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

Based on (p,q,r)

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

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

    	(p,q,r,s)
    p|q s|r	p|q s|r
    p q|r s	p q|r s
    p q r s|	p q r s|
    |p q r s	|p q r s

  • Non-convex (special)
• Based on (p,q,r,s,...,t)

Complex

p|q s|r

(2|2 2|2) => 4|2 4	(2|2 2|3) => 4|2 6	(2|2 2|4) => 4|2 8	2|2 3|3	2|2 3|4	(3|2 2|3) => 6|2 6	(3|2 2|4) => 6|2 8	. . .  Inf|Inf Inf|Inf
(2|2 2|2) => 4|2 4	2|2 3|2	(2|2 4|2) => 5|2 4	2|2 3|3	2|2 4|3	(2|3 3|2) => 4|3 4	2|3 4|2	. . .  Inf|Inf Inf|Inf
(2|2 2|2) => 4|2 4	2|2 3|2	(2|2 4|2) => 5|2 4	3|2 3|2	3|2 4|2	(2|3 3|2) => 4|3 4	2|3 4|2	. . .  Inf|Inf Inf|Inf
(2|2 2|2) => 4|2 4	(3|2 2|2) => 6|2 4	(4|2 2|2) => 8|2 4	3|2 3|2	4|2 3|2	(3|2 2|3) => 6|2 6	(4|2 2|3) => 8|2 6	. . .  Inf|Inf Inf|Inf

p q|r s

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

p q r s|

(2 2 2 2|) => 4|2 4

(2 2 2 3|) => 4 6|2

(2 2 2 4|) => 4 8|2

(2 2 3 3|) => 2 2|2 3

2 2 3 4|

(2 3 2 3|) => 2|4 6

(2 3 2 4|) => 6 8|2

. . .  Inf Inf Inf Inf|

|p q r s

(|2 2 2 2) => 4|2 4

|2 2 2 3

(|2 2 2 4) => 5|2 4

|2 2 3 3

|2 2 3 4

|2 3 2 3

|2 3 2 4

. . .  |Inf Inf Inf Inf