Polytope of Type {2,93,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,93,4}*1488
if this polytope has a name.
Group : SmallGroup(1488,209)
Rank : 4
Schlafli Type : {2,93,4}
Number of vertices, edges, etc : 2, 93, 186, 4
Order of s₀s₁s₂s₃ : 186
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   31-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  5)(  7,123)(  8,125)(  9,124)( 10,126)( 11,119)( 12,121)( 13,120)
( 14,122)( 15,115)( 16,117)( 17,116)( 18,118)( 19,111)( 20,113)( 21,112)
( 22,114)( 23,107)( 24,109)( 25,108)( 26,110)( 27,103)( 28,105)( 29,104)
( 30,106)( 31, 99)( 32,101)( 33,100)( 34,102)( 35, 95)( 36, 97)( 37, 96)
( 38, 98)( 39, 91)( 40, 93)( 41, 92)( 42, 94)( 43, 87)( 44, 89)( 45, 88)
( 46, 90)( 47, 83)( 48, 85)( 49, 84)( 50, 86)( 51, 79)( 52, 81)( 53, 80)
( 54, 82)( 55, 75)( 56, 77)( 57, 76)( 58, 78)( 59, 71)( 60, 73)( 61, 72)
( 62, 74)( 63, 67)( 64, 69)( 65, 68)( 66, 70);;
s2 := (  3,  7)(  4,  8)(  5, 10)(  6,  9)( 11,123)( 12,124)( 13,126)( 14,125)
( 15,119)( 16,120)( 17,122)( 18,121)( 19,115)( 20,116)( 21,118)( 22,117)
( 23,111)( 24,112)( 25,114)( 26,113)( 27,107)( 28,108)( 29,110)( 30,109)
( 31,103)( 32,104)( 33,106)( 34,105)( 35, 99)( 36,100)( 37,102)( 38,101)
( 39, 95)( 40, 96)( 41, 98)( 42, 97)( 43, 91)( 44, 92)( 45, 94)( 46, 93)
( 47, 87)( 48, 88)( 49, 90)( 50, 89)( 51, 83)( 52, 84)( 53, 86)( 54, 85)
( 55, 79)( 56, 80)( 57, 82)( 58, 81)( 59, 75)( 60, 76)( 61, 78)( 62, 77)
( 63, 71)( 64, 72)( 65, 74)( 66, 73)( 69, 70);;
s3 := (  3,  6)(  4,  5)(  7, 10)(  8,  9)( 11, 14)( 12, 13)( 15, 18)( 16, 17)
( 19, 22)( 20, 21)( 23, 26)( 24, 25)( 27, 30)( 28, 29)( 31, 34)( 32, 33)
( 35, 38)( 36, 37)( 39, 42)( 40, 41)( 43, 46)( 44, 45)( 47, 50)( 48, 49)
( 51, 54)( 52, 53)( 55, 58)( 56, 57)( 59, 62)( 60, 61)( 63, 66)( 64, 65)
( 67, 70)( 68, 69)( 71, 74)( 72, 73)( 75, 78)( 76, 77)( 79, 82)( 80, 81)
( 83, 86)( 84, 85)( 87, 90)( 88, 89)( 91, 94)( 92, 93)( 95, 98)( 96, 97)
( 99,102)(100,101)(103,106)(104,105)(107,110)(108,109)(111,114)(112,113)
(115,118)(116,117)(119,122)(120,121)(123,126)(124,125);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3, s3*s2*s1*s3*s2*s3*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*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(126)!(1,2);
s1 := Sym(126)!(  4,  5)(  7,123)(  8,125)(  9,124)( 10,126)( 11,119)( 12,121)
( 13,120)( 14,122)( 15,115)( 16,117)( 17,116)( 18,118)( 19,111)( 20,113)
( 21,112)( 22,114)( 23,107)( 24,109)( 25,108)( 26,110)( 27,103)( 28,105)
( 29,104)( 30,106)( 31, 99)( 32,101)( 33,100)( 34,102)( 35, 95)( 36, 97)
( 37, 96)( 38, 98)( 39, 91)( 40, 93)( 41, 92)( 42, 94)( 43, 87)( 44, 89)
( 45, 88)( 46, 90)( 47, 83)( 48, 85)( 49, 84)( 50, 86)( 51, 79)( 52, 81)
( 53, 80)( 54, 82)( 55, 75)( 56, 77)( 57, 76)( 58, 78)( 59, 71)( 60, 73)
( 61, 72)( 62, 74)( 63, 67)( 64, 69)( 65, 68)( 66, 70);
s2 := Sym(126)!(  3,  7)(  4,  8)(  5, 10)(  6,  9)( 11,123)( 12,124)( 13,126)
( 14,125)( 15,119)( 16,120)( 17,122)( 18,121)( 19,115)( 20,116)( 21,118)
( 22,117)( 23,111)( 24,112)( 25,114)( 26,113)( 27,107)( 28,108)( 29,110)
( 30,109)( 31,103)( 32,104)( 33,106)( 34,105)( 35, 99)( 36,100)( 37,102)
( 38,101)( 39, 95)( 40, 96)( 41, 98)( 42, 97)( 43, 91)( 44, 92)( 45, 94)
( 46, 93)( 47, 87)( 48, 88)( 49, 90)( 50, 89)( 51, 83)( 52, 84)( 53, 86)
( 54, 85)( 55, 79)( 56, 80)( 57, 82)( 58, 81)( 59, 75)( 60, 76)( 61, 78)
( 62, 77)( 63, 71)( 64, 72)( 65, 74)( 66, 73)( 69, 70);
s3 := Sym(126)!(  3,  6)(  4,  5)(  7, 10)(  8,  9)( 11, 14)( 12, 13)( 15, 18)
( 16, 17)( 19, 22)( 20, 21)( 23, 26)( 24, 25)( 27, 30)( 28, 29)( 31, 34)
( 32, 33)( 35, 38)( 36, 37)( 39, 42)( 40, 41)( 43, 46)( 44, 45)( 47, 50)
( 48, 49)( 51, 54)( 52, 53)( 55, 58)( 56, 57)( 59, 62)( 60, 61)( 63, 66)
( 64, 65)( 67, 70)( 68, 69)( 71, 74)( 72, 73)( 75, 78)( 76, 77)( 79, 82)
( 80, 81)( 83, 86)( 84, 85)( 87, 90)( 88, 89)( 91, 94)( 92, 93)( 95, 98)
( 96, 97)( 99,102)(100,101)(103,106)(104,105)(107,110)(108,109)(111,114)
(112,113)(115,118)(116,117)(119,122)(120,121)(123,126)(124,125);
poly := sub<Sym(126)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s2*s1*s3*s2*s3*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*s1*s2*s1*s2 >;

to this polytope