Polytope of Type {2,116}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,116}*464
if this polytope has a name.
Group : SmallGroup(464,37)
Rank : 3
Schlafli Type : {2,116}
Number of vertices, edges, etc : 2, 116, 116
Order of s₀s₁s₂ : 116
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,116,2} of size 928
   {2,116,4} of size 1856
Vertex Figure Of :
   {2,2,116} of size 928
   {3,2,116} of size 1392
   {4,2,116} of size 1856
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,58}*232
   4-fold quotients : {2,29}*116
   29-fold quotients : {2,4}*16
   58-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,116}*928, {2,232}*928
   3-fold covers : {6,116}*1392a, {2,348}*1392
   4-fold covers : {8,116}*1856a, {4,232}*1856a, {8,116}*1856b, {4,232}*1856b, {4,116}*1856, {2,464}*1856
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (Magma) :

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