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Polytope of Type {22,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,6,4}*1056a
Also Known As : {{22,6|2},{6,4|2}}. if this polytope has another name.
Group : SmallGroup(1056,926)
Rank : 4
Schlafli Type : {22,6,4}
Number of vertices, edges, etc : 22, 66, 12, 4
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 : {22,6,2}*528
   3-fold quotients : {22,2,4}*352
   6-fold quotients : {11,2,4}*176, {22,2,2}*176
   11-fold quotients : {2,6,4}*96a
   12-fold quotients : {11,2,2}*88
   22-fold quotients : {2,6,2}*48
   33-fold quotients : {2,2,4}*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)( 68, 77)( 69, 76)
( 70, 75)( 71, 74)( 72, 73)( 79, 88)( 80, 87)( 81, 86)( 82, 85)( 83, 84)
( 90, 99)( 91, 98)( 92, 97)( 93, 96)( 94, 95)(101,110)(102,109)(103,108)
(104,107)(105,106)(112,121)(113,120)(114,119)(115,118)(116,117)(123,132)
(124,131)(125,130)(126,129)(127,128);;
s1 := (  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);;
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)( 67,111)( 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);;
s3 := (  1, 67)(  2, 68)(  3, 69)(  4, 70)(  5, 71)(  6, 72)(  7, 73)(  8, 74)
(  9, 75)( 10, 76)( 11, 77)( 12, 78)( 13, 79)( 14, 80)( 15, 81)( 16, 82)
( 17, 83)( 18, 84)( 19, 85)( 20, 86)( 21, 87)( 22, 88)( 23, 89)( 24, 90)
( 25, 91)( 26, 92)( 27, 93)( 28, 94)( 29, 95)( 30, 96)( 31, 97)( 32, 98)
( 33, 99)( 34,100)( 35,101)( 36,102)( 37,103)( 38,104)( 39,105)( 40,106)
( 41,107)( 42,108)( 43,109)( 44,110)( 45,111)( 46,112)( 47,113)( 48,114)
( 49,115)( 50,116)( 51,117)( 52,118)( 53,119)( 54,120)( 55,121)( 56,122)
( 57,123)( 58,124)( 59,125)( 60,126)( 61,127)( 62,128)( 63,129)( 64,130)
( 65,131)( 66,132);;
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*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, 
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(132)!(  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)( 68, 77)
( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79, 88)( 80, 87)( 81, 86)( 82, 85)
( 83, 84)( 90, 99)( 91, 98)( 92, 97)( 93, 96)( 94, 95)(101,110)(102,109)
(103,108)(104,107)(105,106)(112,121)(113,120)(114,119)(115,118)(116,117)
(123,132)(124,131)(125,130)(126,129)(127,128);
s1 := 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);
s2 := 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);
s3 := Sym(132)!(  1, 67)(  2, 68)(  3, 69)(  4, 70)(  5, 71)(  6, 72)(  7, 73)
(  8, 74)(  9, 75)( 10, 76)( 11, 77)( 12, 78)( 13, 79)( 14, 80)( 15, 81)
( 16, 82)( 17, 83)( 18, 84)( 19, 85)( 20, 86)( 21, 87)( 22, 88)( 23, 89)
( 24, 90)( 25, 91)( 26, 92)( 27, 93)( 28, 94)( 29, 95)( 30, 96)( 31, 97)
( 32, 98)( 33, 99)( 34,100)( 35,101)( 36,102)( 37,103)( 38,104)( 39,105)
( 40,106)( 41,107)( 42,108)( 43,109)( 44,110)( 45,111)( 46,112)( 47,113)
( 48,114)( 49,115)( 50,116)( 51,117)( 52,118)( 53,119)( 54,120)( 55,121)
( 56,122)( 57,123)( 58,124)( 59,125)( 60,126)( 61,127)( 62,128)( 63,129)
( 64,130)( 65,131)( 66,132);
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*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, 
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 >; 
 
References : None.
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