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Polytope of Type {2,18,22}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,18,22}*1584
if this polytope has a name.
Group : SmallGroup(1584,368)
Rank : 4
Schlafli Type : {2,18,22}
Number of vertices, edges, etc : 2, 18, 198, 22
Order of s0s1s2s3 : 198
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   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) :
   3-fold quotients : {2,6,22}*528
   9-fold quotients : {2,2,22}*176
   11-fold quotients : {2,18,2}*144
   18-fold quotients : {2,2,11}*88
   22-fold quotients : {2,9,2}*72
   33-fold quotients : {2,6,2}*48
   66-fold quotients : {2,3,2}*24
   99-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  4,  5)(  7,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)( 25, 26)
( 28, 29)( 31, 32)( 34, 35)( 36, 71)( 37, 70)( 38, 69)( 39, 74)( 40, 73)
( 41, 72)( 42, 77)( 43, 76)( 44, 75)( 45, 80)( 46, 79)( 47, 78)( 48, 83)
( 49, 82)( 50, 81)( 51, 86)( 52, 85)( 53, 84)( 54, 89)( 55, 88)( 56, 87)
( 57, 92)( 58, 91)( 59, 90)( 60, 95)( 61, 94)( 62, 93)( 63, 98)( 64, 97)
( 65, 96)( 66,101)( 67,100)( 68, 99)(103,104)(106,107)(109,110)(112,113)
(115,116)(118,119)(121,122)(124,125)(127,128)(130,131)(133,134)(135,170)
(136,169)(137,168)(138,173)(139,172)(140,171)(141,176)(142,175)(143,174)
(144,179)(145,178)(146,177)(147,182)(148,181)(149,180)(150,185)(151,184)
(152,183)(153,188)(154,187)(155,186)(156,191)(157,190)(158,189)(159,194)
(160,193)(161,192)(162,197)(163,196)(164,195)(165,200)(166,199)(167,198);;
s2 := (  3, 36)(  4, 38)(  5, 37)(  6, 66)(  7, 68)(  8, 67)(  9, 63)( 10, 65)
( 11, 64)( 12, 60)( 13, 62)( 14, 61)( 15, 57)( 16, 59)( 17, 58)( 18, 54)
( 19, 56)( 20, 55)( 21, 51)( 22, 53)( 23, 52)( 24, 48)( 25, 50)( 26, 49)
( 27, 45)( 28, 47)( 29, 46)( 30, 42)( 31, 44)( 32, 43)( 33, 39)( 34, 41)
( 35, 40)( 69, 71)( 72,101)( 73,100)( 74, 99)( 75, 98)( 76, 97)( 77, 96)
( 78, 95)( 79, 94)( 80, 93)( 81, 92)( 82, 91)( 83, 90)( 84, 89)( 85, 88)
( 86, 87)(102,135)(103,137)(104,136)(105,165)(106,167)(107,166)(108,162)
(109,164)(110,163)(111,159)(112,161)(113,160)(114,156)(115,158)(116,157)
(117,153)(118,155)(119,154)(120,150)(121,152)(122,151)(123,147)(124,149)
(125,148)(126,144)(127,146)(128,145)(129,141)(130,143)(131,142)(132,138)
(133,140)(134,139)(168,170)(171,200)(172,199)(173,198)(174,197)(175,196)
(176,195)(177,194)(178,193)(179,192)(180,191)(181,190)(182,189)(183,188)
(184,187)(185,186);;
s3 := (  3,105)(  4,106)(  5,107)(  6,102)(  7,103)(  8,104)(  9,132)( 10,133)
( 11,134)( 12,129)( 13,130)( 14,131)( 15,126)( 16,127)( 17,128)( 18,123)
( 19,124)( 20,125)( 21,120)( 22,121)( 23,122)( 24,117)( 25,118)( 26,119)
( 27,114)( 28,115)( 29,116)( 30,111)( 31,112)( 32,113)( 33,108)( 34,109)
( 35,110)( 36,138)( 37,139)( 38,140)( 39,135)( 40,136)( 41,137)( 42,165)
( 43,166)( 44,167)( 45,162)( 46,163)( 47,164)( 48,159)( 49,160)( 50,161)
( 51,156)( 52,157)( 53,158)( 54,153)( 55,154)( 56,155)( 57,150)( 58,151)
( 59,152)( 60,147)( 61,148)( 62,149)( 63,144)( 64,145)( 65,146)( 66,141)
( 67,142)( 68,143)( 69,171)( 70,172)( 71,173)( 72,168)( 73,169)( 74,170)
( 75,198)( 76,199)( 77,200)( 78,195)( 79,196)( 80,197)( 81,192)( 82,193)
( 83,194)( 84,189)( 85,190)( 86,191)( 87,186)( 88,187)( 89,188)( 90,183)
( 91,184)( 92,185)( 93,180)( 94,181)( 95,182)( 96,177)( 97,178)( 98,179)
( 99,174)(100,175)(101,176);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*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, 
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(200)!(1,2);
s1 := Sym(200)!(  4,  5)(  7,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)
( 25, 26)( 28, 29)( 31, 32)( 34, 35)( 36, 71)( 37, 70)( 38, 69)( 39, 74)
( 40, 73)( 41, 72)( 42, 77)( 43, 76)( 44, 75)( 45, 80)( 46, 79)( 47, 78)
( 48, 83)( 49, 82)( 50, 81)( 51, 86)( 52, 85)( 53, 84)( 54, 89)( 55, 88)
( 56, 87)( 57, 92)( 58, 91)( 59, 90)( 60, 95)( 61, 94)( 62, 93)( 63, 98)
( 64, 97)( 65, 96)( 66,101)( 67,100)( 68, 99)(103,104)(106,107)(109,110)
(112,113)(115,116)(118,119)(121,122)(124,125)(127,128)(130,131)(133,134)
(135,170)(136,169)(137,168)(138,173)(139,172)(140,171)(141,176)(142,175)
(143,174)(144,179)(145,178)(146,177)(147,182)(148,181)(149,180)(150,185)
(151,184)(152,183)(153,188)(154,187)(155,186)(156,191)(157,190)(158,189)
(159,194)(160,193)(161,192)(162,197)(163,196)(164,195)(165,200)(166,199)
(167,198);
s2 := Sym(200)!(  3, 36)(  4, 38)(  5, 37)(  6, 66)(  7, 68)(  8, 67)(  9, 63)
( 10, 65)( 11, 64)( 12, 60)( 13, 62)( 14, 61)( 15, 57)( 16, 59)( 17, 58)
( 18, 54)( 19, 56)( 20, 55)( 21, 51)( 22, 53)( 23, 52)( 24, 48)( 25, 50)
( 26, 49)( 27, 45)( 28, 47)( 29, 46)( 30, 42)( 31, 44)( 32, 43)( 33, 39)
( 34, 41)( 35, 40)( 69, 71)( 72,101)( 73,100)( 74, 99)( 75, 98)( 76, 97)
( 77, 96)( 78, 95)( 79, 94)( 80, 93)( 81, 92)( 82, 91)( 83, 90)( 84, 89)
( 85, 88)( 86, 87)(102,135)(103,137)(104,136)(105,165)(106,167)(107,166)
(108,162)(109,164)(110,163)(111,159)(112,161)(113,160)(114,156)(115,158)
(116,157)(117,153)(118,155)(119,154)(120,150)(121,152)(122,151)(123,147)
(124,149)(125,148)(126,144)(127,146)(128,145)(129,141)(130,143)(131,142)
(132,138)(133,140)(134,139)(168,170)(171,200)(172,199)(173,198)(174,197)
(175,196)(176,195)(177,194)(178,193)(179,192)(180,191)(181,190)(182,189)
(183,188)(184,187)(185,186);
s3 := Sym(200)!(  3,105)(  4,106)(  5,107)(  6,102)(  7,103)(  8,104)(  9,132)
( 10,133)( 11,134)( 12,129)( 13,130)( 14,131)( 15,126)( 16,127)( 17,128)
( 18,123)( 19,124)( 20,125)( 21,120)( 22,121)( 23,122)( 24,117)( 25,118)
( 26,119)( 27,114)( 28,115)( 29,116)( 30,111)( 31,112)( 32,113)( 33,108)
( 34,109)( 35,110)( 36,138)( 37,139)( 38,140)( 39,135)( 40,136)( 41,137)
( 42,165)( 43,166)( 44,167)( 45,162)( 46,163)( 47,164)( 48,159)( 49,160)
( 50,161)( 51,156)( 52,157)( 53,158)( 54,153)( 55,154)( 56,155)( 57,150)
( 58,151)( 59,152)( 60,147)( 61,148)( 62,149)( 63,144)( 64,145)( 65,146)
( 66,141)( 67,142)( 68,143)( 69,171)( 70,172)( 71,173)( 72,168)( 73,169)
( 74,170)( 75,198)( 76,199)( 77,200)( 78,195)( 79,196)( 80,197)( 81,192)
( 82,193)( 83,194)( 84,189)( 85,190)( 86,191)( 87,186)( 88,187)( 89,188)
( 90,183)( 91,184)( 92,185)( 93,180)( 94,181)( 95,182)( 96,177)( 97,178)
( 98,179)( 99,174)(100,175)(101,176);
poly := sub<Sym(200)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*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, 
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 >; 
 

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