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

Based on (p,q,r)

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

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

  • Non-convex (special)

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

Complex

p|q r

(3|3 3) => 6|2 3	(4|3 3) => 8|2 3	(5|3 3) => 10|2 3	4|3 4	5|3 4	5|3 5	. . .  Inf|Inf Inf
(3|3 3) => 6|2 3	3|3 4	3|3 5	4|3 4	4|3 5	5|3 5	. . .  Inf|Inf Inf
(3|3 3) => 6|2 3	3|3 4	3|3 5	(3|4 4) => 6|2 4	3|4 5	(3|5 5) => 6|2 5	. . .  Inf|Inf Inf

p q|r

(3 3|3) => 2|3 6	(3 3|4) => 2|3 8	(3 3|5) => 2|3 10	3 4|4	3 4|5	3 5|5	. . .  Inf Inf|Inf
(3 3|3) => 2|3 6	3 4|3	3 5|3	3 4|4	3 5|4	3 5|5	. . .  Inf Inf|Inf
(3 3|3) => 2|3 6	3 4|3	3 5|3	(4 4|3) => 2|4 6	4 5|3	(5 5|3) => 2|5 6	. . .  Inf Inf|Inf

p q r|

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

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

(3 3 5|) => 2 10|3

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

3 4 5|

(3 5 5|) => 2 6|5

. . .  Inf Inf Inf|

|p q r

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

|3 3 4

|3 3 5

|3 4 4

|3 4 5

|3 5 5

. . .  |Inf Inf Inf