Uniform Tessellations - Based on (2,p,q) - Convex (general)

Based on (p,q,r)

• Based on (2,2,p)
• Based on (2,3,p)
• Based on (2,p,q)
  The figures based on (2,4,4) are the uniform tessellations on the Euclid plane. The others are the uniform tessellations on the Hyperbolic plane.
  • Convex (general)
    

    	(2,p,q)
    p|q r	p|2 q(*) , 2|p q
    p q|r	2 p|q , p q|2
    p q r|	2 p q|
    |p q r	|2 p q

      (*) regular tessellation
  • Non-convex (general)
  • Non-convex (special)
• Based on (p,q,r)

Based on (p,q,r,...,s)

Complex

p|2 q

3|2 3	3|2 4	3|2 5	3|2 6	3|2 7	. . .  3|2 Inf
4|2 3	4|2 4	4|2 5	4|2 6	4|2 7	. . .  4|2 Inf
5|2 3	5|2 4	5|2 5	5|2 6	5|2 7	. . .  5|2 Inf
6|2 3	6|2 4	6|2 5	6|2 6	6|2 7	. . .  6|2 Inf
7|2 3	7|2 4	7|2 5	7|2 6	7|2 7	. . .  7|2 Inf
:	:	:	:	:	. . .  Inf|2 Inf

2|p q

(2|3 3) => 4|2 3	2|3 4	2|3 5	2|3 6	2|3 7	. . .  2|3 Inf
2|4 3	(2|4 4) => 4|2 4	2|4 5	2|4 6	2|4 7	. . .  2|4 Inf
2|5 3	2|5 4	(2|5 5) => 4|2 5	2|5 6	2|5 7	. . .  2|5 Inf
2|6 3	2|6 4	2|6 5	(2|6 6) => 4|2 6	2|6 7	. . .  2|6 Inf
2|7 3	2|7 4	2|7 5	2|7 6	(2|7 7) => 4|2 7	. . .  2|7 Inf
:	:	:	:	:	. . .  2|Inf Inf

2 p|q

2 3|3	2 3|4	2 3|5	2 3|6	2 3|7	. . .  2 3|Inf
2 4|3	2 4|4	2 4|5	2 4|6	2 4|7	. . .  2 4|Inf
2 5|3	2 5|4	2 5|5	2 5|6	2 5|7	. . .  2 5|Inf
(2 6|3) => 3|2 6	2 6|4	2 6|5	2 6|6	2 6|7	. . .  2 6|Inf
2 7|3	2 7|4	2 7|5	2 7|6	2 7|7	. . .  2 7|Inf
:	:	:	:	:	. . .  2 Inf|Inf

p q|2

(3 3|2) => 2|3 4	3 4|2	3 5|2	3 6|2	3 7|2	. . .  3 Inf|2
4 3|2	(4 4|2) => 4|2 4	4 5|2	4 6|2	4 7|2	. . .  4 Inf|2
5 3|2	5 4|2	(5 5|2) => 2|4 5	5 6|2	5 7|2	. . .  5 Inf|2
6 3|2	6 4|2	6 5|2	(6 6|2) => 2|4 6	6 7|2	. . .  6 Inf|2
7 3|2	7 4|2	7 5|2	7 6|2	(7 7|2) => 2|4 7	. . .  7 Inf|2
:	:	:	:	:	. . .  Inf Inf|2

2 p q

(2 3 3|) => 2|4 3	2 3 4|	2 3 5|	2 3 6|	2 4 7|	. . .  2 3 Inf|
2 4 3|	(2 4 4|) => 2|4 4	2 4 5|	2 4 6|	2 4 7|	. . .  2 4 Inf|
2 5 3|	2 5 4|	(2 5 5|) => 2|4 5	2 5 6|	2 5 7|	. . .  2 5 Inf|
2 6 3|	2 6 4|	2 6 5|	(2 6 6|) => 2|4 6	2 6 7|	. . .  2 6 Inf|
2 7 3|	2 7 4|	2 7 5|	2 7 6|	(2 7 7|) => 2|4 7	. . .  2 7 Inf|
:	:	:	:	:	. . .  2 Inf Inf|

|2 p q

(|2 3 3) => 5|2 3	|2 3 4	|2 3 5	|2 3 6	|2 3 7	. . .  |2 3 Inf
|2 4 3	|2 4 4	|2 4 5	|2 4 6	|2 4 7	. . .  |2 4 Inf
|2 5 3	|2 5 4	|2 5 5	|2 5 6	|2 5 7	. . .  |2 5 Inf
|2 6 3	|2 6 4	|2 6 5	|2 6 6	|2 6 7	. . .  |2 6 Inf
|2 7 3	|2 7 4	|2 7 5	|2 7 6	|2 7 7	. . .  |2 7 Inf
:	:	:	:	:	. . .  |2 Inf Inf