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Polytope of Type {22,6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,6,6}*1584b
if this polytope has a name.
Group : SmallGroup(1584,675)
Rank : 4
Schlafli Type : {22,6,6}
Number of vertices, edges, etc : 22, 66, 18, 6
Order of s0s1s2s3 : 66
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 : {22,6,3}*792
   3-fold quotients : {22,2,6}*528
   6-fold quotients : {11,2,6}*264, {22,2,3}*264
   9-fold quotients : {22,2,2}*176
   11-fold quotients : {2,6,6}*144b
   12-fold quotients : {11,2,3}*132
   18-fold quotients : {11,2,2}*88
   22-fold quotients : {2,6,3}*72
   33-fold quotients : {2,2,6}*48
   66-fold quotients : {2,2,3}*24
   99-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)(134,143)(135,142)(136,141)(137,140)
(138,139)(145,154)(146,153)(147,152)(148,151)(149,150)(156,165)(157,164)
(158,163)(159,162)(160,161)(167,176)(168,175)(169,174)(170,173)(171,172)
(178,187)(179,186)(180,185)(181,184)(182,183)(189,198)(190,197)(191,196)
(192,195)(193,194);;
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)
(133,134)(135,143)(136,142)(137,141)(138,140)(144,156)(145,155)(146,165)
(147,164)(148,163)(149,162)(150,161)(151,160)(152,159)(153,158)(154,157)
(166,167)(168,176)(169,175)(170,174)(171,173)(177,189)(178,188)(179,198)
(180,197)(181,196)(182,195)(183,194)(184,193)(185,192)(186,191)(187,190);;
s2 := (  1, 12)(  2, 13)(  3, 14)(  4, 15)(  5, 16)(  6, 17)(  7, 18)(  8, 19)
(  9, 20)( 10, 21)( 11, 22)( 34, 78)( 35, 79)( 36, 80)( 37, 81)( 38, 82)
( 39, 83)( 40, 84)( 41, 85)( 42, 86)( 43, 87)( 44, 88)( 45, 67)( 46, 68)
( 47, 69)( 48, 70)( 49, 71)( 50, 72)( 51, 73)( 52, 74)( 53, 75)( 54, 76)
( 55, 77)( 56, 89)( 57, 90)( 58, 91)( 59, 92)( 60, 93)( 61, 94)( 62, 95)
( 63, 96)( 64, 97)( 65, 98)( 66, 99)(100,111)(101,112)(102,113)(103,114)
(104,115)(105,116)(106,117)(107,118)(108,119)(109,120)(110,121)(133,177)
(134,178)(135,179)(136,180)(137,181)(138,182)(139,183)(140,184)(141,185)
(142,186)(143,187)(144,166)(145,167)(146,168)(147,169)(148,170)(149,171)
(150,172)(151,173)(152,174)(153,175)(154,176)(155,188)(156,189)(157,190)
(158,191)(159,192)(160,193)(161,194)(162,195)(163,196)(164,197)(165,198);;
s3 := (  1,133)(  2,134)(  3,135)(  4,136)(  5,137)(  6,138)(  7,139)(  8,140)
(  9,141)( 10,142)( 11,143)( 12,155)( 13,156)( 14,157)( 15,158)( 16,159)
( 17,160)( 18,161)( 19,162)( 20,163)( 21,164)( 22,165)( 23,144)( 24,145)
( 25,146)( 26,147)( 27,148)( 28,149)( 29,150)( 30,151)( 31,152)( 32,153)
( 33,154)( 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)( 67,166)( 68,167)( 69,168)( 70,169)( 71,170)( 72,171)
( 73,172)( 74,173)( 75,174)( 76,175)( 77,176)( 78,188)( 79,189)( 80,190)
( 81,191)( 82,192)( 83,193)( 84,194)( 85,195)( 86,196)( 87,197)( 88,198)
( 89,177)( 90,178)( 91,179)( 92,180)( 93,181)( 94,182)( 95,183)( 96,184)
( 97,185)( 98,186)( 99,187);;
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, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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(198)!(  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)(134,143)(135,142)(136,141)
(137,140)(138,139)(145,154)(146,153)(147,152)(148,151)(149,150)(156,165)
(157,164)(158,163)(159,162)(160,161)(167,176)(168,175)(169,174)(170,173)
(171,172)(178,187)(179,186)(180,185)(181,184)(182,183)(189,198)(190,197)
(191,196)(192,195)(193,194);
s1 := Sym(198)!(  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)(133,134)(135,143)(136,142)(137,141)(138,140)(144,156)(145,155)
(146,165)(147,164)(148,163)(149,162)(150,161)(151,160)(152,159)(153,158)
(154,157)(166,167)(168,176)(169,175)(170,174)(171,173)(177,189)(178,188)
(179,198)(180,197)(181,196)(182,195)(183,194)(184,193)(185,192)(186,191)
(187,190);
s2 := Sym(198)!(  1, 12)(  2, 13)(  3, 14)(  4, 15)(  5, 16)(  6, 17)(  7, 18)
(  8, 19)(  9, 20)( 10, 21)( 11, 22)( 34, 78)( 35, 79)( 36, 80)( 37, 81)
( 38, 82)( 39, 83)( 40, 84)( 41, 85)( 42, 86)( 43, 87)( 44, 88)( 45, 67)
( 46, 68)( 47, 69)( 48, 70)( 49, 71)( 50, 72)( 51, 73)( 52, 74)( 53, 75)
( 54, 76)( 55, 77)( 56, 89)( 57, 90)( 58, 91)( 59, 92)( 60, 93)( 61, 94)
( 62, 95)( 63, 96)( 64, 97)( 65, 98)( 66, 99)(100,111)(101,112)(102,113)
(103,114)(104,115)(105,116)(106,117)(107,118)(108,119)(109,120)(110,121)
(133,177)(134,178)(135,179)(136,180)(137,181)(138,182)(139,183)(140,184)
(141,185)(142,186)(143,187)(144,166)(145,167)(146,168)(147,169)(148,170)
(149,171)(150,172)(151,173)(152,174)(153,175)(154,176)(155,188)(156,189)
(157,190)(158,191)(159,192)(160,193)(161,194)(162,195)(163,196)(164,197)
(165,198);
s3 := Sym(198)!(  1,133)(  2,134)(  3,135)(  4,136)(  5,137)(  6,138)(  7,139)
(  8,140)(  9,141)( 10,142)( 11,143)( 12,155)( 13,156)( 14,157)( 15,158)
( 16,159)( 17,160)( 18,161)( 19,162)( 20,163)( 21,164)( 22,165)( 23,144)
( 24,145)( 25,146)( 26,147)( 27,148)( 28,149)( 29,150)( 30,151)( 31,152)
( 32,153)( 33,154)( 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)( 67,166)( 68,167)( 69,168)( 70,169)( 71,170)
( 72,171)( 73,172)( 74,173)( 75,174)( 76,175)( 77,176)( 78,188)( 79,189)
( 80,190)( 81,191)( 82,192)( 83,193)( 84,194)( 85,195)( 86,196)( 87,197)
( 88,198)( 89,177)( 90,178)( 91,179)( 92,180)( 93,181)( 94,182)( 95,183)
( 96,184)( 97,185)( 98,186)( 99,187);
poly := sub<Sym(198)|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, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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.
to this polytope