Polytope of Type {4,93}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,93}*744
if this polytope has a name.
Group : SmallGroup(744,43)
Rank : 3
Schlafli Type : {4,93}
Number of vertices, edges, etc : 4, 186, 93
Order of s₀s₁s₂ : 93
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,93,2} of size 1488
Vertex Figure Of :
   {2,4,93} of size 1488
Quotients (Maximal Quotients in Boldface) :
   31-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,93}*1488, {4,186}*1488b, {4,186}*1488c
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope