Polytope of Type {4,62,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,62,2}*992
if this polytope has a name.
Group : SmallGroup(992,177)
Rank : 4
Schlafli Type : {4,62,2}
Number of vertices, edges, etc : 4, 124, 62, 2
Order of s₀s₁s₂s₃ : 124
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,62,2,2} of size 1984
Vertex Figure Of :
   {2,4,62,2} of size 1984
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,62,2}*496
   4-fold quotients : {2,31,2}*248
   31-fold quotients : {4,2,2}*32
   62-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,124,2}*1984, {4,62,4}*1984, {8,62,2}*1984
Permutation Representation (GAP) :

s0 := ( 63, 94)( 64, 95)( 65, 96)( 66, 97)( 67, 98)( 68, 99)( 69,100)( 70,101)
( 71,102)( 72,103)( 73,104)( 74,105)( 75,106)( 76,107)( 77,108)( 78,109)
( 79,110)( 80,111)( 81,112)( 82,113)( 83,114)( 84,115)( 85,116)( 86,117)
( 87,118)( 88,119)( 89,120)( 90,121)( 91,122)( 92,123)( 93,124);;
s1 := (  1, 63)(  2, 93)(  3, 92)(  4, 91)(  5, 90)(  6, 89)(  7, 88)(  8, 87)
(  9, 86)( 10, 85)( 11, 84)( 12, 83)( 13, 82)( 14, 81)( 15, 80)( 16, 79)
( 17, 78)( 18, 77)( 19, 76)( 20, 75)( 21, 74)( 22, 73)( 23, 72)( 24, 71)
( 25, 70)( 26, 69)( 27, 68)( 28, 67)( 29, 66)( 30, 65)( 31, 64)( 32, 94)
( 33,124)( 34,123)( 35,122)( 36,121)( 37,120)( 38,119)( 39,118)( 40,117)
( 41,116)( 42,115)( 43,114)( 44,113)( 45,112)( 46,111)( 47,110)( 48,109)
( 49,108)( 50,107)( 51,106)( 52,105)( 53,104)( 54,103)( 55,102)( 56,101)
( 57,100)( 58, 99)( 59, 98)( 60, 97)( 61, 96)( 62, 95);;
s2 := (  1,  2)(  3, 31)(  4, 30)(  5, 29)(  6, 28)(  7, 27)(  8, 26)(  9, 25)
( 10, 24)( 11, 23)( 12, 22)( 13, 21)( 14, 20)( 15, 19)( 16, 18)( 32, 33)
( 34, 62)( 35, 61)( 36, 60)( 37, 59)( 38, 58)( 39, 57)( 40, 56)( 41, 55)
( 42, 54)( 43, 53)( 44, 52)( 45, 51)( 46, 50)( 47, 49)( 63, 64)( 65, 93)
( 66, 92)( 67, 91)( 68, 90)( 69, 89)( 70, 88)( 71, 87)( 72, 86)( 73, 85)
( 74, 84)( 75, 83)( 76, 82)( 77, 81)( 78, 80)( 94, 95)( 96,124)( 97,123)
( 98,122)( 99,121)(100,120)(101,119)(102,118)(103,117)(104,116)(105,115)
(106,114)(107,113)(108,112)(109,111);;
s3 := (125,126);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(126)!( 63, 94)( 64, 95)( 65, 96)( 66, 97)( 67, 98)( 68, 99)( 69,100)
( 70,101)( 71,102)( 72,103)( 73,104)( 74,105)( 75,106)( 76,107)( 77,108)
( 78,109)( 79,110)( 80,111)( 81,112)( 82,113)( 83,114)( 84,115)( 85,116)
( 86,117)( 87,118)( 88,119)( 89,120)( 90,121)( 91,122)( 92,123)( 93,124);
s1 := Sym(126)!(  1, 63)(  2, 93)(  3, 92)(  4, 91)(  5, 90)(  6, 89)(  7, 88)
(  8, 87)(  9, 86)( 10, 85)( 11, 84)( 12, 83)( 13, 82)( 14, 81)( 15, 80)
( 16, 79)( 17, 78)( 18, 77)( 19, 76)( 20, 75)( 21, 74)( 22, 73)( 23, 72)
( 24, 71)( 25, 70)( 26, 69)( 27, 68)( 28, 67)( 29, 66)( 30, 65)( 31, 64)
( 32, 94)( 33,124)( 34,123)( 35,122)( 36,121)( 37,120)( 38,119)( 39,118)
( 40,117)( 41,116)( 42,115)( 43,114)( 44,113)( 45,112)( 46,111)( 47,110)
( 48,109)( 49,108)( 50,107)( 51,106)( 52,105)( 53,104)( 54,103)( 55,102)
( 56,101)( 57,100)( 58, 99)( 59, 98)( 60, 97)( 61, 96)( 62, 95);
s2 := Sym(126)!(  1,  2)(  3, 31)(  4, 30)(  5, 29)(  6, 28)(  7, 27)(  8, 26)
(  9, 25)( 10, 24)( 11, 23)( 12, 22)( 13, 21)( 14, 20)( 15, 19)( 16, 18)
( 32, 33)( 34, 62)( 35, 61)( 36, 60)( 37, 59)( 38, 58)( 39, 57)( 40, 56)
( 41, 55)( 42, 54)( 43, 53)( 44, 52)( 45, 51)( 46, 50)( 47, 49)( 63, 64)
( 65, 93)( 66, 92)( 67, 91)( 68, 90)( 69, 89)( 70, 88)( 71, 87)( 72, 86)
( 73, 85)( 74, 84)( 75, 83)( 76, 82)( 77, 81)( 78, 80)( 94, 95)( 96,124)
( 97,123)( 98,122)( 99,121)(100,120)(101,119)(102,118)(103,117)(104,116)
(105,115)(106,114)(107,113)(108,112)(109,111);
s3 := Sym(126)!(125,126);
poly := sub<Sym(126)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*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 >;

to this polytope