Polytope of Type {2,87,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,87,4}*1392
if this polytope has a name.
Group : SmallGroup(1392,188)
Rank : 4
Schlafli Type : {2,87,4}
Number of vertices, edges, etc : 2, 87, 174, 4
Order of s₀s₁s₂s₃ : 174
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) :
   29-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope