Polytope of Type {2,44,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,44,6}*1056a
if this polytope has a name.
Group : SmallGroup(1056,917)
Rank : 4
Schlafli Type : {2,44,6}
Number of vertices, edges, etc : 2, 44, 132, 6
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 : {2,22,6}*528
   3-fold quotients : {2,44,2}*352
   6-fold quotients : {2,22,2}*176
   11-fold quotients : {2,4,6}*96a
   12-fold quotients : {2,11,2}*88
   22-fold quotients : {2,2,6}*48
   33-fold quotients : {2,4,2}*32
   44-fold quotients : {2,2,3}*24
   66-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4, 13)(  5, 12)(  6, 11)(  7, 10)(  8,  9)( 15, 24)( 16, 23)( 17, 22)
( 18, 21)( 19, 20)( 26, 35)( 27, 34)( 28, 33)( 29, 32)( 30, 31)( 37, 46)
( 38, 45)( 39, 44)( 40, 43)( 41, 42)( 48, 57)( 49, 56)( 50, 55)( 51, 54)
( 52, 53)( 59, 68)( 60, 67)( 61, 66)( 62, 65)( 63, 64)( 69,102)( 70,112)
( 71,111)( 72,110)( 73,109)( 74,108)( 75,107)( 76,106)( 77,105)( 78,104)
( 79,103)( 80,113)( 81,123)( 82,122)( 83,121)( 84,120)( 85,119)( 86,118)
( 87,117)( 88,116)( 89,115)( 90,114)( 91,124)( 92,134)( 93,133)( 94,132)
( 95,131)( 96,130)( 97,129)( 98,128)( 99,127)(100,126)(101,125);;
s2 := (  3, 70)(  4, 69)(  5, 79)(  6, 78)(  7, 77)(  8, 76)(  9, 75)( 10, 74)
( 11, 73)( 12, 72)( 13, 71)( 14, 92)( 15, 91)( 16,101)( 17,100)( 18, 99)
( 19, 98)( 20, 97)( 21, 96)( 22, 95)( 23, 94)( 24, 93)( 25, 81)( 26, 80)
( 27, 90)( 28, 89)( 29, 88)( 30, 87)( 31, 86)( 32, 85)( 33, 84)( 34, 83)
( 35, 82)( 36,103)( 37,102)( 38,112)( 39,111)( 40,110)( 41,109)( 42,108)
( 43,107)( 44,106)( 45,105)( 46,104)( 47,125)( 48,124)( 49,134)( 50,133)
( 51,132)( 52,131)( 53,130)( 54,129)( 55,128)( 56,127)( 57,126)( 58,114)
( 59,113)( 60,123)( 61,122)( 62,121)( 63,120)( 64,119)( 65,118)( 66,117)
( 67,116)( 68,115);;
s3 := (  3, 14)(  4, 15)(  5, 16)(  6, 17)(  7, 18)(  8, 19)(  9, 20)( 10, 21)
( 11, 22)( 12, 23)( 13, 24)( 36, 47)( 37, 48)( 38, 49)( 39, 50)( 40, 51)
( 41, 52)( 42, 53)( 43, 54)( 44, 55)( 45, 56)( 46, 57)( 69, 80)( 70, 81)
( 71, 82)( 72, 83)( 73, 84)( 74, 85)( 75, 86)( 76, 87)( 77, 88)( 78, 89)
( 79, 90)(102,113)(103,114)(104,115)(105,116)(106,117)(107,118)(108,119)
(109,120)(110,121)(111,122)(112,123);;
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*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(134)!(1,2);
s1 := Sym(134)!(  4, 13)(  5, 12)(  6, 11)(  7, 10)(  8,  9)( 15, 24)( 16, 23)
( 17, 22)( 18, 21)( 19, 20)( 26, 35)( 27, 34)( 28, 33)( 29, 32)( 30, 31)
( 37, 46)( 38, 45)( 39, 44)( 40, 43)( 41, 42)( 48, 57)( 49, 56)( 50, 55)
( 51, 54)( 52, 53)( 59, 68)( 60, 67)( 61, 66)( 62, 65)( 63, 64)( 69,102)
( 70,112)( 71,111)( 72,110)( 73,109)( 74,108)( 75,107)( 76,106)( 77,105)
( 78,104)( 79,103)( 80,113)( 81,123)( 82,122)( 83,121)( 84,120)( 85,119)
( 86,118)( 87,117)( 88,116)( 89,115)( 90,114)( 91,124)( 92,134)( 93,133)
( 94,132)( 95,131)( 96,130)( 97,129)( 98,128)( 99,127)(100,126)(101,125);
s2 := Sym(134)!(  3, 70)(  4, 69)(  5, 79)(  6, 78)(  7, 77)(  8, 76)(  9, 75)
( 10, 74)( 11, 73)( 12, 72)( 13, 71)( 14, 92)( 15, 91)( 16,101)( 17,100)
( 18, 99)( 19, 98)( 20, 97)( 21, 96)( 22, 95)( 23, 94)( 24, 93)( 25, 81)
( 26, 80)( 27, 90)( 28, 89)( 29, 88)( 30, 87)( 31, 86)( 32, 85)( 33, 84)
( 34, 83)( 35, 82)( 36,103)( 37,102)( 38,112)( 39,111)( 40,110)( 41,109)
( 42,108)( 43,107)( 44,106)( 45,105)( 46,104)( 47,125)( 48,124)( 49,134)
( 50,133)( 51,132)( 52,131)( 53,130)( 54,129)( 55,128)( 56,127)( 57,126)
( 58,114)( 59,113)( 60,123)( 61,122)( 62,121)( 63,120)( 64,119)( 65,118)
( 66,117)( 67,116)( 68,115);
s3 := Sym(134)!(  3, 14)(  4, 15)(  5, 16)(  6, 17)(  7, 18)(  8, 19)(  9, 20)
( 10, 21)( 11, 22)( 12, 23)( 13, 24)( 36, 47)( 37, 48)( 38, 49)( 39, 50)
( 40, 51)( 41, 52)( 42, 53)( 43, 54)( 44, 55)( 45, 56)( 46, 57)( 69, 80)
( 70, 81)( 71, 82)( 72, 83)( 73, 84)( 74, 85)( 75, 86)( 76, 87)( 77, 88)
( 78, 89)( 79, 90)(102,113)(103,114)(104,115)(105,116)(106,117)(107,118)
(108,119)(109,120)(110,121)(111,122)(112,123);
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*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*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 >;

to this polytope