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Polytope of Type {44,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {44,6,2}*1056a
if this polytope has a name.
Group : SmallGroup(1056,917)
Rank : 4
Schlafli Type : {44,6,2}
Number of vertices, edges, etc : 44, 132, 6, 2
Order of s0s1s2s3 : 132
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {22,6,2}*528
   3-fold quotients : {44,2,2}*352
   6-fold quotients : {22,2,2}*176
   11-fold quotients : {4,6,2}*96a
   12-fold quotients : {11,2,2}*88
   22-fold quotients : {2,6,2}*48
   33-fold quotients : {4,2,2}*32
   44-fold quotients : {2,3,2}*24
   66-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  2, 11)(  3, 10)(  4,  9)(  5,  8)(  6,  7)( 13, 22)( 14, 21)( 15, 20)
( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)( 35, 44)
( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 46, 55)( 47, 54)( 48, 53)( 49, 52)
( 50, 51)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 67,100)( 68,110)
( 69,109)( 70,108)( 71,107)( 72,106)( 73,105)( 74,104)( 75,103)( 76,102)
( 77,101)( 78,111)( 79,121)( 80,120)( 81,119)( 82,118)( 83,117)( 84,116)
( 85,115)( 86,114)( 87,113)( 88,112)( 89,122)( 90,132)( 91,131)( 92,130)
( 93,129)( 94,128)( 95,127)( 96,126)( 97,125)( 98,124)( 99,123);;
s1 := (  1, 68)(  2, 67)(  3, 77)(  4, 76)(  5, 75)(  6, 74)(  7, 73)(  8, 72)
(  9, 71)( 10, 70)( 11, 69)( 12, 90)( 13, 89)( 14, 99)( 15, 98)( 16, 97)
( 17, 96)( 18, 95)( 19, 94)( 20, 93)( 21, 92)( 22, 91)( 23, 79)( 24, 78)
( 25, 88)( 26, 87)( 27, 86)( 28, 85)( 29, 84)( 30, 83)( 31, 82)( 32, 81)
( 33, 80)( 34,101)( 35,100)( 36,110)( 37,109)( 38,108)( 39,107)( 40,106)
( 41,105)( 42,104)( 43,103)( 44,102)( 45,123)( 46,122)( 47,132)( 48,131)
( 49,130)( 50,129)( 51,128)( 52,127)( 53,126)( 54,125)( 55,124)( 56,112)
( 57,111)( 58,121)( 59,120)( 60,119)( 61,118)( 62,117)( 63,116)( 64,115)
( 65,114)( 66,113);;
s2 := (  1, 12)(  2, 13)(  3, 14)(  4, 15)(  5, 16)(  6, 17)(  7, 18)(  8, 19)
(  9, 20)( 10, 21)( 11, 22)( 34, 45)( 35, 46)( 36, 47)( 37, 48)( 38, 49)
( 39, 50)( 40, 51)( 41, 52)( 42, 53)( 43, 54)( 44, 55)( 67, 78)( 68, 79)
( 69, 80)( 70, 81)( 71, 82)( 72, 83)( 73, 84)( 74, 85)( 75, 86)( 76, 87)
( 77, 88)(100,111)(101,112)(102,113)(103,114)(104,115)(105,116)(106,117)
(107,118)(108,119)(109,120)(110,121);;
s3 := (133,134);;
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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(134)!(  2, 11)(  3, 10)(  4,  9)(  5,  8)(  6,  7)( 13, 22)( 14, 21)
( 15, 20)( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)
( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 46, 55)( 47, 54)( 48, 53)
( 49, 52)( 50, 51)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 67,100)
( 68,110)( 69,109)( 70,108)( 71,107)( 72,106)( 73,105)( 74,104)( 75,103)
( 76,102)( 77,101)( 78,111)( 79,121)( 80,120)( 81,119)( 82,118)( 83,117)
( 84,116)( 85,115)( 86,114)( 87,113)( 88,112)( 89,122)( 90,132)( 91,131)
( 92,130)( 93,129)( 94,128)( 95,127)( 96,126)( 97,125)( 98,124)( 99,123);
s1 := Sym(134)!(  1, 68)(  2, 67)(  3, 77)(  4, 76)(  5, 75)(  6, 74)(  7, 73)
(  8, 72)(  9, 71)( 10, 70)( 11, 69)( 12, 90)( 13, 89)( 14, 99)( 15, 98)
( 16, 97)( 17, 96)( 18, 95)( 19, 94)( 20, 93)( 21, 92)( 22, 91)( 23, 79)
( 24, 78)( 25, 88)( 26, 87)( 27, 86)( 28, 85)( 29, 84)( 30, 83)( 31, 82)
( 32, 81)( 33, 80)( 34,101)( 35,100)( 36,110)( 37,109)( 38,108)( 39,107)
( 40,106)( 41,105)( 42,104)( 43,103)( 44,102)( 45,123)( 46,122)( 47,132)
( 48,131)( 49,130)( 50,129)( 51,128)( 52,127)( 53,126)( 54,125)( 55,124)
( 56,112)( 57,111)( 58,121)( 59,120)( 60,119)( 61,118)( 62,117)( 63,116)
( 64,115)( 65,114)( 66,113);
s2 := Sym(134)!(  1, 12)(  2, 13)(  3, 14)(  4, 15)(  5, 16)(  6, 17)(  7, 18)
(  8, 19)(  9, 20)( 10, 21)( 11, 22)( 34, 45)( 35, 46)( 36, 47)( 37, 48)
( 38, 49)( 39, 50)( 40, 51)( 41, 52)( 42, 53)( 43, 54)( 44, 55)( 67, 78)
( 68, 79)( 69, 80)( 70, 81)( 71, 82)( 72, 83)( 73, 84)( 74, 85)( 75, 86)
( 76, 87)( 77, 88)(100,111)(101,112)(102,113)(103,114)(104,115)(105,116)
(106,117)(107,118)(108,119)(109,120)(110,121);
s3 := Sym(134)!(133,134);
poly := sub<Sym(134)|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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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