Polytope of Type {3,6} with group SmallGroup(1452,22)

Overview

Group: SmallGroup(1452,22)
Rank: 3
Schläfli Type: {3,6}
Vertices, edges, …: 121, 363, 242
Order of s₀s₁s₂: 22
Order of s₀s₁s₂s₁: 6
Also known as: {3,6}_(11,0), {3,6}₂₂. if this polytope has another name.

Special Properties

Toroidal
Locally Spherical
Orientable

Quotients maximal quotients in bold

No regular quotients.

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*s2*s1*s0*(s2*s1)^2*s2> of order 11

22 facets

22 of {3}*6

11 vertex figures

11 of {6}*12

P/N, where N=<s0*s1*s0*s2*s1*(s0*(s2*s1)^2)^2*s2> of order 11

22 facets

22 of {3}*6

11 vertex figures

11 of {6}*12

Representations

Permutation Representation (GAP)

s0 := (  2, 30)(  3, 48)(  4, 77)(  5, 95)(  6,113)(  7, 21)(  8, 39)(  9, 57)( 10, 86)( 11,104)( 12, 54)( 13, 72)( 14, 90)( 15,119)( 17, 34)( 18, 63)( 19, 81)( 20,110)( 22, 25)( 23, 96)( 24,114)( 26, 40)( 27, 58)( 28, 87)( 29,105)( 32, 49)( 33, 67)( 36, 64)( 37, 82)( 38,100)( 41, 55)( 42, 73)( 43, 91)( 44,120)( 45, 59)( 46, 88)( 47,106)( 51, 68)( 52, 97)( 53,115)( 56,101)( 60, 74)( 61, 92)( 62,121)( 66, 83)( 70, 98)( 71,116)( 75, 78)( 76,107)( 79, 93)( 80,111)( 85,102)( 89,117)( 94,108)(109,112);;
s1 := (  2, 24)(  3, 47)(  4, 70)(  5, 93)(  6,116)(  7, 18)(  8, 41)(  9, 64)( 10, 87)( 11,110)( 12,111)( 14, 36)( 15, 59)( 16, 82)( 17,105)( 19, 30)( 20, 53)( 21, 76)( 22, 99)( 23,100)( 26, 48)( 27, 71)( 28, 94)( 29,117)( 31, 42)( 32, 65)( 33, 88)( 34, 89)( 35,112)( 38, 60)( 39, 83)( 40,106)( 43, 54)( 44, 77)( 45, 78)( 46,101)( 50, 72)( 51, 95)( 52,118)( 55, 66)( 56, 67)( 57, 90)( 58,113)( 62, 84)( 63,107)( 68, 79)( 69,102)( 74, 96)( 75,119)( 80, 91)( 81,114)( 86,108)( 92,103)( 98,120)(104,115);;
s2 := (  1, 35)(  2, 17)(  3,120)(  4, 91)(  5, 73)(  6, 55)(  7, 26)(  9,100)( 10, 82)( 11, 64)( 12,114)( 13, 96)( 14, 67)( 15, 49)( 16, 31)( 18,105)( 19, 87)( 20, 58)( 21, 40)( 23, 72)( 24, 54)( 27,110)( 28, 81)( 29, 63)( 30, 34)( 32,119)( 33, 90)( 36,104)( 37, 86)( 38, 57)( 41,113)( 42, 95)( 43, 77)( 44, 48)( 45,109)( 46, 80)( 47, 62)( 50,118)( 51, 89)( 52, 71)( 59,112)( 60, 94)( 61, 76)( 65,103)( 66, 85)( 68,117)( 69, 99)( 74,108)( 75, 79)( 78, 93)( 83,102)( 88,111)( 92,107)( 97,116)(106,121);;
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, s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(121)!(  2, 30)(  3, 48)(  4, 77)(  5, 95)(  6,113)(  7, 21)(  8, 39)(  9, 57)( 10, 86)( 11,104)( 12, 54)( 13, 72)( 14, 90)( 15,119)( 17, 34)( 18, 63)( 19, 81)( 20,110)( 22, 25)( 23, 96)( 24,114)( 26, 40)( 27, 58)( 28, 87)( 29,105)( 32, 49)( 33, 67)( 36, 64)( 37, 82)( 38,100)( 41, 55)( 42, 73)( 43, 91)( 44,120)( 45, 59)( 46, 88)( 47,106)( 51, 68)( 52, 97)( 53,115)( 56,101)( 60, 74)( 61, 92)( 62,121)( 66, 83)( 70, 98)( 71,116)( 75, 78)( 76,107)( 79, 93)( 80,111)( 85,102)( 89,117)( 94,108)(109,112);
s1 := Sym(121)!(  2, 24)(  3, 47)(  4, 70)(  5, 93)(  6,116)(  7, 18)(  8, 41)(  9, 64)( 10, 87)( 11,110)( 12,111)( 14, 36)( 15, 59)( 16, 82)( 17,105)( 19, 30)( 20, 53)( 21, 76)( 22, 99)( 23,100)( 26, 48)( 27, 71)( 28, 94)( 29,117)( 31, 42)( 32, 65)( 33, 88)( 34, 89)( 35,112)( 38, 60)( 39, 83)( 40,106)( 43, 54)( 44, 77)( 45, 78)( 46,101)( 50, 72)( 51, 95)( 52,118)( 55, 66)( 56, 67)( 57, 90)( 58,113)( 62, 84)( 63,107)( 68, 79)( 69,102)( 74, 96)( 75,119)( 80, 91)( 81,114)( 86,108)( 92,103)( 98,120)(104,115);
s2 := Sym(121)!(  1, 35)(  2, 17)(  3,120)(  4, 91)(  5, 73)(  6, 55)(  7, 26)(  9,100)( 10, 82)( 11, 64)( 12,114)( 13, 96)( 14, 67)( 15, 49)( 16, 31)( 18,105)( 19, 87)( 20, 58)( 21, 40)( 23, 72)( 24, 54)( 27,110)( 28, 81)( 29, 63)( 30, 34)( 32,119)( 33, 90)( 36,104)( 37, 86)( 38, 57)( 41,113)( 42, 95)( 43, 77)( 44, 48)( 45,109)( 46, 80)( 47, 62)( 50,118)( 51, 89)( 52, 71)( 59,112)( 60, 94)( 61, 76)( 65,103)( 66, 85)( 68,117)( 69, 99)( 74,108)( 75, 79)( 78, 93)( 83,102)( 88,111)( 92,107)( 97,116)(106,121);
poly := sub<Sym(121)|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, s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

References

None.

to this polytope.