Polytope of Type {87,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {87,6}*1392
if this polytope has a name.
Group : SmallGroup(1392,185)
Rank : 3
Schlafli Type : {87,6}
Number of vertices, edges, etc : 116, 348, 8
Order of s₀s₁s₂ : 116
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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) :
   12-fold quotients : {29,2}*116
   29-fold quotients : {3,6}*48
   58-fold quotients : {3,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope