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User:Tomruen/tempx

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Symmetries

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Right triangle domains

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[p,q] = *pq2

332

432

442

532

542

552

632

642

652

662

732

742

752

762

772

832

842

852

862

872

882

∞32

∞42

∞52

i62

∞72

∞82

∞∞2

Isosceles/equilateral triangle domains

[edit]
[1+,2p,q] = *pqq (orbifold), p=2..4,∞, q=2..8,∞

332

333

433

533

633

733

833

∞33

442

443

444

445

446

447

448

∞44

552

553

554

555

556

558

555

∞55

662

663

664

665

666

667

668

∞66

772

773

774

775

776

777

778

∞77

882

883

884

885

886

887

888

∞88

∞∞2

∞∞3

∞∞4

∞∞5

∞∞6

∞∞7

∞∞8

∞∞∞

Kite/rhombus/square domains

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[2p,1+,2q] = *p2q2 (orbifold), p=2..4,∞, q=2..4,∞

*2222

*3222

*3232

*4222

*4232

*4242

*∞222

*∞232

*∞242

*∞2∞2

Regular polygon domains

[edit]
[1+,2p,1+,2q] = p*q (orbifold) = {p,2q}, p=3..8,∞; q=2..8,∞

3*2 ={3,4}

4*2 ={4,4}

5*2 ={5,4}

6*2 ={6,4}

7*2 ={7,4}

8*2 ={8,4}

∞*2 ={∞,4}

3*3 ={3,6}

4*3 ={4,6}

5*3 ={5,6}

6*3 ={6,6}

7*3 ={7,6}

8*3 ={8,6}

∞*3 ={∞,6}

3*4 ={3,8}

4*4 ={4,8}

5*4 ={5,8}

6*4 ={6,8}

7*4 ={7,8}

8*4 ={8,8}

∞*4 ={∞,8}

3*5 ={3,10}

4*5 ={4,10}

5*5 ={5,10}

6*5 ={6,10}

7*5 ={7,10}

8*5 ={8,10}

∞*5 ={∞,10}

3*6 ={3,12}

4*6 ={4,12}

5*6 ={5,12}

6*6 ={6,12}

7*6 ={7,12}

8*6 ={8,12}

∞*6 ={∞,12}

3*7

4*7

5*7

6*7

7*7

8*7

∞*7

3*8

4*8

5*8

6*8

7*8

8*8

∞*8

3*∞

4*∞

5*∞

6*∞

7*∞

8*∞

∞*∞

2-uniform polygon domains

[edit]
[(2p,2q,r+)] = r*pq (orbifold), p,q=2..4,∞, r=2..8,∞

2*22

2*23

2*24

2*2∞

2*33

2*34

2*3∞

2*44

2*4∞

2*∞∞

3*22

3*23

3*24

3*2∞

3*33

3*34

3*3∞

3*44

3*4∞

3*∞∞

4*22

4*23

4*24

4*2∞

4*33

4*34

4*3∞

4*44

4*4∞

4*∞∞

5*22

5*23

5*24

5*2∞

5*33

5*34

5*3∞

5*44

5*4∞

5*∞∞

6*22

6*23

6*24

6*2∞

6*33

6*34

6*3∞

6*44

6*4∞

6*∞∞

7*22

7*23

7*24

7*2∞

7*33

7*34

7*3∞

7*44

7*4∞

7*∞∞

∞*22

∞*23

∞*24

∞*2∞

∞*33

∞*34

∞*3∞

∞*44

∞*4∞

∞*∞∞