Polytope of Type {2,124}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,124}*496
if this polytope has a name.
Group : SmallGroup(496,29)
Rank : 3
Schlafli Type : {2,124}
Number of vertices, edges, etc : 2, 124, 124
Order of s₀s₁s₂ : 124
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,124,2} of size 992
   {2,124,4} of size 1984
Vertex Figure Of :
   {2,2,124} of size 992
   {3,2,124} of size 1488
   {4,2,124} of size 1984
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,62}*248
   4-fold quotients : {2,31}*124
   31-fold quotients : {2,4}*16
   62-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,124}*992, {2,248}*992
   3-fold covers : {6,124}*1488a, {2,372}*1488
   4-fold covers : {8,124}*1984a, {4,248}*1984a, {8,124}*1984b, {4,248}*1984b, {4,124}*1984, {2,496}*1984
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4, 33)(  5, 32)(  6, 31)(  7, 30)(  8, 29)(  9, 28)( 10, 27)( 11, 26)
( 12, 25)( 13, 24)( 14, 23)( 15, 22)( 16, 21)( 17, 20)( 18, 19)( 35, 64)
( 36, 63)( 37, 62)( 38, 61)( 39, 60)( 40, 59)( 41, 58)( 42, 57)( 43, 56)
( 44, 55)( 45, 54)( 46, 53)( 47, 52)( 48, 51)( 49, 50)( 65, 96)( 66,126)
( 67,125)( 68,124)( 69,123)( 70,122)( 71,121)( 72,120)( 73,119)( 74,118)
( 75,117)( 76,116)( 77,115)( 78,114)( 79,113)( 80,112)( 81,111)( 82,110)
( 83,109)( 84,108)( 85,107)( 86,106)( 87,105)( 88,104)( 89,103)( 90,102)
( 91,101)( 92,100)( 93, 99)( 94, 98)( 95, 97);;
s2 := (  3, 66)(  4, 65)(  5, 95)(  6, 94)(  7, 93)(  8, 92)(  9, 91)( 10, 90)
( 11, 89)( 12, 88)( 13, 87)( 14, 86)( 15, 85)( 16, 84)( 17, 83)( 18, 82)
( 19, 81)( 20, 80)( 21, 79)( 22, 78)( 23, 77)( 24, 76)( 25, 75)( 26, 74)
( 27, 73)( 28, 72)( 29, 71)( 30, 70)( 31, 69)( 32, 68)( 33, 67)( 34, 97)
( 35, 96)( 36,126)( 37,125)( 38,124)( 39,123)( 40,122)( 41,121)( 42,120)
( 43,119)( 44,118)( 45,117)( 46,116)( 47,115)( 48,114)( 49,113)( 50,112)
( 51,111)( 52,110)( 53,109)( 54,108)( 55,107)( 56,106)( 57,105)( 58,104)
( 59,103)( 60,102)( 61,101)( 62,100)( 63, 99)( 64, 98);;
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(126)!(1,2);
s1 := Sym(126)!(  4, 33)(  5, 32)(  6, 31)(  7, 30)(  8, 29)(  9, 28)( 10, 27)
( 11, 26)( 12, 25)( 13, 24)( 14, 23)( 15, 22)( 16, 21)( 17, 20)( 18, 19)
( 35, 64)( 36, 63)( 37, 62)( 38, 61)( 39, 60)( 40, 59)( 41, 58)( 42, 57)
( 43, 56)( 44, 55)( 45, 54)( 46, 53)( 47, 52)( 48, 51)( 49, 50)( 65, 96)
( 66,126)( 67,125)( 68,124)( 69,123)( 70,122)( 71,121)( 72,120)( 73,119)
( 74,118)( 75,117)( 76,116)( 77,115)( 78,114)( 79,113)( 80,112)( 81,111)
( 82,110)( 83,109)( 84,108)( 85,107)( 86,106)( 87,105)( 88,104)( 89,103)
( 90,102)( 91,101)( 92,100)( 93, 99)( 94, 98)( 95, 97);
s2 := Sym(126)!(  3, 66)(  4, 65)(  5, 95)(  6, 94)(  7, 93)(  8, 92)(  9, 91)
( 10, 90)( 11, 89)( 12, 88)( 13, 87)( 14, 86)( 15, 85)( 16, 84)( 17, 83)
( 18, 82)( 19, 81)( 20, 80)( 21, 79)( 22, 78)( 23, 77)( 24, 76)( 25, 75)
( 26, 74)( 27, 73)( 28, 72)( 29, 71)( 30, 70)( 31, 69)( 32, 68)( 33, 67)
( 34, 97)( 35, 96)( 36,126)( 37,125)( 38,124)( 39,123)( 40,122)( 41,121)
( 42,120)( 43,119)( 44,118)( 45,117)( 46,116)( 47,115)( 48,114)( 49,113)
( 50,112)( 51,111)( 52,110)( 53,109)( 54,108)( 55,107)( 56,106)( 57,105)
( 58,104)( 59,103)( 60,102)( 61,101)( 62,100)( 63, 99)( 64, 98);
poly := sub<Sym(126)|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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope