Polytope of Type {6,93}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,93}*1488
if this polytope has a name.
Group : SmallGroup(1488,207)
Rank : 3
Schlafli Type : {6,93}
Number of vertices, edges, etc : 8, 372, 124
Order of s₀s₁s₂ : 124
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   12-fold quotients : {2,31}*124
   31-fold quotients : {6,3}*48
   62-fold quotients : {3,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope