[(3342)3; (33434)2]

[(3342)4; 33434]

[(3342)3; (33434)2]

[(36)3; (3342)2]

[(36)2; (3342)2; 33434]

[(3342)3; (33434)2]

[(3342)4; 33434]

[(3342)3; (33434)2]

[(3342)2; (33434)3]

[3342; (33434)4]

[(36)2; 3342; (33434)2]

[346; (3342)2; (33434)2]

[(3342)2; (33434)3]

[(3342)2; (33434)3]

[3342; (33434)4]

[(36)2; 3342; (33434)2]

[346; (3342)2; (33434)2]

[(3342)2; (33434)3]

[(36)2; 3342; (33434)2]

[(36)2; 3342; (33434)2]

[36; (33434)4]

[36; (33434)4]

[(36)4; 346]

[(36)2; 3342; (33434)2]

[(36)2; 3342; (33434)2]

[36; (33434)4]

[36; (33434)4]

[(36)4; 346]

[(36)4; 346]

[(36)4; 346]

[(36)2; (346)3]

[(36)2; (346)3]

[(36)3; (346)2]

[(36)4; 346]

[(36)4; 346]

[(36)2; (346)3]

[(36)2; (346)3]

[(36)3; (346)2]

[(36)3; (346)2]

[(36)3; (346)2]

[(36)3; (346)2]

[36; (346)4]

[(36)2; (346)3]

[(36)3; (346)2]

[(36)3; (346)2]

[(36)3; (346)2]

[36; (346)4]

[(36)2; (346)3]

[(36)2; (346)3]

[(36)2; (346)3]

[(36)2; (346)3]

[(36)2; (346)3]

all n-gonal duals

edit

Triangles

edit

V6.6.6

V4.6.12

V4.82

V3.122
Regular Semiregular

V6.6.6

V4.6.12

V4.82

V3.122

Quadrilaterals

edit

V4.4.4.4

V3.6.3.6

V3.3.6.6

V3.4.4.6

V3.4.6.4

V3.4.3.12

V3.3.4.12
Regular Semiregular

V4.4.4.4

V3.6.3.6

V3.4.6.4
2-uniform
3-uniform
3-uniform
3-uniform
4-uniform
4-uniform
4-uniform
4-uniform
4-uniform
4-uniform
4-uniform
4-uniform

Pentagons

edit

V3.3.4.3.4

V3.3.3.4.4

V3.3.3.3.6
Semiregular

V32.4.3.4

V33.42

V34.6
2-uniform
3-uniform
4-uniform

Hexagons

edit

V3.3.3.3.3.3

V3.3.3.3.3.3 = 6.6.6

References

edit
  • Grunbaum, Branko; Shephard, Geoffrey C. (1977). "Tilings by regular polygons". Math. Mag. 50 (5): 227–247. doi:10.2307/2689529. JSTOR 2689529.
  • Grünbaum, Branko; Shephard, G. C. (1978). "The ninety-one types of isogonal tilings in the plane". Trans. Am. Math. Soc. 252: 335–353. doi:10.1090/S0002-9947-1978-0496813-3. MR 0496813.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  • Debroey, I.; Landuyt, F. (1981). "Equitransitive edge-to-edge tilings". Geometriae Dedicata. 11 (1): 47–60. doi:10.1007/BF00183189.
  • Grünbaum, Branko; Shephard, G. C. (1987). Tilings and Patterns. W. H. Freeman and Company. ISBN 0-7167-1193-1.{{cite book}}: CS1 maint: multiple names: authors list (link)
  • Ren, Ding; Reay, John R. (1987). "The boundary characteristic and Pick's theorem in the Archimedean planar tilings". J. Combinat. Theory A. 44 (1): 110–119. doi:10.1016/0097-3165(87)90063-X.
  • Chavey, D. (1989). "Tilings by Regular Polygons—II: A Catalog of Tilings". Computers & Mathematics with Applications. 17: 147–165. doi:10.1016/0898-1221(89)90156-9.
  • Order in Space: A design source book, Keith Critchlow, 1970 ISBN 978-0-670-52830-1
  • Sommerville, Duncan MacLaren Young (1958). An Introduction to the Geometry of n Dimensions. Dover Publications. Chapter X: The Regular Polytopes
  • Préa, P. (1997). "Distance sequences and percolation thresholds in Archimedean Tilings". Mathl. Comput. Modelling. 26 (8–10): 317–320. doi:10.1016/S0895-7177(97)00216-1.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  • Kovic, Jurij (2011). "Symmetry-type graphs of Platonic and Archimedean solids". Math. Commun. 16 (2): 491–507.
  • Pellicer, Daniel; Williams, Gordon (2012). "Minimal covers of the Archimedean Tilings". El. J. Combinat. 19 (3): #P6. doi:10.37236/2512.
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