Polytope of Type {2,114}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,114}*456
if this polytope has a name.
Group : SmallGroup(456,53)
Rank : 3
Schlafli Type : {2,114}
Number of vertices, edges, etc : 2, 114, 114
Order of s₀s₁s₂ : 114
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,114,2} of size 912
   {2,114,4} of size 1824
   {2,114,4} of size 1824
   {2,114,4} of size 1824
Vertex Figure Of :
   {2,2,114} of size 912
   {3,2,114} of size 1368
   {4,2,114} of size 1824
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,57}*228
   3-fold quotients : {2,38}*152
   6-fold quotients : {2,19}*76
   19-fold quotients : {2,6}*24
   38-fold quotients : {2,3}*12
   57-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,228}*912, {4,114}*912a
   3-fold covers : {2,342}*1368, {6,114}*1368b, {6,114}*1368c
   4-fold covers : {4,228}*1824a, {2,456}*1824, {8,114}*1824, {4,114}*1824
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope