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Polytope of Type {6,4,22}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,22}*1056
Also Known As : {{6,4|2},{4,22|2}}. if this polytope has another name.
Group : SmallGroup(1056,926)
Rank : 4
Schlafli Type : {6,4,22}
Number of vertices, edges, etc : 6, 12, 44, 22
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 : {6,2,22}*528
   3-fold quotients : {2,4,22}*352
   4-fold quotients : {3,2,22}*264, {6,2,11}*264
   6-fold quotients : {2,2,22}*176
   8-fold quotients : {3,2,11}*132
   11-fold quotients : {6,4,2}*96a
   12-fold quotients : {2,2,11}*88
   22-fold quotients : {6,2,2}*48
   33-fold quotients : {2,4,2}*32
   44-fold quotients : {3,2,2}*24
   66-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 12, 23)( 13, 24)( 14, 25)( 15, 26)( 16, 27)( 17, 28)( 18, 29)( 19, 30)
( 20, 31)( 21, 32)( 22, 33)( 45, 56)( 46, 57)( 47, 58)( 48, 59)( 49, 60)
( 50, 61)( 51, 62)( 52, 63)( 53, 64)( 54, 65)( 55, 66)( 78, 89)( 79, 90)
( 80, 91)( 81, 92)( 82, 93)( 83, 94)( 84, 95)( 85, 96)( 86, 97)( 87, 98)
( 88, 99)(111,122)(112,123)(113,124)(114,125)(115,126)(116,127)(117,128)
(118,129)(119,130)(120,131)(121,132);;
s1 := (  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)( 67,111)( 68,112)
( 69,113)( 70,114)( 71,115)( 72,116)( 73,117)( 74,118)( 75,119)( 76,120)
( 77,121)( 78,100)( 79,101)( 80,102)( 81,103)( 82,104)( 83,105)( 84,106)
( 85,107)( 86,108)( 87,109)( 88,110)( 89,122)( 90,123)( 91,124)( 92,125)
( 93,126)( 94,127)( 95,128)( 96,129)( 97,130)( 98,131)( 99,132);;
s2 := (  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);;
s3 := (  1,  2)(  3, 11)(  4, 10)(  5,  9)(  6,  8)( 12, 13)( 14, 22)( 15, 21)
( 16, 20)( 17, 19)( 23, 24)( 25, 33)( 26, 32)( 27, 31)( 28, 30)( 34, 35)
( 36, 44)( 37, 43)( 38, 42)( 39, 41)( 45, 46)( 47, 55)( 48, 54)( 49, 53)
( 50, 52)( 56, 57)( 58, 66)( 59, 65)( 60, 64)( 61, 63)( 67, 68)( 69, 77)
( 70, 76)( 71, 75)( 72, 74)( 78, 79)( 80, 88)( 81, 87)( 82, 86)( 83, 85)
( 89, 90)( 91, 99)( 92, 98)( 93, 97)( 94, 96)(100,101)(102,110)(103,109)
(104,108)(105,107)(111,112)(113,121)(114,120)(115,119)(116,118)(122,123)
(124,132)(125,131)(126,130)(127,129);;
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(132)!( 12, 23)( 13, 24)( 14, 25)( 15, 26)( 16, 27)( 17, 28)( 18, 29)
( 19, 30)( 20, 31)( 21, 32)( 22, 33)( 45, 56)( 46, 57)( 47, 58)( 48, 59)
( 49, 60)( 50, 61)( 51, 62)( 52, 63)( 53, 64)( 54, 65)( 55, 66)( 78, 89)
( 79, 90)( 80, 91)( 81, 92)( 82, 93)( 83, 94)( 84, 95)( 85, 96)( 86, 97)
( 87, 98)( 88, 99)(111,122)(112,123)(113,124)(114,125)(115,126)(116,127)
(117,128)(118,129)(119,130)(120,131)(121,132);
s1 := 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)( 67,111)
( 68,112)( 69,113)( 70,114)( 71,115)( 72,116)( 73,117)( 74,118)( 75,119)
( 76,120)( 77,121)( 78,100)( 79,101)( 80,102)( 81,103)( 82,104)( 83,105)
( 84,106)( 85,107)( 86,108)( 87,109)( 88,110)( 89,122)( 90,123)( 91,124)
( 92,125)( 93,126)( 94,127)( 95,128)( 96,129)( 97,130)( 98,131)( 99,132);
s2 := 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);
s3 := Sym(132)!(  1,  2)(  3, 11)(  4, 10)(  5,  9)(  6,  8)( 12, 13)( 14, 22)
( 15, 21)( 16, 20)( 17, 19)( 23, 24)( 25, 33)( 26, 32)( 27, 31)( 28, 30)
( 34, 35)( 36, 44)( 37, 43)( 38, 42)( 39, 41)( 45, 46)( 47, 55)( 48, 54)
( 49, 53)( 50, 52)( 56, 57)( 58, 66)( 59, 65)( 60, 64)( 61, 63)( 67, 68)
( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 78, 79)( 80, 88)( 81, 87)( 82, 86)
( 83, 85)( 89, 90)( 91, 99)( 92, 98)( 93, 97)( 94, 96)(100,101)(102,110)
(103,109)(104,108)(105,107)(111,112)(113,121)(114,120)(115,119)(116,118)
(122,123)(124,132)(125,131)(126,130)(127,129);
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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 
References : None.
to this polytope