Polytope of Type {22,18,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,18,2}*1584
if this polytope has a name.
Group : SmallGroup(1584,368)
Rank : 4
Schlafli Type : {22,18,2}
Number of vertices, edges, etc : 22, 198, 18, 2
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 : {22,6,2}*528
9-fold quotients : {22,2,2}*176
11-fold quotients : {2,18,2}*144
18-fold quotients : {11,2,2}*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 := ( 4, 31)( 5, 32)( 6, 33)( 7, 28)( 8, 29)( 9, 30)( 10, 25)( 11, 26)( 12, 27)( 13, 22)( 14, 23)( 15, 24)( 16, 19)( 17, 20)( 18, 21)( 37, 64)( 38, 65)( 39, 66)( 40, 61)( 41, 62)( 42, 63)( 43, 58)( 44, 59)( 45, 60)( 46, 55)( 47, 56)( 48, 57)( 49, 52)( 50, 53)( 51, 54)( 70, 97)( 71, 98)( 72, 99)( 73, 94)( 74, 95)( 75, 96)( 76, 91)( 77, 92)( 78, 93)( 79, 88)( 80, 89)( 81, 90)( 82, 85)( 83, 86)( 84, 87)(103,130)(104,131)(105,132)(106,127)(107,128)(108,129)(109,124)(110,125)(111,126)(112,121)(113,122)(114,123)(115,118)(116,119)(117,120)(136,163)(137,164)(138,165)(139,160)(140,161)(141,162)(142,157)(143,158)(144,159)(145,154)(146,155)(147,156)(148,151)(149,152)(150,153)(169,196)(170,197)(171,198)(172,193)(173,194)(174,195)(175,190)(176,191)(177,192)(178,187)(179,188)(180,189)(181,184)(182,185)(183,186);;
s1 := ( 1, 4)( 2, 6)( 3, 5)( 7, 31)( 8, 33)( 9, 32)( 10, 28)( 11, 30)( 12, 29)( 13, 25)( 14, 27)( 15, 26)( 16, 22)( 17, 24)( 18, 23)( 20, 21)( 34, 72)( 35, 71)( 36, 70)( 37, 69)( 38, 68)( 39, 67)( 40, 99)( 41, 98)( 42, 97)( 43, 96)( 44, 95)( 45, 94)( 46, 93)( 47, 92)( 48, 91)( 49, 90)( 50, 89)( 51, 88)( 52, 87)( 53, 86)( 54, 85)( 55, 84)( 56, 83)( 57, 82)( 58, 81)( 59, 80)( 60, 79)( 61, 78)( 62, 77)( 63, 76)( 64, 75)( 65, 74)( 66, 73)(100,103)(101,105)(102,104)(106,130)(107,132)(108,131)(109,127)(110,129)(111,128)(112,124)(113,126)(114,125)(115,121)(116,123)(117,122)(119,120)(133,171)(134,170)(135,169)(136,168)(137,167)(138,166)(139,198)(140,197)(141,196)(142,195)(143,194)(144,193)(145,192)(146,191)(147,190)(148,189)(149,188)(150,187)(151,186)(152,185)(153,184)(154,183)(155,182)(156,181)(157,180)(158,179)(159,178)(160,177)(161,176)(162,175)(163,174)(164,173)(165,172);;
s2 := ( 1,133)( 2,135)( 3,134)( 4,136)( 5,138)( 6,137)( 7,139)( 8,141)( 9,140)( 10,142)( 11,144)( 12,143)( 13,145)( 14,147)( 15,146)( 16,148)( 17,150)( 18,149)( 19,151)( 20,153)( 21,152)( 22,154)( 23,156)( 24,155)( 25,157)( 26,159)( 27,158)( 28,160)( 29,162)( 30,161)( 31,163)( 32,165)( 33,164)( 34,100)( 35,102)( 36,101)( 37,103)( 38,105)( 39,104)( 40,106)( 41,108)( 42,107)( 43,109)( 44,111)( 45,110)( 46,112)( 47,114)( 48,113)( 49,115)( 50,117)( 51,116)( 52,118)( 53,120)( 54,119)( 55,121)( 56,123)( 57,122)( 58,124)( 59,126)( 60,125)( 61,127)( 62,129)( 63,128)( 64,130)( 65,132)( 66,131)( 67,168)( 68,167)( 69,166)( 70,171)( 71,170)( 72,169)( 73,174)( 74,173)( 75,172)( 76,177)( 77,176)( 78,175)( 79,180)( 80,179)( 81,178)( 82,183)( 83,182)( 84,181)( 85,186)( 86,185)( 87,184)( 88,189)( 89,188)( 90,187)( 91,192)( 92,191)( 93,190)( 94,195)( 95,194)( 96,193)( 97,198)( 98,197)( 99,196);;
s3 := (199,200);;
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, s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1, 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,
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(200)!( 4, 31)( 5, 32)( 6, 33)( 7, 28)( 8, 29)( 9, 30)( 10, 25)( 11, 26)( 12, 27)( 13, 22)( 14, 23)( 15, 24)( 16, 19)( 17, 20)( 18, 21)( 37, 64)( 38, 65)( 39, 66)( 40, 61)( 41, 62)( 42, 63)( 43, 58)( 44, 59)( 45, 60)( 46, 55)( 47, 56)( 48, 57)( 49, 52)( 50, 53)( 51, 54)( 70, 97)( 71, 98)( 72, 99)( 73, 94)( 74, 95)( 75, 96)( 76, 91)( 77, 92)( 78, 93)( 79, 88)( 80, 89)( 81, 90)( 82, 85)( 83, 86)( 84, 87)(103,130)(104,131)(105,132)(106,127)(107,128)(108,129)(109,124)(110,125)(111,126)(112,121)(113,122)(114,123)(115,118)(116,119)(117,120)(136,163)(137,164)(138,165)(139,160)(140,161)(141,162)(142,157)(143,158)(144,159)(145,154)(146,155)(147,156)(148,151)(149,152)(150,153)(169,196)(170,197)(171,198)(172,193)(173,194)(174,195)(175,190)(176,191)(177,192)(178,187)(179,188)(180,189)(181,184)(182,185)(183,186);
s1 := Sym(200)!( 1, 4)( 2, 6)( 3, 5)( 7, 31)( 8, 33)( 9, 32)( 10, 28)( 11, 30)( 12, 29)( 13, 25)( 14, 27)( 15, 26)( 16, 22)( 17, 24)( 18, 23)( 20, 21)( 34, 72)( 35, 71)( 36, 70)( 37, 69)( 38, 68)( 39, 67)( 40, 99)( 41, 98)( 42, 97)( 43, 96)( 44, 95)( 45, 94)( 46, 93)( 47, 92)( 48, 91)( 49, 90)( 50, 89)( 51, 88)( 52, 87)( 53, 86)( 54, 85)( 55, 84)( 56, 83)( 57, 82)( 58, 81)( 59, 80)( 60, 79)( 61, 78)( 62, 77)( 63, 76)( 64, 75)( 65, 74)( 66, 73)(100,103)(101,105)(102,104)(106,130)(107,132)(108,131)(109,127)(110,129)(111,128)(112,124)(113,126)(114,125)(115,121)(116,123)(117,122)(119,120)(133,171)(134,170)(135,169)(136,168)(137,167)(138,166)(139,198)(140,197)(141,196)(142,195)(143,194)(144,193)(145,192)(146,191)(147,190)(148,189)(149,188)(150,187)(151,186)(152,185)(153,184)(154,183)(155,182)(156,181)(157,180)(158,179)(159,178)(160,177)(161,176)(162,175)(163,174)(164,173)(165,172);
s2 := Sym(200)!( 1,133)( 2,135)( 3,134)( 4,136)( 5,138)( 6,137)( 7,139)( 8,141)( 9,140)( 10,142)( 11,144)( 12,143)( 13,145)( 14,147)( 15,146)( 16,148)( 17,150)( 18,149)( 19,151)( 20,153)( 21,152)( 22,154)( 23,156)( 24,155)( 25,157)( 26,159)( 27,158)( 28,160)( 29,162)( 30,161)( 31,163)( 32,165)( 33,164)( 34,100)( 35,102)( 36,101)( 37,103)( 38,105)( 39,104)( 40,106)( 41,108)( 42,107)( 43,109)( 44,111)( 45,110)( 46,112)( 47,114)( 48,113)( 49,115)( 50,117)( 51,116)( 52,118)( 53,120)( 54,119)( 55,121)( 56,123)( 57,122)( 58,124)( 59,126)( 60,125)( 61,127)( 62,129)( 63,128)( 64,130)( 65,132)( 66,131)( 67,168)( 68,167)( 69,166)( 70,171)( 71,170)( 72,169)( 73,174)( 74,173)( 75,172)( 76,177)( 77,176)( 78,175)( 79,180)( 80,179)( 81,178)( 82,183)( 83,182)( 84,181)( 85,186)( 86,185)( 87,184)( 88,189)( 89,188)( 90,187)( 91,192)( 92,191)( 93,190)( 94,195)( 95,194)( 96,193)( 97,198)( 98,197)( 99,196);
s3 := Sym(200)!(199,200);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1,
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,
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 >;
to this polytope