Polytope of Type {2,22,18}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,22,18}*1584
if this polytope has a name.
Group : SmallGroup(1584,368)
Rank : 4
Schlafli Type : {2,22,18}
Number of vertices, edges, etc : 2, 22, 198, 18
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 : {2,22,6}*528
   9-fold quotients : {2,22,2}*176
   11-fold quotients : {2,2,18}*144
   18-fold quotients : {2,11,2}*88
   22-fold quotients : {2,2,9}*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 := (1,2);;
s1 := (  6, 33)(  7, 34)(  8, 35)(  9, 30)( 10, 31)( 11, 32)( 12, 27)( 13, 28)
( 14, 29)( 15, 24)( 16, 25)( 17, 26)( 18, 21)( 19, 22)( 20, 23)( 39, 66)
( 40, 67)( 41, 68)( 42, 63)( 43, 64)( 44, 65)( 45, 60)( 46, 61)( 47, 62)
( 48, 57)( 49, 58)( 50, 59)( 51, 54)( 52, 55)( 53, 56)( 72, 99)( 73,100)
( 74,101)( 75, 96)( 76, 97)( 77, 98)( 78, 93)( 79, 94)( 80, 95)( 81, 90)
( 82, 91)( 83, 92)( 84, 87)( 85, 88)( 86, 89)(105,132)(106,133)(107,134)
(108,129)(109,130)(110,131)(111,126)(112,127)(113,128)(114,123)(115,124)
(116,125)(117,120)(118,121)(119,122)(138,165)(139,166)(140,167)(141,162)
(142,163)(143,164)(144,159)(145,160)(146,161)(147,156)(148,157)(149,158)
(150,153)(151,154)(152,155)(171,198)(172,199)(173,200)(174,195)(175,196)
(176,197)(177,192)(178,193)(179,194)(180,189)(181,190)(182,191)(183,186)
(184,187)(185,188);;
s2 := (  3,  6)(  4,  8)(  5,  7)(  9, 33)( 10, 35)( 11, 34)( 12, 30)( 13, 32)
( 14, 31)( 15, 27)( 16, 29)( 17, 28)( 18, 24)( 19, 26)( 20, 25)( 22, 23)
( 36, 74)( 37, 73)( 38, 72)( 39, 71)( 40, 70)( 41, 69)( 42,101)( 43,100)
( 44, 99)( 45, 98)( 46, 97)( 47, 96)( 48, 95)( 49, 94)( 50, 93)( 51, 92)
( 52, 91)( 53, 90)( 54, 89)( 55, 88)( 56, 87)( 57, 86)( 58, 85)( 59, 84)
( 60, 83)( 61, 82)( 62, 81)( 63, 80)( 64, 79)( 65, 78)( 66, 77)( 67, 76)
( 68, 75)(102,105)(103,107)(104,106)(108,132)(109,134)(110,133)(111,129)
(112,131)(113,130)(114,126)(115,128)(116,127)(117,123)(118,125)(119,124)
(121,122)(135,173)(136,172)(137,171)(138,170)(139,169)(140,168)(141,200)
(142,199)(143,198)(144,197)(145,196)(146,195)(147,194)(148,193)(149,192)
(150,191)(151,190)(152,189)(153,188)(154,187)(155,186)(156,185)(157,184)
(158,183)(159,182)(160,181)(161,180)(162,179)(163,178)(164,177)(165,176)
(166,175)(167,174);;
s3 := (  3,135)(  4,137)(  5,136)(  6,138)(  7,140)(  8,139)(  9,141)( 10,143)
( 11,142)( 12,144)( 13,146)( 14,145)( 15,147)( 16,149)( 17,148)( 18,150)
( 19,152)( 20,151)( 21,153)( 22,155)( 23,154)( 24,156)( 25,158)( 26,157)
( 27,159)( 28,161)( 29,160)( 30,162)( 31,164)( 32,163)( 33,165)( 34,167)
( 35,166)( 36,102)( 37,104)( 38,103)( 39,105)( 40,107)( 41,106)( 42,108)
( 43,110)( 44,109)( 45,111)( 46,113)( 47,112)( 48,114)( 49,116)( 50,115)
( 51,117)( 52,119)( 53,118)( 54,120)( 55,122)( 56,121)( 57,123)( 58,125)
( 59,124)( 60,126)( 61,128)( 62,127)( 63,129)( 64,131)( 65,130)( 66,132)
( 67,134)( 68,133)( 69,170)( 70,169)( 71,168)( 72,173)( 73,172)( 74,171)
( 75,176)( 76,175)( 77,174)( 78,179)( 79,178)( 80,177)( 81,182)( 82,181)
( 83,180)( 84,185)( 85,184)( 86,183)( 87,188)( 88,187)( 89,186)( 90,191)
( 91,190)( 92,189)( 93,194)( 94,193)( 95,192)( 96,197)( 97,196)( 98,195)
( 99,200)(100,199)(101,198);;
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, 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, 
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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(200)!(1,2);
s1 := Sym(200)!(  6, 33)(  7, 34)(  8, 35)(  9, 30)( 10, 31)( 11, 32)( 12, 27)
( 13, 28)( 14, 29)( 15, 24)( 16, 25)( 17, 26)( 18, 21)( 19, 22)( 20, 23)
( 39, 66)( 40, 67)( 41, 68)( 42, 63)( 43, 64)( 44, 65)( 45, 60)( 46, 61)
( 47, 62)( 48, 57)( 49, 58)( 50, 59)( 51, 54)( 52, 55)( 53, 56)( 72, 99)
( 73,100)( 74,101)( 75, 96)( 76, 97)( 77, 98)( 78, 93)( 79, 94)( 80, 95)
( 81, 90)( 82, 91)( 83, 92)( 84, 87)( 85, 88)( 86, 89)(105,132)(106,133)
(107,134)(108,129)(109,130)(110,131)(111,126)(112,127)(113,128)(114,123)
(115,124)(116,125)(117,120)(118,121)(119,122)(138,165)(139,166)(140,167)
(141,162)(142,163)(143,164)(144,159)(145,160)(146,161)(147,156)(148,157)
(149,158)(150,153)(151,154)(152,155)(171,198)(172,199)(173,200)(174,195)
(175,196)(176,197)(177,192)(178,193)(179,194)(180,189)(181,190)(182,191)
(183,186)(184,187)(185,188);
s2 := Sym(200)!(  3,  6)(  4,  8)(  5,  7)(  9, 33)( 10, 35)( 11, 34)( 12, 30)
( 13, 32)( 14, 31)( 15, 27)( 16, 29)( 17, 28)( 18, 24)( 19, 26)( 20, 25)
( 22, 23)( 36, 74)( 37, 73)( 38, 72)( 39, 71)( 40, 70)( 41, 69)( 42,101)
( 43,100)( 44, 99)( 45, 98)( 46, 97)( 47, 96)( 48, 95)( 49, 94)( 50, 93)
( 51, 92)( 52, 91)( 53, 90)( 54, 89)( 55, 88)( 56, 87)( 57, 86)( 58, 85)
( 59, 84)( 60, 83)( 61, 82)( 62, 81)( 63, 80)( 64, 79)( 65, 78)( 66, 77)
( 67, 76)( 68, 75)(102,105)(103,107)(104,106)(108,132)(109,134)(110,133)
(111,129)(112,131)(113,130)(114,126)(115,128)(116,127)(117,123)(118,125)
(119,124)(121,122)(135,173)(136,172)(137,171)(138,170)(139,169)(140,168)
(141,200)(142,199)(143,198)(144,197)(145,196)(146,195)(147,194)(148,193)
(149,192)(150,191)(151,190)(152,189)(153,188)(154,187)(155,186)(156,185)
(157,184)(158,183)(159,182)(160,181)(161,180)(162,179)(163,178)(164,177)
(165,176)(166,175)(167,174);
s3 := Sym(200)!(  3,135)(  4,137)(  5,136)(  6,138)(  7,140)(  8,139)(  9,141)
( 10,143)( 11,142)( 12,144)( 13,146)( 14,145)( 15,147)( 16,149)( 17,148)
( 18,150)( 19,152)( 20,151)( 21,153)( 22,155)( 23,154)( 24,156)( 25,158)
( 26,157)( 27,159)( 28,161)( 29,160)( 30,162)( 31,164)( 32,163)( 33,165)
( 34,167)( 35,166)( 36,102)( 37,104)( 38,103)( 39,105)( 40,107)( 41,106)
( 42,108)( 43,110)( 44,109)( 45,111)( 46,113)( 47,112)( 48,114)( 49,116)
( 50,115)( 51,117)( 52,119)( 53,118)( 54,120)( 55,122)( 56,121)( 57,123)
( 58,125)( 59,124)( 60,126)( 61,128)( 62,127)( 63,129)( 64,131)( 65,130)
( 66,132)( 67,134)( 68,133)( 69,170)( 70,169)( 71,168)( 72,173)( 73,172)
( 74,171)( 75,176)( 76,175)( 77,174)( 78,179)( 79,178)( 80,177)( 81,182)
( 82,181)( 83,180)( 84,185)( 85,184)( 86,183)( 87,188)( 88,187)( 89,186)
( 90,191)( 91,190)( 92,189)( 93,194)( 94,193)( 95,192)( 96,197)( 97,196)
( 98,195)( 99,200)(100,199)(101,198);
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, 
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, 
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*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope