User:Tomruen/tempx

Symmetries

Right triangle domains

[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

[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

[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

[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

[(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∞	∞*∞∞