User:Tamfang/H2

Shown in the conformal ('stereographic') disc model. In each, the origin is equidistant from the three defining mirrors.

Made by crude little Python programs. Full size is 2520 pixels (least common multiple of 1,2,3,4,5,6,7,8,9,10).

hyperbolic tilings on triangles of finite area

Ranked by the area of the fundamental triangle.

p q r	xxx	xox	oox	oxx	oxo	xxo	xoo	snub
2 3 7 area π/42
2 3 8 area π/24
2 4 5 area π/20
3 3 4 area π/12
2 4 6 area π/12
2 5 5 area π/10
2 4 7 area 3π/28
2 4 8 area π/8
3 3 5 area 2π/15
2 5 6 area 2π/15
2 5 7 area 11π/70
3 4 4 area π/6
3 3 6 area π/6
2 6 6 area π/6
2 3 ∞ area π/6
2 5 8 area 7π/40
3 3 7 area 4π/21
2 6 7 area 4π/21
3 3 8 area 5π/24
2 6 8 area 5π/24
2 7 7 area 3π/14
3 4 5 area 13π/60
2 7 8 area 13π/56
4 4 4 area π/4
3 4 6 area π/4
2 8 8 area π/4
2 4 ∞ area π/4
3 5 5 area 4π/15
3 4 7 area 23π/84
3 4 8 area 7π/24
4 4 5 area 3π/10
3 5 6 area 3π/10
2 5 ∞ area 3π/10
3 5 7 area 34π/105
4 4 6 area π/3
3 6 6 area π/3
3 3 ∞ area π/3
2 6 ∞ area π/3
3 5 8 area 41π/120
4 5 5 area 7π/20
4 4 7 area 5π/14
3 6 7 area 5π/14
2 7 ∞ area 5π/14
4 4 8 area 3π/8
3 6 8 area 3π/8
2 8 ∞ area 3π/8
3 7 7 area 8π/21
4 5 6 area 23π/60
3 7 8 area 67π/168
5 5 5 area 2π/5
4 5 7 area 57π/140
4 6 6 area 5π/12
3 8 8 area 5π/12
3 4 ∞ area 5π/12
4 5 8 area 17π/40
5 5 6 area 13π/30
4 6 7 area 37π/84
5 5 7 area 16π/35
4 6 8 area 11π/24
4 7 7 area 13π/28
5 6 6 area 7π/15
3 5 ∞ area 7π/15
5 5 8 area 19π/40
4 7 8 area 27π/56
5 6 7 area 103π/210
6 6 6 area π/2
4 8 8 area π/2
4 4 ∞ area π/2
3 6 ∞ area π/2
2 ∞ ∞ area π/2
5 6 8 area 61π/120
5 7 7 area 18π/35
6 6 7 area 11π/21
3 7 ∞ area 11π/21
5 7 8 area 149π/280
6 6 8 area 13π/24
3 8 ∞ area 13π/24
6 7 7 area 23π/42
5 8 8 area 11π/20
4 5 ∞ area 11π/20
6 7 8 area 95π/168
7 7 7 area 4π/7
6 8 8 area 7π/12
4 6 ∞ area 7π/12
7 7 8 area 33π/56
5 5 ∞ area 3π/5
7 8 8 area 17π/28
4 7 ∞ area 17π/28
8 8 8 area 5π/8
4 8 ∞ area 5π/8
5 6 ∞ area 19π/30
5 7 ∞ area 23π/35
6 6 ∞ area 2π/3
3 ∞ ∞ area 2π/3
5 8 ∞ area 27π/40
6 7 ∞ area 29π/42
6 8 ∞ area 17π/24
7 7 ∞ area 5π/7
7 8 ∞ area 41π/56
8 8 ∞ area 3π/4
4 ∞ ∞ area 3π/4
5 ∞ ∞ area 4π/5
6 ∞ ∞ area 5π/6
7 ∞ ∞ area 6π/7
8 ∞ ∞ area 7π/8
∞ ∞ ∞ area π
2 2 iπ/λ area ill-defined, as this is really degenerate Euclidean rather than hyperbolic

hyperbolic tilings on tiles of infinite area

p q r	xxx	xox	oox	oxx	oxo	xxo	xoo	snub
2 ∞ iπ/λ (10%)	File:H2checkers 2iu.png	File:H2 tiling 2iu-5.png File:H2chess 2iud.png	File:H2 tiling 2iu-1.png File:H2chess 2iub.png	File:H2 tiling 2iu-3.png File:H2chess 2iuf.png	File:H2 tiling 2iu-2.png File:H2chess 2iua.png	File:H2 tiling 2iu-6.png File:H2chess 2iue.png	File:H2 tiling 2iu-4.png File:H2chess 2iuc.png	File:H2 snub 2iua.png File:H2 snub 2iub.png