Polytope of Type {116,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {116,6}*1392b
if this polytope has a name.
Group : SmallGroup(1392,185)
Rank : 3
Schlafli Type : {116,6}
Number of vertices, edges, etc : 116, 348, 6
Order of s₀s₁s₂ : 87
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) :
   29-fold quotients : {4,6}*48b
   58-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope