Polytope of Type {124,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {124,6}*1488b
if this polytope has a name.
Group : SmallGroup(1488,207)
Rank : 3
Schlafli Type : {124,6}
Number of vertices, edges, etc : 124, 372, 6
Order of s₀s₁s₂ : 93
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   31-fold quotients : {4,6}*48b
   62-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope