Uniform Tessellations - Based on (2,p,q) - Convex (general)
Last update: 2002/10/16
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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
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. . . 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
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. . . 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
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. . . 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
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. . . 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|
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. . . 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
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. . . |2 Inf Inf
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