Polytope of Type {4,87}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,87}*696
if this polytope has a name.
Group : SmallGroup(696,35)
Rank : 3
Schlafli Type : {4,87}
Number of vertices, edges, etc : 4, 174, 87
Order of s₀s₁s₂ : 87
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,87,2} of size 1392
Vertex Figure Of :
   {2,4,87} of size 1392
Quotients (Maximal Quotients in Boldface) :
   29-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,87}*1392, {4,174}*1392b, {4,174}*1392c
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);;
s1 := (  2,  3)(  5,113)(  6,115)(  7,114)(  8,116)(  9,109)( 10,111)( 11,110)
( 12,112)( 13,105)( 14,107)( 15,106)( 16,108)( 17,101)( 18,103)( 19,102)
( 20,104)( 21, 97)( 22, 99)( 23, 98)( 24,100)( 25, 93)( 26, 95)( 27, 94)
( 28, 96)( 29, 89)( 30, 91)( 31, 90)( 32, 92)( 33, 85)( 34, 87)( 35, 86)
( 36, 88)( 37, 81)( 38, 83)( 39, 82)( 40, 84)( 41, 77)( 42, 79)( 43, 78)
( 44, 80)( 45, 73)( 46, 75)( 47, 74)( 48, 76)( 49, 69)( 50, 71)( 51, 70)
( 52, 72)( 53, 65)( 54, 67)( 55, 66)( 56, 68)( 57, 61)( 58, 63)( 59, 62)
( 60, 64);;
s2 := (  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);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope