User:Tomruen/Uniform polyhedron table

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

{| class="wikitable" ! (p q r) ! q&#124;pr ! p&#124;qr ! r&#124;pq ! qr&#124;p ! pr&#124;q ! qp&#124;r ! pqr&#124; ! &#124;pqr ! colspan=9|

Dihedral

 * (2 2 2)
 * [di:(2)^2]
 * [hos:4.4]
 * [[Image:Uniform polyhedron 222-t012.png|50px]]4.4.4
 * [[Image:Tetrahedron.png|50px]]3.3.3
 * [hos:4.4]
 * [[Image:Uniform polyhedron 222-t012.png|50px]]4.4.4
 * [[Image:Tetrahedron.png|50px]]3.3.3
 * [[Image:Uniform polyhedron 222-t012.png|50px]]4.4.4
 * [[Image:Tetrahedron.png|50px]]3.3.3


 * (3 2 2)
 * [di:(3)^2]
 * [di:(2)^3]
 * [hos:6.6]
 * [[Image:Triangular prism.png|50px]]3.4.4
 * [[Image:Hexagonal prism.png|50px]]6.4.4
 * [[Image:Octahedron.png|50px]]3.3.3.3
 * [[Image:Hexagonal prism.png|50px]]6.4.4
 * [[Image:Octahedron.png|50px]]3.3.3.3
 * [[Image:Octahedron.png|50px]]3.3.3.3


 * (4 2 2)
 * [di:(4)^2]
 * [di:(2)^4]
 * [hos:8.8]
 * [[Image:Tetragonal prism.png|50px]]4.4.4
 * [[Image:Octagonal prism.png|50px]]8.4.4
 * [[Image:Square antiprism.png|50px]]3.3.3.4
 * [[Image:Octagonal prism.png|50px]]8.4.4
 * [[Image:Square antiprism.png|50px]]<BR>3.3.3.4
 * [[Image:Square antiprism.png|50px]]<BR>3.3.3.4


 * (5 2 2)
 * [di:(5)^2]
 * [di:(2)^5]
 * [hos:10.10]
 * [[Image:Pentagonal prism.png|50px]]<BR>5.4.4
 * [[Image:Decagonal prism.png|50px]]<BR>10.4.4
 * [[Image:Square antiprism.png|50px]]<BR>3.3.3.5
 * [[Image:Decagonal prism.png|50px]]<BR>10.4.4
 * [[Image:Square antiprism.png|50px]]<BR>3.3.3.5
 * [[Image:Square antiprism.png|50px]]<BR>3.3.3.5


 * (6 2 2)
 * [di:(6)^2]
 * [di:(2)^6]
 * [hos:12.12]
 * [[Image:Hexagonal prism.png|50px]]<BR>6.4.4
 * [[Image:Dodecagonal prism.png|50px]]<BR>12.4.4
 * [[Image:Hexagonal antiprism.png|50px]]<BR>3.3.3.6
 * [[Image:Dodecagonal prism.png|50px]]<BR>12.4.4
 * [[Image:Hexagonal antiprism.png|50px]]<BR>3.3.3.6
 * [[Image:Hexagonal antiprism.png|50px]]<BR>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
 * 14.4.4
 * 3.3.3.7
 * 3.3.3.7


 * (8 2 2)
 * [di:(8)^2]
 * [di:(2)^8]
 * [hos:16.16]
 * [[Image:Octagonal prism.png|50px]]<BR>8.4.4
 * 16.4.4
 * [[Image:Octagonal antiprism.png|50px]]<BR>3.3.3.8
 * 16.4.4
 * [[Image:Octagonal antiprism.png|50px]]<BR>3.3.3.8
 * [[Image:Octagonal antiprism.png|50px]]<BR>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
 * 18.4.4
 * 3.3.3.9
 * 3.3.3.9


 * (10 2 2)
 * [di:(10)^2]
 * [di:(2)^10]
 * [hos:20.20]
 * [[Image:Decagonal prism.png|50px]]<BR>10.4.4
 * 20.4.4
 * [[Image:Decagonal antiprism.png|50px]]<BR>3.3.3.10
 * 20.4.4
 * [[Image:Decagonal antiprism.png|50px]]<BR>3.3.3.10
 * [[Image:Decagonal antiprism.png|50px]]<BR>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
 * 22.4.4
 * 3.3.3.11
 * 3.3.3.11


 * (12 2 2)
 * [di:(12)^2]
 * [di:(2)^12]
 * [hos:24.24]
 * [[Image:Dodecagonal prism.png|50px]]<BR>12.4.4
 * 24.4.4
 * [[Image:Dodecagonal antiprism.png|50px]]<BR>3.3.3.12
 * 24.4.4
 * [[Image:Dodecagonal antiprism.png|50px]]<BR>3.3.3.12
 * [[Image:Dodecagonal antiprism.png|50px]]<BR>3.3.3.12


 * (5/2 2 2)
 * [di:(5/2)^2]
 * [di:(2)^5/2]
 * [hos:5.5]
 * [[Image:Pentagrammic prism.png|50px]]<BR>5/2.4.4
 * 5.4.4
 * [[Image:Pentagrammic antiprism.png|50px]]<BR>3.3.3.5/2
 * 5.4.4
 * [[Image:Pentagrammic antiprism.png|50px]]<BR>3.3.3.5/2
 * [[Image:Pentagrammic antiprism.png|50px]]<BR>3.3.3.5/2


 * (5/3 2 2)
 * [[Image:Pentagrammic crossed antiprism.png|50px]]<BR>3.3.3.5/3
 * [[Image:Pentagrammic crossed antiprism.png|50px]]<BR>3.3.3.5/3
 * [[Image:Pentagrammic crossed antiprism.png|50px]]<BR>3.3.3.5/3
 * [[Image:Pentagrammic crossed antiprism.png|50px]]<BR>3.3.3.5/3
 * [[Image:Pentagrammic crossed antiprism.png|50px]]<BR>3.3.3.5/3
 * [[Image:Pentagrammic crossed antiprism.png|50px]]<BR>3.3.3.5/3
 * [[Image:Pentagrammic crossed antiprism.png|50px]]<BR>3.3.3.5/3
 * [[Image:Pentagrammic crossed antiprism.png|50px]]<BR>3.3.3.5/3
 * [[Image:Pentagrammic crossed antiprism.png|50px]]<BR>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
 * 7.4.4
 * 3.3.3.7/2
 * 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
 * 14/3.4.4
 * 3.3.3.7/3
 * 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
 * 16/3.4.4
 * 3.3.3.8/3
 * 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
 * 9.4.4
 * 3.3.3.9/2
 * 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
 * 9/2.4.4
 * 3.3.3.9/4
 * 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
 * 20/3.4.4
 * 3.3.3.10/3
 * 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
 * 11.4.4
 * 3.3.3.11/2
 * 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
 * 22/3.4.4
 * 3.3.3.11/3
 * 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
 * 11/2.4.4
 * 3.3.3.11/4
 * 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
 * 22/5.4.4
 * 3.3.3.11/5
 * 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
 * 24/5.4.4
 * 3.3.3.12/5
 * 3.3.3.12/5

! colspan=9|

Tetrahedral

 * (3 3 2)
 * (3)^3
 * [[Image:Uniform polyhedron-33-t1.png|50px]]<BR>(3.3)^2
 * [[Image:Uniform polyhedron-33-t01.png|50px]]<BR>3.6.6
 * [[Image:Uniform polyhedron-33-t02.png|50px]]<BR>3.4.3.4
 * [[Image:Uniform polyhedron-33-t012.png|50px]]<BR>6.6.43
 * [[Image:Uniform polyhedron-33-t02.png|50px]]<BR>3.4.3.4
 * [[Image:Uniform polyhedron-33-t012.png|50px]]<BR>6.6.43
 * [[Image:Uniform polyhedron-33-t012.png|50px]]<BR>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
 * [[Image:Tetrahemihexahedron.png|50px]]<BR>3/2.4.3.4
 * 6.6/2.4
 * 3.3ĕẼMWὂᾟοΥἚ
 * 3.3ĕẼMWὂᾟοΥἚ

Octahedral

 * (4 3 2)
 * [[Image:Hexahedron.png|50px]]<BR>(4)^3
 * [[Image:Octahedron.png|50px]]<BR>(3)^4
 * [[Image:Cuboctahedron.png|50px]]<BR>(4.3)^2
 * [[Image:Truncated hexahedron.png|50px]]<BR>3.8.8
 * [[Image:Truncated octahedron.png|50px]]<BR>4.6.6
 * [[Image:Small rhombicuboctahedron.png|50px]]<BR>3.4.4.4
 * [[Image:Great rhombicuboctahedron.png|50px]]<BR>8.6.4
 * [[Image:Snub hexahedron.png|50px]]<BR>3.3.3.3.4
 * [[Image:Snub hexahedron.png|50px]]<BR>3.3.3.3.4


 * (3 3 3/2)
 * (3.3/2)^3
 * [[Image:Octahemioctahedron.png|50px]]<BR>3.6.3/2.6
 * [[Image:Uniform polyhedron-33-t1.png|50px]]<BR>3.6/2.3.6/2
 * [[Image:Uniform polyhedron-33-t01.png|50px]]<BR>6.6.6/2
 * [[Image:Octahedron.png|50px]]<BR>3.3/2.3.3.3.3
 * [[Image:Uniform polyhedron-33-t1.png|50px]]<BR>3.6/2.3.6/2
 * [[Image:Uniform polyhedron-33-t01.png|50px]]<BR>6.6.6/2
 * [[Image:Octahedron.png|50px]]<BR>3.3/2.3.3.3.3
 * [[Image:Octahedron.png|50px]]<BR>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
 * 4.6/2.4.6/2
 * 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
 * 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
 * [[Image:Uniform great rhombicuboctahedron.png|50px]]<BR>3/2.4.4.4
 * 8.6/2.4
 * 3.3.3/2.3.4
 * 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
 * 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
 * 3.3.3/2.3.4/3

! colspan=9|

Icosahedral

 * (5 3 2)
 * [[Image:Dodecahedron.png|50px]]<BR>(5)^3
 * [[Image:Icosahedron.png|50px]]<BR>(3)^5
 * [[Image:Icosidodecahedron.png|50px]]<BR>(5.3)^2
 * [[Image:Truncated dodecahedron.png|50px]]<BR>3.10.10
 * [[Image:Truncated icosahedron.png|50px]]<BR>5.6.6
 * [[Image:Small rhombicosidodecahedron.png|50px]]<BR>3.4.5.4
 * [[Image:Great rhombicosidodecahedron.png|50px]]<BR>10.6.4
 * [[Image:Snub dodecahedron ccw.png|50px]]<BR>3.3.3.3.5
 * [[Image:Snub dodecahedron ccw.png|50px]]<BR>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
 * 10/2.6.6
 * 3.3.3.3.3.5/2
 * 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
 * 5.6/2.5.6/2
 * 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
 * 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
 * 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
 * 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
 * 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
 * 5.10/4.5.10/4
 * 10.10.10/4
 * 3.5/4.3.5.3.5
 * 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
 * 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
 * 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
 * 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
 * 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
 * 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
 * 10/2.10/3.10/3
 * 3.5/3.3.5/3.3.5/2
 * 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
 * 10/3.6.6
 * 3.3.3.3.3.5/3
 * 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
 * 10/2.6/2.6/2
 * 3.3/2.3.3/2.3.5/2
 * 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
 * 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
 * 5.10/3.5.10/3
 * 10.10.10/3
 * 3.5/3.3.5.3.5
 * 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
 * 3.3.3.5/3.3.5

! colspan=9|

Euclidean

 * (4 4 2)
 * (4)^4
 * (4.4)^2
 * 4.8.8
 * 4.4.4.4
 * 8.8.4
 * 3.3.4.3.4
 * 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
 * 3.6.3.6
 * 6.6.6
 * 3.3.3.3.3.3
 * 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
 * 3.3.3.3.6

! colspan=9|

Hyperbolic

 * (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
 * 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
 * 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
 * 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
 * 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
 * 3.3.3.3.8


 * (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
 * 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
 * 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
 * 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
 * 3.3.9/2.3.9


 * }