Polytope of Type {22,4,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,4,6}*1056
Also Known As : {{22,4|2},{4,6|2}}. if this polytope has another name.
Group : SmallGroup(1056,926)
Rank : 4
Schlafli Type : {22,4,6}
Number of vertices, edges, etc : 22, 44, 12, 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 : {22,2,6}*528
3-fold quotients : {22,4,2}*352
4-fold quotients : {11,2,6}*264, {22,2,3}*264
6-fold quotients : {22,2,2}*176
8-fold quotients : {11,2,3}*132
11-fold quotients : {2,4,6}*96a
12-fold quotients : {11,2,2}*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.
Irregular Quotients (of which this is a minimal cover):
None.
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, 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)( 67,101)( 68,100)( 69,110)( 70,109)( 71,108)( 72,107)( 73,106)( 74,105)( 75,104)( 76,103)( 77,102)( 78,112)( 79,111)( 80,121)( 81,120)( 82,119)( 83,118)( 84,117)( 85,116)( 86,115)( 87,114)( 88,113)( 89,123)( 90,122)( 91,132)( 92,131)( 93,130)( 94,129)( 95,128)( 96,127)( 97,126)( 98,125)( 99,124);;
s2 := ( 1, 67)( 2, 68)( 3, 69)( 4, 70)( 5, 71)( 6, 72)( 7, 73)( 8, 74)( 9, 75)( 10, 76)( 11, 77)( 12, 89)( 13, 90)( 14, 91)( 15, 92)( 16, 93)( 17, 94)( 18, 95)( 19, 96)( 20, 97)( 21, 98)( 22, 99)( 23, 78)( 24, 79)( 25, 80)( 26, 81)( 27, 82)( 28, 83)( 29, 84)( 30, 85)( 31, 86)( 32, 87)( 33, 88)( 34,100)( 35,101)( 36,102)( 37,103)( 38,104)( 39,105)( 40,106)( 41,107)( 42,108)( 43,109)( 44,110)( 45,122)( 46,123)( 47,124)( 48,125)( 49,126)( 50,127)( 51,128)( 52,129)( 53,130)( 54,131)( 55,132)( 56,111)( 57,112)( 58,113)( 59,114)( 60,115)( 61,116)( 62,117)( 63,118)( 64,119)( 65,120)( 66,121);;
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*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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, 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)( 67,101)( 68,100)( 69,110)( 70,109)( 71,108)( 72,107)( 73,106)( 74,105)( 75,104)( 76,103)( 77,102)( 78,112)( 79,111)( 80,121)( 81,120)( 82,119)( 83,118)( 84,117)( 85,116)( 86,115)( 87,114)( 88,113)( 89,123)( 90,122)( 91,132)( 92,131)( 93,130)( 94,129)( 95,128)( 96,127)( 97,126)( 98,125)( 99,124);
s2 := 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, 89)( 13, 90)( 14, 91)( 15, 92)( 16, 93)( 17, 94)( 18, 95)( 19, 96)( 20, 97)( 21, 98)( 22, 99)( 23, 78)( 24, 79)( 25, 80)( 26, 81)( 27, 82)( 28, 83)( 29, 84)( 30, 85)( 31, 86)( 32, 87)( 33, 88)( 34,100)( 35,101)( 36,102)( 37,103)( 38,104)( 39,105)( 40,106)( 41,107)( 42,108)( 43,109)( 44,110)( 45,122)( 46,123)( 47,124)( 48,125)( 49,126)( 50,127)( 51,128)( 52,129)( 53,130)( 54,131)( 55,132)( 56,111)( 57,112)( 58,113)( 59,114)( 60,115)( 61,116)( 62,117)( 63,118)( 64,119)( 65,120)( 66,121);
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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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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