Polytope of Type {202}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {202}*404
Also Known As : 202-gon, {202}. if this polytope has another name.
Group : SmallGroup(404,4)
Rank : 2
Schlafli Type : {202}
Number of vertices, edges, etc : 202, 202
Order of s0s1 : 202
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{202,2} of size 808
{202,4} of size 1616
Vertex Figure Of :
{2,202} of size 808
{4,202} of size 1616
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {101}*202
101-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {404}*808
3-fold covers : {606}*1212
4-fold covers : {808}*1616
Permutation Representation (GAP) :
s0 := ( 2,101)( 3,100)( 4, 99)( 5, 98)( 6, 97)( 7, 96)( 8, 95)( 9, 94)
( 10, 93)( 11, 92)( 12, 91)( 13, 90)( 14, 89)( 15, 88)( 16, 87)( 17, 86)
( 18, 85)( 19, 84)( 20, 83)( 21, 82)( 22, 81)( 23, 80)( 24, 79)( 25, 78)
( 26, 77)( 27, 76)( 28, 75)( 29, 74)( 30, 73)( 31, 72)( 32, 71)( 33, 70)
( 34, 69)( 35, 68)( 36, 67)( 37, 66)( 38, 65)( 39, 64)( 40, 63)( 41, 62)
( 42, 61)( 43, 60)( 44, 59)( 45, 58)( 46, 57)( 47, 56)( 48, 55)( 49, 54)
( 50, 53)( 51, 52)(103,202)(104,201)(105,200)(106,199)(107,198)(108,197)
(109,196)(110,195)(111,194)(112,193)(113,192)(114,191)(115,190)(116,189)
(117,188)(118,187)(119,186)(120,185)(121,184)(122,183)(123,182)(124,181)
(125,180)(126,179)(127,178)(128,177)(129,176)(130,175)(131,174)(132,173)
(133,172)(134,171)(135,170)(136,169)(137,168)(138,167)(139,166)(140,165)
(141,164)(142,163)(143,162)(144,161)(145,160)(146,159)(147,158)(148,157)
(149,156)(150,155)(151,154)(152,153);;
s1 := ( 1,103)( 2,102)( 3,202)( 4,201)( 5,200)( 6,199)( 7,198)( 8,197)
( 9,196)( 10,195)( 11,194)( 12,193)( 13,192)( 14,191)( 15,190)( 16,189)
( 17,188)( 18,187)( 19,186)( 20,185)( 21,184)( 22,183)( 23,182)( 24,181)
( 25,180)( 26,179)( 27,178)( 28,177)( 29,176)( 30,175)( 31,174)( 32,173)
( 33,172)( 34,171)( 35,170)( 36,169)( 37,168)( 38,167)( 39,166)( 40,165)
( 41,164)( 42,163)( 43,162)( 44,161)( 45,160)( 46,159)( 47,158)( 48,157)
( 49,156)( 50,155)( 51,154)( 52,153)( 53,152)( 54,151)( 55,150)( 56,149)
( 57,148)( 58,147)( 59,146)( 60,145)( 61,144)( 62,143)( 63,142)( 64,141)
( 65,140)( 66,139)( 67,138)( 68,137)( 69,136)( 70,135)( 71,134)( 72,133)
( 73,132)( 74,131)( 75,130)( 76,129)( 77,128)( 78,127)( 79,126)( 80,125)
( 81,124)( 82,123)( 83,122)( 84,121)( 85,120)( 86,119)( 87,118)( 88,117)
( 89,116)( 90,115)( 91,114)( 92,113)( 93,112)( 94,111)( 95,110)( 96,109)
( 97,108)( 98,107)( 99,106)(100,105)(101,104);;
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*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(202)!( 2,101)( 3,100)( 4, 99)( 5, 98)( 6, 97)( 7, 96)( 8, 95)
( 9, 94)( 10, 93)( 11, 92)( 12, 91)( 13, 90)( 14, 89)( 15, 88)( 16, 87)
( 17, 86)( 18, 85)( 19, 84)( 20, 83)( 21, 82)( 22, 81)( 23, 80)( 24, 79)
( 25, 78)( 26, 77)( 27, 76)( 28, 75)( 29, 74)( 30, 73)( 31, 72)( 32, 71)
( 33, 70)( 34, 69)( 35, 68)( 36, 67)( 37, 66)( 38, 65)( 39, 64)( 40, 63)
( 41, 62)( 42, 61)( 43, 60)( 44, 59)( 45, 58)( 46, 57)( 47, 56)( 48, 55)
( 49, 54)( 50, 53)( 51, 52)(103,202)(104,201)(105,200)(106,199)(107,198)
(108,197)(109,196)(110,195)(111,194)(112,193)(113,192)(114,191)(115,190)
(116,189)(117,188)(118,187)(119,186)(120,185)(121,184)(122,183)(123,182)
(124,181)(125,180)(126,179)(127,178)(128,177)(129,176)(130,175)(131,174)
(132,173)(133,172)(134,171)(135,170)(136,169)(137,168)(138,167)(139,166)
(140,165)(141,164)(142,163)(143,162)(144,161)(145,160)(146,159)(147,158)
(148,157)(149,156)(150,155)(151,154)(152,153);
s1 := Sym(202)!( 1,103)( 2,102)( 3,202)( 4,201)( 5,200)( 6,199)( 7,198)
( 8,197)( 9,196)( 10,195)( 11,194)( 12,193)( 13,192)( 14,191)( 15,190)
( 16,189)( 17,188)( 18,187)( 19,186)( 20,185)( 21,184)( 22,183)( 23,182)
( 24,181)( 25,180)( 26,179)( 27,178)( 28,177)( 29,176)( 30,175)( 31,174)
( 32,173)( 33,172)( 34,171)( 35,170)( 36,169)( 37,168)( 38,167)( 39,166)
( 40,165)( 41,164)( 42,163)( 43,162)( 44,161)( 45,160)( 46,159)( 47,158)
( 48,157)( 49,156)( 50,155)( 51,154)( 52,153)( 53,152)( 54,151)( 55,150)
( 56,149)( 57,148)( 58,147)( 59,146)( 60,145)( 61,144)( 62,143)( 63,142)
( 64,141)( 65,140)( 66,139)( 67,138)( 68,137)( 69,136)( 70,135)( 71,134)
( 72,133)( 73,132)( 74,131)( 75,130)( 76,129)( 77,128)( 78,127)( 79,126)
( 80,125)( 81,124)( 82,123)( 83,122)( 84,121)( 85,120)( 86,119)( 87,118)
( 88,117)( 89,116)( 90,115)( 91,114)( 92,113)( 93,112)( 94,111)( 95,110)
( 96,109)( 97,108)( 98,107)( 99,106)(100,105)(101,104);
poly := sub<Sym(202)|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*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
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