Polytope of Type {93,6} with group SmallGroup(1488,207)

Overview

Group: SmallGroup(1488,207)
Rank: 3
Schläfli Type: {93,6}
Vertices, edges, …: 124, 372, 8
Order of s₀s₁s₂: 124
Order of s₀s₁s₂s₁: 6
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

12-fold

{31,2}*124

31-fold

{3,6}*48

62-fold

{3,3}*24

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := (  3,  4)(  5,121)(  6,122)(  7,124)(  8,123)(  9,117)( 10,118)( 11,120)( 12,119)( 13,113)( 14,114)( 15,116)( 16,115)( 17,109)( 18,110)( 19,112)( 20,111)( 21,105)( 22,106)( 23,108)( 24,107)( 25,101)( 26,102)( 27,104)( 28,103)( 29, 97)( 30, 98)( 31,100)( 32, 99)( 33, 93)( 34, 94)( 35, 96)( 36, 95)( 37, 89)( 38, 90)( 39, 92)( 40, 91)( 41, 85)( 42, 86)( 43, 88)( 44, 87)( 45, 81)( 46, 82)( 47, 84)( 48, 83)( 49, 77)( 50, 78)( 51, 80)( 52, 79)( 53, 73)( 54, 74)( 55, 76)( 56, 75)( 57, 69)( 58, 70)( 59, 72)( 60, 71)( 61, 65)( 62, 66)( 63, 68)( 64, 67);;
s1 := (  1,  5)(  2,  8)(  3,  7)(  4,  6)(  9,121)( 10,124)( 11,123)( 12,122)( 13,117)( 14,120)( 15,119)( 16,118)( 17,113)( 18,116)( 19,115)( 20,114)( 21,109)( 22,112)( 23,111)( 24,110)( 25,105)( 26,108)( 27,107)( 28,106)( 29,101)( 30,104)( 31,103)( 32,102)( 33, 97)( 34,100)( 35, 99)( 36, 98)( 37, 93)( 38, 96)( 39, 95)( 40, 94)( 41, 89)( 42, 92)( 43, 91)( 44, 90)( 45, 85)( 46, 88)( 47, 87)( 48, 86)( 49, 81)( 50, 84)( 51, 83)( 52, 82)( 53, 77)( 54, 80)( 55, 79)( 56, 78)( 57, 73)( 58, 76)( 59, 75)( 60, 74)( 61, 69)( 62, 72)( 63, 71)( 64, 70)( 66, 68);;
s2 := (  1,  2)(  5,  6)(  9, 10)( 13, 14)( 17, 18)( 21, 22)( 25, 26)( 29, 30)( 33, 34)( 37, 38)( 41, 42)( 45, 46)( 49, 50)( 53, 54)( 57, 58)( 61, 62)( 65, 66)( 69, 70)( 73, 74)( 77, 78)( 81, 82)( 85, 86)( 89, 90)( 93, 94)( 97, 98)(101,102)(105,106)(109,110)(113,114)(117,118)(121,122);;
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*s2*s1*s0*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(124)!(  3,  4)(  5,121)(  6,122)(  7,124)(  8,123)(  9,117)( 10,118)( 11,120)( 12,119)( 13,113)( 14,114)( 15,116)( 16,115)( 17,109)( 18,110)( 19,112)( 20,111)( 21,105)( 22,106)( 23,108)( 24,107)( 25,101)( 26,102)( 27,104)( 28,103)( 29, 97)( 30, 98)( 31,100)( 32, 99)( 33, 93)( 34, 94)( 35, 96)( 36, 95)( 37, 89)( 38, 90)( 39, 92)( 40, 91)( 41, 85)( 42, 86)( 43, 88)( 44, 87)( 45, 81)( 46, 82)( 47, 84)( 48, 83)( 49, 77)( 50, 78)( 51, 80)( 52, 79)( 53, 73)( 54, 74)( 55, 76)( 56, 75)( 57, 69)( 58, 70)( 59, 72)( 60, 71)( 61, 65)( 62, 66)( 63, 68)( 64, 67);
s1 := Sym(124)!(  1,  5)(  2,  8)(  3,  7)(  4,  6)(  9,121)( 10,124)( 11,123)( 12,122)( 13,117)( 14,120)( 15,119)( 16,118)( 17,113)( 18,116)( 19,115)( 20,114)( 21,109)( 22,112)( 23,111)( 24,110)( 25,105)( 26,108)( 27,107)( 28,106)( 29,101)( 30,104)( 31,103)( 32,102)( 33, 97)( 34,100)( 35, 99)( 36, 98)( 37, 93)( 38, 96)( 39, 95)( 40, 94)( 41, 89)( 42, 92)( 43, 91)( 44, 90)( 45, 85)( 46, 88)( 47, 87)( 48, 86)( 49, 81)( 50, 84)( 51, 83)( 52, 82)( 53, 77)( 54, 80)( 55, 79)( 56, 78)( 57, 73)( 58, 76)( 59, 75)( 60, 74)( 61, 69)( 62, 72)( 63, 71)( 64, 70)( 66, 68);
s2 := Sym(124)!(  1,  2)(  5,  6)(  9, 10)( 13, 14)( 17, 18)( 21, 22)( 25, 26)( 29, 30)( 33, 34)( 37, 38)( 41, 42)( 45, 46)( 49, 50)( 53, 54)( 57, 58)( 61, 62)( 65, 66)( 69, 70)( 73, 74)( 77, 78)( 81, 82)( 85, 86)( 89, 90)( 93, 94)( 97, 98)(101,102)(105,106)(109,110)(113,114)(117,118)(121,122);
poly := sub<Sym(124)|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*s2*s1*s0*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2 >;

References