Polytope of Type {198}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {198}*396
Also Known As : 198-gon, {198}. if this polytope has another name.
Group : SmallGroup(396,9)
Rank : 2
Schlafli Type : {198}
Number of vertices, edges, etc : 198, 198
Order of s0s1 : 198
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{198,2} of size 792
{198,4} of size 1584
{198,4} of size 1584
{198,4} of size 1584
Vertex Figure Of :
{2,198} of size 792
{4,198} of size 1584
{4,198} of size 1584
{4,198} of size 1584
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {99}*198
3-fold quotients : {66}*132
6-fold quotients : {33}*66
9-fold quotients : {22}*44
11-fold quotients : {18}*36
18-fold quotients : {11}*22
22-fold quotients : {9}*18
33-fold quotients : {6}*12
66-fold quotients : {3}*6
99-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {396}*792
3-fold covers : {594}*1188
4-fold covers : {792}*1584
5-fold covers : {990}*1980
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 31)( 5, 33)( 6, 32)( 7, 28)( 8, 30)( 9, 29)( 10, 25)
( 11, 27)( 12, 26)( 13, 22)( 14, 24)( 15, 23)( 16, 19)( 17, 21)( 18, 20)
( 34, 68)( 35, 67)( 36, 69)( 37, 98)( 38, 97)( 39, 99)( 40, 95)( 41, 94)
( 42, 96)( 43, 92)( 44, 91)( 45, 93)( 46, 89)( 47, 88)( 48, 90)( 49, 86)
( 50, 85)( 51, 87)( 52, 83)( 53, 82)( 54, 84)( 55, 80)( 56, 79)( 57, 81)
( 58, 77)( 59, 76)( 60, 78)( 61, 74)( 62, 73)( 63, 75)( 64, 71)( 65, 70)
( 66, 72)(101,102)(103,130)(104,132)(105,131)(106,127)(107,129)(108,128)
(109,124)(110,126)(111,125)(112,121)(113,123)(114,122)(115,118)(116,120)
(117,119)(133,167)(134,166)(135,168)(136,197)(137,196)(138,198)(139,194)
(140,193)(141,195)(142,191)(143,190)(144,192)(145,188)(146,187)(147,189)
(148,185)(149,184)(150,186)(151,182)(152,181)(153,183)(154,179)(155,178)
(156,180)(157,176)(158,175)(159,177)(160,173)(161,172)(162,174)(163,170)
(164,169)(165,171);;
s1 := ( 1,136)( 2,138)( 3,137)( 4,133)( 5,135)( 6,134)( 7,163)( 8,165)
( 9,164)( 10,160)( 11,162)( 12,161)( 13,157)( 14,159)( 15,158)( 16,154)
( 17,156)( 18,155)( 19,151)( 20,153)( 21,152)( 22,148)( 23,150)( 24,149)
( 25,145)( 26,147)( 27,146)( 28,142)( 29,144)( 30,143)( 31,139)( 32,141)
( 33,140)( 34,103)( 35,105)( 36,104)( 37,100)( 38,102)( 39,101)( 40,130)
( 41,132)( 42,131)( 43,127)( 44,129)( 45,128)( 46,124)( 47,126)( 48,125)
( 49,121)( 50,123)( 51,122)( 52,118)( 53,120)( 54,119)( 55,115)( 56,117)
( 57,116)( 58,112)( 59,114)( 60,113)( 61,109)( 62,111)( 63,110)( 64,106)
( 65,108)( 66,107)( 67,170)( 68,169)( 69,171)( 70,167)( 71,166)( 72,168)
( 73,197)( 74,196)( 75,198)( 76,194)( 77,193)( 78,195)( 79,191)( 80,190)
( 81,192)( 82,188)( 83,187)( 84,189)( 85,185)( 86,184)( 87,186)( 88,182)
( 89,181)( 90,183)( 91,179)( 92,178)( 93,180)( 94,176)( 95,175)( 96,177)
( 97,173)( 98,172)( 99,174);;
poly := Group([s0,s1]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;; s1 := F.2;;
rels := [ s0*s0, s1*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*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*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*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*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*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*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*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*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*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(198)!( 2, 3)( 4, 31)( 5, 33)( 6, 32)( 7, 28)( 8, 30)( 9, 29)
( 10, 25)( 11, 27)( 12, 26)( 13, 22)( 14, 24)( 15, 23)( 16, 19)( 17, 21)
( 18, 20)( 34, 68)( 35, 67)( 36, 69)( 37, 98)( 38, 97)( 39, 99)( 40, 95)
( 41, 94)( 42, 96)( 43, 92)( 44, 91)( 45, 93)( 46, 89)( 47, 88)( 48, 90)
( 49, 86)( 50, 85)( 51, 87)( 52, 83)( 53, 82)( 54, 84)( 55, 80)( 56, 79)
( 57, 81)( 58, 77)( 59, 76)( 60, 78)( 61, 74)( 62, 73)( 63, 75)( 64, 71)
( 65, 70)( 66, 72)(101,102)(103,130)(104,132)(105,131)(106,127)(107,129)
(108,128)(109,124)(110,126)(111,125)(112,121)(113,123)(114,122)(115,118)
(116,120)(117,119)(133,167)(134,166)(135,168)(136,197)(137,196)(138,198)
(139,194)(140,193)(141,195)(142,191)(143,190)(144,192)(145,188)(146,187)
(147,189)(148,185)(149,184)(150,186)(151,182)(152,181)(153,183)(154,179)
(155,178)(156,180)(157,176)(158,175)(159,177)(160,173)(161,172)(162,174)
(163,170)(164,169)(165,171);
s1 := Sym(198)!( 1,136)( 2,138)( 3,137)( 4,133)( 5,135)( 6,134)( 7,163)
( 8,165)( 9,164)( 10,160)( 11,162)( 12,161)( 13,157)( 14,159)( 15,158)
( 16,154)( 17,156)( 18,155)( 19,151)( 20,153)( 21,152)( 22,148)( 23,150)
( 24,149)( 25,145)( 26,147)( 27,146)( 28,142)( 29,144)( 30,143)( 31,139)
( 32,141)( 33,140)( 34,103)( 35,105)( 36,104)( 37,100)( 38,102)( 39,101)
( 40,130)( 41,132)( 42,131)( 43,127)( 44,129)( 45,128)( 46,124)( 47,126)
( 48,125)( 49,121)( 50,123)( 51,122)( 52,118)( 53,120)( 54,119)( 55,115)
( 56,117)( 57,116)( 58,112)( 59,114)( 60,113)( 61,109)( 62,111)( 63,110)
( 64,106)( 65,108)( 66,107)( 67,170)( 68,169)( 69,171)( 70,167)( 71,166)
( 72,168)( 73,197)( 74,196)( 75,198)( 76,194)( 77,193)( 78,195)( 79,191)
( 80,190)( 81,192)( 82,188)( 83,187)( 84,189)( 85,185)( 86,184)( 87,186)
( 88,182)( 89,181)( 90,183)( 91,179)( 92,178)( 93,180)( 94,176)( 95,175)
( 96,177)( 97,173)( 98,172)( 99,174);
poly := sub<Sym(198)|s0,s1>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*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*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*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*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*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*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*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*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*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*s0*s1 >;
References : None.
to this polytope