Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,3}

Atlas Canonical Name {6,3}*1200

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Overview

Group
SmallGroup(1200,985)
Rank
3
Schläfli Type
{6,3}
Vertices, edges, …
200, 300, 100
Order of s0s1s2
20
Order of s0s1s2s1
6
Also known as
{6,3}(10,0), {6,3}20. if this polytope has another name.

Special Properties

  • Toroidal
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

4-fold

25-fold

50-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s0*s1)^3> of order 2

52 facets

100 vertex figures

P/N, where N=<((s1*s0)^2*s1*s2)^5> of order 2

50 facets

100 vertex figures

P/N, where N=<s1*s0*(s1*s2*(s1*s0)^2)^4*s1*s2*s1> of order 4

25 facets

50 vertex figures

P/N, where N=<s0*s1*s0*(s2*(s1*s0)^2*s1)^4*s2*s1> of order 4

25 facets

50 vertex figures

P/N, where N=<(s0*s1)^2*s0*(s2*(s1*s0)^2)^2*s2*s1*s0*s1*s2> of order 5

20 facets

40 vertex figures

P/N, where N=<((s1*s0)^2*s1*s2)^2> of order 5

20 facets

40 vertex figures

P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2> of order 10

10 facets

20 vertex figures

P/N, where N=<(s0*s1)^3, s1*(s2*(s1*s0)^2)^2*s2*s1*s0*s1*s2> of order 10

12 facets

20 vertex figures

P/N, where N=<(s0*s1)^3, s0*s2*(s1*s0)^2*s1*s2> of order 10

12 facets

20 vertex figures

P/N, where N=<((s1*s0)^2*s1*s2)^2, s0*s1*s0*s2*(s1*s0)^2*s1*(s2*(s1*s0)^2)^2*s2*(s1*s0)^2*s2*s1> of order 10

10 facets

20 vertex figures

P/N, where N=<s0*s1*(s2*(s1*s0)^2)^2*s2*s1*s0*s1> of order 10

10 facets

20 vertex figures

P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, s0*(s1*s2*(s1*s0)^2)^2*s2*s1> of order 20

5 facets

10 vertex figures

Representations

Permutation Representation (GAP) 
s0 := (  6, 25)(  7, 21)(  8, 22)(  9, 23)( 10, 24)( 11, 19)( 12, 20)( 13, 16)( 14, 17)( 15, 18)( 31, 50)( 32, 46)( 33, 47)( 34, 48)( 35, 49)( 36, 44)( 37, 45)( 38, 41)( 39, 42)( 40, 43)( 51, 76)( 52, 77)( 53, 78)( 54, 79)( 55, 80)( 56,100)( 57, 96)( 58, 97)( 59, 98)( 60, 99)( 61, 94)( 62, 95)( 63, 91)( 64, 92)( 65, 93)( 66, 88)( 67, 89)( 68, 90)( 69, 86)( 70, 87)( 71, 82)( 72, 83)( 73, 84)( 74, 85)( 75, 81);;
s1 := (  2,  7)(  3, 13)(  4, 19)(  5, 25)(  6, 21)(  9, 14)( 10, 20)( 11, 16)( 12, 22)( 18, 23)( 26, 76)( 27, 82)( 28, 88)( 29, 94)( 30,100)( 31, 96)( 32, 77)( 33, 83)( 34, 89)( 35, 95)( 36, 91)( 37, 97)( 38, 78)( 39, 84)( 40, 90)( 41, 86)( 42, 92)( 43, 98)( 44, 79)( 45, 85)( 46, 81)( 47, 87)( 48, 93)( 49, 99)( 50, 80)( 52, 57)( 53, 63)( 54, 69)( 55, 75)( 56, 71)( 59, 64)( 60, 70)( 61, 66)( 62, 72)( 68, 73);;
s2 := (  1, 27)(  2, 26)(  3, 30)(  4, 29)(  5, 28)(  6, 33)(  7, 32)(  8, 31)(  9, 35)( 10, 34)( 11, 39)( 12, 38)( 13, 37)( 14, 36)( 15, 40)( 16, 45)( 17, 44)( 18, 43)( 19, 42)( 20, 41)( 21, 46)( 22, 50)( 23, 49)( 24, 48)( 25, 47)( 51, 52)( 53, 55)( 56, 58)( 59, 60)( 61, 64)( 62, 63)( 66, 70)( 67, 69)( 72, 75)( 73, 74)( 76, 77)( 78, 80)( 81, 83)( 84, 85)( 86, 89)( 87, 88)( 91, 95)( 92, 94)( 97,100)( 98, 99);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(100)!(  6, 25)(  7, 21)(  8, 22)(  9, 23)( 10, 24)( 11, 19)( 12, 20)( 13, 16)( 14, 17)( 15, 18)( 31, 50)( 32, 46)( 33, 47)( 34, 48)( 35, 49)( 36, 44)( 37, 45)( 38, 41)( 39, 42)( 40, 43)( 51, 76)( 52, 77)( 53, 78)( 54, 79)( 55, 80)( 56,100)( 57, 96)( 58, 97)( 59, 98)( 60, 99)( 61, 94)( 62, 95)( 63, 91)( 64, 92)( 65, 93)( 66, 88)( 67, 89)( 68, 90)( 69, 86)( 70, 87)( 71, 82)( 72, 83)( 73, 84)( 74, 85)( 75, 81);
s1 := Sym(100)!(  2,  7)(  3, 13)(  4, 19)(  5, 25)(  6, 21)(  9, 14)( 10, 20)( 11, 16)( 12, 22)( 18, 23)( 26, 76)( 27, 82)( 28, 88)( 29, 94)( 30,100)( 31, 96)( 32, 77)( 33, 83)( 34, 89)( 35, 95)( 36, 91)( 37, 97)( 38, 78)( 39, 84)( 40, 90)( 41, 86)( 42, 92)( 43, 98)( 44, 79)( 45, 85)( 46, 81)( 47, 87)( 48, 93)( 49, 99)( 50, 80)( 52, 57)( 53, 63)( 54, 69)( 55, 75)( 56, 71)( 59, 64)( 60, 70)( 61, 66)( 62, 72)( 68, 73);
s2 := Sym(100)!(  1, 27)(  2, 26)(  3, 30)(  4, 29)(  5, 28)(  6, 33)(  7, 32)(  8, 31)(  9, 35)( 10, 34)( 11, 39)( 12, 38)( 13, 37)( 14, 36)( 15, 40)( 16, 45)( 17, 44)( 18, 43)( 19, 42)( 20, 41)( 21, 46)( 22, 50)( 23, 49)( 24, 48)( 25, 47)( 51, 52)( 53, 55)( 56, 58)( 59, 60)( 61, 64)( 62, 63)( 66, 70)( 67, 69)( 72, 75)( 73, 74)( 76, 77)( 78, 80)( 81, 83)( 84, 85)( 86, 89)( 87, 88)( 91, 95)( 92, 94)( 97,100)( 98, 99);
poly := sub<Sym(100)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1 >;

References

None.

to this polytope.

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