Polytope of Type {4,22,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,22,6}*1056
Also Known As : {{4,22|2},{22,6|2}}. if this polytope has another name.
Group : SmallGroup(1056,926)
Rank : 4
Schlafli Type : {4,22,6}
Number of vertices, edges, etc : 4, 44, 66, 6
Order of s₀s₁s₂s₃ : 132
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   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 : {4,22,2}*352
   6-fold quotients : {2,22,2}*176
   11-fold quotients : {4,2,6}*96
   12-fold quotients : {2,11,2}*88
   22-fold quotients : {4,2,3}*48, {2,2,6}*48
   33-fold quotients : {4,2,2}*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 := ( 67,100)( 68,101)( 69,102)( 70,103)( 71,104)( 72,105)( 73,106)( 74,107)
( 75,108)( 76,109)( 77,110)( 78,111)( 79,112)( 80,113)( 81,114)( 82,115)
( 83,116)( 84,117)( 85,118)( 86,119)( 87,120)( 88,121)( 89,122)( 90,123)
( 91,124)( 92,125)( 93,126)( 94,127)( 95,128)( 96,129)( 97,130)( 98,131)
( 99,132);;
s1 := (  1, 67)(  2, 77)(  3, 76)(  4, 75)(  5, 74)(  6, 73)(  7, 72)(  8, 71)
(  9, 70)( 10, 69)( 11, 68)( 12, 78)( 13, 88)( 14, 87)( 15, 86)( 16, 85)
( 17, 84)( 18, 83)( 19, 82)( 20, 81)( 21, 80)( 22, 79)( 23, 89)( 24, 99)
( 25, 98)( 26, 97)( 27, 96)( 28, 95)( 29, 94)( 30, 93)( 31, 92)( 32, 91)
( 33, 90)( 34,100)( 35,110)( 36,109)( 37,108)( 38,107)( 39,106)( 40,105)
( 41,104)( 42,103)( 43,102)( 44,101)( 45,111)( 46,121)( 47,120)( 48,119)
( 49,118)( 50,117)( 51,116)( 52,115)( 53,114)( 54,113)( 55,112)( 56,122)
( 57,132)( 58,131)( 59,130)( 60,129)( 61,128)( 62,127)( 63,126)( 64,125)
( 65,124)( 66,123);;
s2 := (  1,  2)(  3, 11)(  4, 10)(  5,  9)(  6,  8)( 12, 24)( 13, 23)( 14, 33)
( 15, 32)( 16, 31)( 17, 30)( 18, 29)( 19, 28)( 20, 27)( 21, 26)( 22, 25)
( 34, 35)( 36, 44)( 37, 43)( 38, 42)( 39, 41)( 45, 57)( 46, 56)( 47, 66)
( 48, 65)( 49, 64)( 50, 63)( 51, 62)( 52, 61)( 53, 60)( 54, 59)( 55, 58)
( 67, 68)( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 78, 90)( 79, 89)( 80, 99)
( 81, 98)( 82, 97)( 83, 96)( 84, 95)( 85, 94)( 86, 93)( 87, 92)( 88, 91)
(100,101)(102,110)(103,109)(104,108)(105,107)(111,123)(112,122)(113,132)
(114,131)(115,130)(116,129)(117,128)(118,127)(119,126)(120,125)(121,124);;
s3 := (  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);;
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, 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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope