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Polytope of Type {2,62,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,62,4}*992
if this polytope has a name.
Group : SmallGroup(992,177)
Rank : 4
Schlafli Type : {2,62,4}
Number of vertices, edges, etc : 2, 62, 124, 4
Order of s0s1s2s3 : 124
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,62,4,2} of size 1984
Vertex Figure Of :
   {2,2,62,4} 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 : {2,2,4}*32
   62-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,124,4}*1984, {4,62,4}*1984, {2,62,8}*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)( 66, 95)( 67, 94)
( 68, 93)( 69, 92)( 70, 91)( 71, 90)( 72, 89)( 73, 88)( 74, 87)( 75, 86)
( 76, 85)( 77, 84)( 78, 83)( 79, 82)( 80, 81)( 97,126)( 98,125)( 99,124)
(100,123)(101,122)(102,121)(103,120)(104,119)(105,118)(106,117)(107,116)
(108,115)(109,114)(110,113)(111,112);;
s2 := (  3,  4)(  5, 33)(  6, 32)(  7, 31)(  8, 30)(  9, 29)( 10, 28)( 11, 27)
( 12, 26)( 13, 25)( 14, 24)( 15, 23)( 16, 22)( 17, 21)( 18, 20)( 34, 35)
( 36, 64)( 37, 63)( 38, 62)( 39, 61)( 40, 60)( 41, 59)( 42, 58)( 43, 57)
( 44, 56)( 45, 55)( 46, 54)( 47, 53)( 48, 52)( 49, 51)( 65, 97)( 66, 96)
( 67,126)( 68,125)( 69,124)( 70,123)( 71,122)( 72,121)( 73,120)( 74,119)
( 75,118)( 76,117)( 77,116)( 78,115)( 79,114)( 80,113)( 81,112)( 82,111)
( 83,110)( 84,109)( 85,108)( 86,107)( 87,106)( 88,105)( 89,104)( 90,103)
( 91,102)( 92,101)( 93,100)( 94, 99)( 95, 98);;
s3 := (  3, 65)(  4, 66)(  5, 67)(  6, 68)(  7, 69)(  8, 70)(  9, 71)( 10, 72)
( 11, 73)( 12, 74)( 13, 75)( 14, 76)( 15, 77)( 16, 78)( 17, 79)( 18, 80)
( 19, 81)( 20, 82)( 21, 83)( 22, 84)( 23, 85)( 24, 86)( 25, 87)( 26, 88)
( 27, 89)( 28, 90)( 29, 91)( 30, 92)( 31, 93)( 32, 94)( 33, 95)( 34, 96)
( 35, 97)( 36, 98)( 37, 99)( 38,100)( 39,101)( 40,102)( 41,103)( 42,104)
( 43,105)( 44,106)( 45,107)( 46,108)( 47,109)( 48,110)( 49,111)( 50,112)
( 51,113)( 52,114)( 53,115)( 54,116)( 55,117)( 56,118)( 57,119)( 58,120)
( 59,121)( 60,122)( 61,123)( 62,124)( 63,125)( 64,126);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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)( 66, 95)
( 67, 94)( 68, 93)( 69, 92)( 70, 91)( 71, 90)( 72, 89)( 73, 88)( 74, 87)
( 75, 86)( 76, 85)( 77, 84)( 78, 83)( 79, 82)( 80, 81)( 97,126)( 98,125)
( 99,124)(100,123)(101,122)(102,121)(103,120)(104,119)(105,118)(106,117)
(107,116)(108,115)(109,114)(110,113)(111,112);
s2 := Sym(126)!(  3,  4)(  5, 33)(  6, 32)(  7, 31)(  8, 30)(  9, 29)( 10, 28)
( 11, 27)( 12, 26)( 13, 25)( 14, 24)( 15, 23)( 16, 22)( 17, 21)( 18, 20)
( 34, 35)( 36, 64)( 37, 63)( 38, 62)( 39, 61)( 40, 60)( 41, 59)( 42, 58)
( 43, 57)( 44, 56)( 45, 55)( 46, 54)( 47, 53)( 48, 52)( 49, 51)( 65, 97)
( 66, 96)( 67,126)( 68,125)( 69,124)( 70,123)( 71,122)( 72,121)( 73,120)
( 74,119)( 75,118)( 76,117)( 77,116)( 78,115)( 79,114)( 80,113)( 81,112)
( 82,111)( 83,110)( 84,109)( 85,108)( 86,107)( 87,106)( 88,105)( 89,104)
( 90,103)( 91,102)( 92,101)( 93,100)( 94, 99)( 95, 98);
s3 := Sym(126)!(  3, 65)(  4, 66)(  5, 67)(  6, 68)(  7, 69)(  8, 70)(  9, 71)
( 10, 72)( 11, 73)( 12, 74)( 13, 75)( 14, 76)( 15, 77)( 16, 78)( 17, 79)
( 18, 80)( 19, 81)( 20, 82)( 21, 83)( 22, 84)( 23, 85)( 24, 86)( 25, 87)
( 26, 88)( 27, 89)( 28, 90)( 29, 91)( 30, 92)( 31, 93)( 32, 94)( 33, 95)
( 34, 96)( 35, 97)( 36, 98)( 37, 99)( 38,100)( 39,101)( 40,102)( 41,103)
( 42,104)( 43,105)( 44,106)( 45,107)( 46,108)( 47,109)( 48,110)( 49,111)
( 50,112)( 51,113)( 52,114)( 53,115)( 54,116)( 55,117)( 56,118)( 57,119)
( 58,120)( 59,121)( 60,122)( 61,123)( 62,124)( 63,125)( 64,126);
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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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