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User:Tomruen/Uniform polyhedron table

< User:Tomruen

Table of vertex figures by Wythoff symbol sets on the sphere and plane:

(p q r) q|pr p|qr r|pq qr|p pr|q qp|r pqr| |pqr

Dihedral

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(2 2 2) [di:(2)^2] - - [hos:4.4] - -
4.4.4
3.3.3
(3 2 2) [di:(3)^2] [di:(2)^3] - [hos:6.6]
3.4.4 		-
6.4.4
3.3.3.3
(4 2 2) [di:(4)^2] [di:(2)^4] - [hos:8.8]
4.4.4 		-
8.4.4
3.3.3.4
(5 2 2) [di:(5)^2] [di:(2)^5] - [hos:10.10]
5.4.4 		-
10.4.4
3.3.3.5
(6 2 2) [di:(6)^2] [di:(2)^6] - [hos:12.12]
6.4.4 		-
12.4.4
3.3.3.6
(7 2 2) [di:(7)^2] [di:(2)^7] - [hos:14.14] 7.4.4 - 14.4.4 3.3.3.7
(8 2 2) [di:(8)^2] [di:(2)^8] - [hos:16.16]
8.4.4 		- 16.4.4
3.3.3.8
(9 2 2) [di:(9)^2] [di:(2)^9] - [hos:18.18] 9.4.4 - 18.4.4 3.3.3.9
(10 2 2) [di:(10)^2] [di:(2)^10] - [hos:20.20]
10.4.4 		- 20.4.4
3.3.3.10
(11 2 2) [di:(11)^2] [di:(2)^11] - [hos:22.22] 11.4.4 - 22.4.4 3.3.3.11
(12 2 2) [di:(12)^2] [di:(2)^12] - [hos:24.24]
12.4.4 		- 24.4.4
3.3.3.12
(5/2 2 2) [di:(5/2)^2] [di:(2)^5/2] - [hos:5.5]
5/2.4.4 		- 5.4.4
3.3.3.5/2
(5/3 2 2) - - - - - - -
3.3.3.5/3
(7/2 2 2) [di:(7/2)^2] [di:(2)^7/2] - [hos:7.7] 7/2.4.4 - 7.4.4 3.3.3.7/2
(7/3 2 2) [di:(7/3)^2] [di:(2)^7/3] - [hos:14/3.14/3] 7/3.4.4 - 14/3.4.4 3.3.3.7/3
(8/3 2 2) [di:(8/3)^2] [di:(2)^8/3] - [hos:16/3.16/3] 8/3.4.4 - 16/3.4.4 3.3.3.8/3
(9/2 2 2) [di:(9/2)^2] [di:(2)^9/2] - [hos:9.9] 9/2.4.4 - 9.4.4 3.3.3.9/2
(9/4 2 2) [di:(9/4)^2] [di:(2)^9/4] - [hos:9/2.9/2] 9/4.4.4 - 9/2.4.4 3.3.3.9/4
(10/3 2 2) [di:(10/3)^2] [di:(2)^10/3] - [hos:20/3.20/3] 10/3.4.4 - 20/3.4.4 3.3.3.10/3
(11/2 2 2) [di:(11/2)^2] [di:(2)^11/2] - [hos:11.11] 11/2.4.4 - 11.4.4 3.3.3.11/2
(11/3 2 2) [di:(11/3)^2] [di:(2)^11/3] - [hos:22/3.22/3] 11/3.4.4 - 22/3.4.4 3.3.3.11/3
(11/4 2 2) [di:(11/4)^2] [di:(2)^11/4] - [hos:11/2.11/2] 11/4.4.4 - 11/2.4.4 3.3.3.11/4
(11/5 2 2) [di:(11/5)^2] [di:(2)^11/5] - [hos:22/5.22/5] 11/5.4.4 - 22/5.4.4 3.3.3.11/5
(12/5 2 2) [di:(12/5)^2] [di:(2)^12/5] - [hos:24/5.24/5] 12/5.4.4 - 24/5.4.4 3.3.3.12/5

Tetrahedral

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(3 3 2) (3)^3 -
(3.3)^2
3.6.6 		-
3.4.3.4
6.6.43
(3 3/2 2) (3)^3/2 (3/2)^3 (3.3/2)^2 3/2.6.6 3.6/2.6/2
3/2.4.3.4 		6.6/2.4 3.3ĕẼMWὂᾟοΥἚ

Octahedral

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(4 3 2)
(4)^3
(3)^4
(4.3)^2
3.8.8
4.6.6
3.4.4.4
8.6.4
3.3.3.3.4
(3 3 3/2) (3.3/2)^3 - -
3.6.3/2.6 		-
3.6/2.3.6/2
6.6.6/2
3.3/2.3.3.3.3
(4 4 3/2) (4.3/2)^4 - (4.4)^3/2 4.8.3/2.8 - 4.6/2.4.6/2 8.8.6/2 3.3/2.3.4.3.4
(4 4/3 3) (4.3)^4/3 (4/3.3)^4 (4.4/3)^3 4/3.8.3.8 4.8/3.3.8/3 4/3.6.4.6 8.8/3.6 3.3.3.4/3.3.4
(4 3/2 2) (4)^3/2 (3/2)^4 (4.3/2)^2 3/2.8.8 4.6/2.6/2
3/2.4.4.4 		8.6/2.4 3.3.3/2.3.4
(4/3 3 2) (4/3)^3 (3)^4/3 (4/3.3)^2 3.8/3.8/3 4/3.6.6 3.4.4/3.4 8/3.6.4 3.3.3.3.4/3
(4/3 3/2 2) (4/3)^3/2 (3/2)^4/3 (4/3.3/2)^2 3/2.8/3.8/3 4/3.6/2.6/2 3/2.4.4/3.4 8/3.6/2.4 3.3.3/2.3.4/3

Icosahedral

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(5 3 2)
(5)^3
(3)^5
(5.3)^2
3.10.10
5.6.6
3.4.5.4
10.6.4
3.3.3.3.5
(5/2 3 3) (5/2.3)^3 (3.3)^5/2 - 3.10/2.3.10/2 5/2.6.3.6 - 10/2.6.6 3.3.3.3.3.5/2
(5 5 3/2) (5.3/2)^5 - (5.5)^3/2 5.10.3/2.10 - 5.6/2.5.6/2 10.10.6/2 3.3/2.3.5.3.5
(5 5/2 2) (5)^5/2 (5/2)^5 (5.5/2)^2 5/2.10.10 5.10/2.10/2 5/2.4.5.4 10.10/2.4 3.3.5/2.3.5
(5 5/3 3) (5.3)^5/3 (5/3.3)^5 (5.5/3)^3 5/3.10.3.10 5.10/3.3.10/3 5/3.6.5.6 10.10/3.6 3.3.3.5/3.3.5
(5 3 3/2) (5.3/2)^3 (3.3/2)^5 (5.3)^3/2 3.10.3/2.10 5.6.3/2.6 3.6/2.5.6/2 10.6.6/2 3.3/2.3.3.3.5
(5 3 3/2) (5.3/2)^3 (3.3/2)^5 (5.3)^3/2 3.10.3/2.10 5.6.3/2.6 3.6/2.5.6/2 10.6.6/2 3.3/2.3.3.3.5
(5 5 5/4) (5.5/4)^5 - - 5.10.5/4.10 - 5.10/4.5.10/4 10.10.10/4 3.5/4.3.5.3.5
(5/2 3 2) (5/2)^3 (3)^5/2 (5/2.3)^2 3.10/2.10/2 5/2.6.6 3.4.5/2.4 10/2.6.4 3.3.3.3.5/2
(5 5/3 2) (5)^5/3 (5/3)^5 (5.5/3)^2 5/3.10.10 5.10/3.10/3 5/3.4.5.4 10.10/3.4 3.3.5/3.3.5
(5/2 5/3 3) (5/2.3)^5/3 (5/3.3)^5/2 (5/2.5/3)^3 5/3.10/2.3.10/2 5/2.10/3.3.10/3 5/3.6.5/2.6 10/2.10/3.6 3.3.3.5/3.3.5/2
(5 5/4 3) (5.3)^5/4 (5/4.3)^5 (5.5/4)^3 5/4.10.3.10 5.10/4.3.10/4 5/4.6.5.6 10.10/4.6 3.3.3.5/4.3.5
(5/3 3 2) (5/3)^3 (3)^5/3 (5/3.3)^2 3.10/3.10/3 5/3.6.6 3.4.5/3.4 10/3.6.4 3.3.3.3.5/3
(5/2 5/3 5/3) (5/2.5/3)^5/3 (5/3.5/3)^5/2 - 5/3.10/2.5/3.10/2 5/2.10/3.5/3.10/3 - 10/2.10/3.10/3 3.5/3.3.5/3.3.5/2
(5/3 3 3) (5/3.3)^3 (3.3)^5/3 - 3.10/3.3.10/3 5/3.6.3.6 - 10/3.6.6 3.3.3.3.3.5/3
(5/2 3/2 3/2) (5/2.3/2)^3/2 (3/2.3/2)^5/2 - 3/2.10/2.3/2.10/2 5/2.6/2.3/2.6/2 - 10/2.6/2.6/2 3.3/2.3.3/2.3.5/2
(5/3 3/2 2) (5/3)^3/2 (3/2)^5/3 (5/3.3/2)^2 3/2.10/3.10/3 5/3.6/2.6/2 3/2.4.5/3.4 10/3.6/2.4 3.3.3/2.3.5/3
(5 5 5/3) (5.5/3)^5 - - 5.10.5/3.10 - 5.10/3.5.10/3 10.10.10/3 3.5/3.3.5.3.5
(5 5/3 3) (5.3)^5/3 (5/3.3)^5 (5.5/3)^3 5/3.10.3.10 5.10/3.3.10/3 5/3.6.5.6 10.10/3.6 3.3.3.5/3.3.5

Euclidean

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(4 4 2) (4)^4 - (4.4)^2 4.8.8 - 4.4.4.4 8.8.4 3.3.4.3.4
(3 3 3) (3.3)^3 - - 3.6.3.6 - - 6.6.6 3.3.3.3.3.3
(6 3 2) (6)^3 (3)^6 (6.3)^2 3.12.12 6.6.6 3.4.6.4 12.6.4 3.3.3.3.6

Hyperbolic

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(7 3 2) (7)^3 (3)^7 (7.3)^2 3.14.14 7.6.6 3.4.7.4 14.6.4 3.3.3.3.7
(5 4 2) (5)^4 (4)^5 (5.4)^2 4.10.10 5.8.8 4.4.5.4 10.8.4 3.3.4.3.5
(6 4 2) (6)^4 (4)^6 (6.4)^2 4.12.12 6.8.8 4.4.6.4 12.8.4 3.3.4.3.6
(5 5 2) (5)^5 - (5.5)^2 5.10.10 - 5.4.5.4 10.10.4 3.3.5.3.5
(8 3 2) (8)^3 (3)^8 (8.3)^2 3.16.16 8.6.6 3.4.8.4 16.6.4 3.3.3.3.8
(3 3/2 2) (3)^3/2 (3/2)^3 (3.3/2)^2 3/2.6.6 3.3.3 3/2.4.3.4 6.3.4 3.3.3/2.3.3
(5 5/2 2) (5)^5/2 (5/2)^5 (5.5/2)^2 5/2.10.10 5.5.5 5/2.4.5.4 10.5.4 3.3.5/2.3.5
(7 7/2 2) (7)^7/2 (7/2)^7 (7.7/2)^2 7/2.14.14 7.7.7 7/2.4.7.4 14.7.4 3.3.7/2.3.7
(9 9/2 2) (9)^9/2 (9/2)^9 (9.9/2)^2 9/2.18.18 9.9.9 9/2.4.9.4 18.9.4 3.3.9/2.3.9
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  NODES
Idea 2
idea 2
Note 1