Uniform Tessellations - Based on (2,3,p) - Non-convex (general)

Based on (p,q,r)

• Based on (2,2,p)
• Based on (2,3,p)
  The figures based on (2,3,3), (2,3,4) or (2,3,5) are the uniform polyhedra. The figures based on (2,3,6) are the uniform tessellations on the Euclid plane. The figures based on (2,3,p>=7) are the uniform tessellations on the Hyperbolic plane.
  • Convex (general)
  • Non-convex (general)
    

    	(2,p,p/2)	(3/2,p,p)	(3,3,p/2)	(3,p,p/3)	(p,p,p/4)
    p|q r	p/2|2 p(*) p|2 p/2(*) 2|p p/2		3|3 p/2	3|p p/3 p|3 p/3	p|p p/4
    p q|r	2 p/2|p p p/2|2	3/2 p|p	3 p/2|3	p p/3|3 3 p/3|p 3 p|p/3	p p/4|p
    p q r|	2 p 3/2,p/2|			3 p p/3|
    |p q r	|2 p p/2		|3 3 p/2	|3 p p/3	|p p p/4

      (*) regular tessellation
  • Non-convex (based on (3,7,7/2))
  • Non-convex (special)
• Based on (2,p,q)
• Based on (p,q,r)

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

Complex

p/2|2 p

5/2|2 5

7/2|2 7

9/2|2 9

. . .  Inf/2|2 Inf

p|2 p/2

5|2 5/2

7|2 7/2

9|2 9/2

. . .  Inf|2 Inf/2

2|p p/2

2|5 5/2

2|7 7/2

2|9 9/2

. . .  2|Inf Inf/2

3|3 p/2

3|3 5/2

3|3 7/2

3|3 9/2

. . .  3|3 Inf/2

3|p p/3

3|5 5/3

3|7 7/3

3|8 8/3

. . .  3|Inf Inf/3

p|3 p/3

7|3 7/3

8|3 8/3

. . .  Inf|3 Inf/3

p|p p/4

7|7 7/4

9|9 9/4

. . .  Inf|Inf Inf/4

2 p/2|p

2 5/2|5

2 7/2|7

2 9/2|9

. . .  2 Inf/2|Inf

p p/2|2

5 5/2|2

7 7/2|2

9 9/2|2

. . .  Inf Inf/2|2

3/2 p|p

3/2 3|3

3/2 4|4

3/2 5|5

3/2 6|6

3/2 7|7

3/2 8|8

3/2 9|9

. . .  3/2 Inf|Inf

3 p/2|3

3 3/2|3

3 5/2|3

3 7/2|3

3 9/2|3

. . .  3 Inf/2|3

p p/3|3

5 5/3|3

7 7/3|3

8 8/3|3

. . .  Inf Inf/3|3

3 p/3|p

3 4/3|4

3 5/3|5

3 7/3|7

3 8/3|8

. . .  3 Inf/3|Inf

3 p|p/3

3 4|4/3

3 5|5/3

3 7|7/3

3 8|8/3

. . .  3 Inf|Inf/3

p p/4|p

7 7/4|7

9 9/4|9

. . .  Inf Inf/4|Inf

2 p 3/2,p/2|

(2 3 3/2,3/2|) => 3 3/2|2

2 4 3/2,4/2|

2 5 3/2,5/2|

2 6 3/2,6/2|

2 7 3/2,7/2|

2 8 3/2,8/2|

2 9 3/2,9/2|

. . .  2 Inf 3/2,Inf/2|

3 p p/3|

3 4 4/3|

3 5 5/3|

3 7 7/3|

3 8 8/3|

. . .  3 Inf Inf/3|

|2 p p/2

|2 5 5/2

|2 7 7/2

|2 9 9/2

. . .  |2 Inf/2 Inf

|3 3 p/2

|3 3 5/2

|3 3 7/2

|3 3 9/2

. . .  |3 3 Inf/2

|3 p p/3

|3 5 5/3

|3 7 7/3

|3 8 8/3

. . .  |3 Inf Inf/3

|p p p/4

|7 7 7/4

|9 9 9/4

. . .  |Inf Inf Inf/4