Polytope of Type {402}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {402}*804
Also Known As : 402-gon, {402}. if this polytope has another name.
Group : SmallGroup(804,14)
Rank : 2
Schlafli Type : {402}
Number of vertices, edges, etc : 402, 402
Order of s0s1 : 402
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{402,2} of size 1608
Vertex Figure Of :
{2,402} of size 1608
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {201}*402
3-fold quotients : {134}*268
6-fold quotients : {67}*134
67-fold quotients : {6}*12
134-fold quotients : {3}*6
201-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {804}*1608
Permutation Representation (GAP) :
s0 := ( 2, 67)( 3, 66)( 4, 65)( 5, 64)( 6, 63)( 7, 62)( 8, 61)( 9, 60)
( 10, 59)( 11, 58)( 12, 57)( 13, 56)( 14, 55)( 15, 54)( 16, 53)( 17, 52)
( 18, 51)( 19, 50)( 20, 49)( 21, 48)( 22, 47)( 23, 46)( 24, 45)( 25, 44)
( 26, 43)( 27, 42)( 28, 41)( 29, 40)( 30, 39)( 31, 38)( 32, 37)( 33, 36)
( 34, 35)( 68,135)( 69,201)( 70,200)( 71,199)( 72,198)( 73,197)( 74,196)
( 75,195)( 76,194)( 77,193)( 78,192)( 79,191)( 80,190)( 81,189)( 82,188)
( 83,187)( 84,186)( 85,185)( 86,184)( 87,183)( 88,182)( 89,181)( 90,180)
( 91,179)( 92,178)( 93,177)( 94,176)( 95,175)( 96,174)( 97,173)( 98,172)
( 99,171)(100,170)(101,169)(102,168)(103,167)(104,166)(105,165)(106,164)
(107,163)(108,162)(109,161)(110,160)(111,159)(112,158)(113,157)(114,156)
(115,155)(116,154)(117,153)(118,152)(119,151)(120,150)(121,149)(122,148)
(123,147)(124,146)(125,145)(126,144)(127,143)(128,142)(129,141)(130,140)
(131,139)(132,138)(133,137)(134,136)(203,268)(204,267)(205,266)(206,265)
(207,264)(208,263)(209,262)(210,261)(211,260)(212,259)(213,258)(214,257)
(215,256)(216,255)(217,254)(218,253)(219,252)(220,251)(221,250)(222,249)
(223,248)(224,247)(225,246)(226,245)(227,244)(228,243)(229,242)(230,241)
(231,240)(232,239)(233,238)(234,237)(235,236)(269,336)(270,402)(271,401)
(272,400)(273,399)(274,398)(275,397)(276,396)(277,395)(278,394)(279,393)
(280,392)(281,391)(282,390)(283,389)(284,388)(285,387)(286,386)(287,385)
(288,384)(289,383)(290,382)(291,381)(292,380)(293,379)(294,378)(295,377)
(296,376)(297,375)(298,374)(299,373)(300,372)(301,371)(302,370)(303,369)
(304,368)(305,367)(306,366)(307,365)(308,364)(309,363)(310,362)(311,361)
(312,360)(313,359)(314,358)(315,357)(316,356)(317,355)(318,354)(319,353)
(320,352)(321,351)(322,350)(323,349)(324,348)(325,347)(326,346)(327,345)
(328,344)(329,343)(330,342)(331,341)(332,340)(333,339)(334,338)(335,337);;
s1 := ( 1,270)( 2,269)( 3,335)( 4,334)( 5,333)( 6,332)( 7,331)( 8,330)
( 9,329)( 10,328)( 11,327)( 12,326)( 13,325)( 14,324)( 15,323)( 16,322)
( 17,321)( 18,320)( 19,319)( 20,318)( 21,317)( 22,316)( 23,315)( 24,314)
( 25,313)( 26,312)( 27,311)( 28,310)( 29,309)( 30,308)( 31,307)( 32,306)
( 33,305)( 34,304)( 35,303)( 36,302)( 37,301)( 38,300)( 39,299)( 40,298)
( 41,297)( 42,296)( 43,295)( 44,294)( 45,293)( 46,292)( 47,291)( 48,290)
( 49,289)( 50,288)( 51,287)( 52,286)( 53,285)( 54,284)( 55,283)( 56,282)
( 57,281)( 58,280)( 59,279)( 60,278)( 61,277)( 62,276)( 63,275)( 64,274)
( 65,273)( 66,272)( 67,271)( 68,203)( 69,202)( 70,268)( 71,267)( 72,266)
( 73,265)( 74,264)( 75,263)( 76,262)( 77,261)( 78,260)( 79,259)( 80,258)
( 81,257)( 82,256)( 83,255)( 84,254)( 85,253)( 86,252)( 87,251)( 88,250)
( 89,249)( 90,248)( 91,247)( 92,246)( 93,245)( 94,244)( 95,243)( 96,242)
( 97,241)( 98,240)( 99,239)(100,238)(101,237)(102,236)(103,235)(104,234)
(105,233)(106,232)(107,231)(108,230)(109,229)(110,228)(111,227)(112,226)
(113,225)(114,224)(115,223)(116,222)(117,221)(118,220)(119,219)(120,218)
(121,217)(122,216)(123,215)(124,214)(125,213)(126,212)(127,211)(128,210)
(129,209)(130,208)(131,207)(132,206)(133,205)(134,204)(135,337)(136,336)
(137,402)(138,401)(139,400)(140,399)(141,398)(142,397)(143,396)(144,395)
(145,394)(146,393)(147,392)(148,391)(149,390)(150,389)(151,388)(152,387)
(153,386)(154,385)(155,384)(156,383)(157,382)(158,381)(159,380)(160,379)
(161,378)(162,377)(163,376)(164,375)(165,374)(166,373)(167,372)(168,371)
(169,370)(170,369)(171,368)(172,367)(173,366)(174,365)(175,364)(176,363)
(177,362)(178,361)(179,360)(180,359)(181,358)(182,357)(183,356)(184,355)
(185,354)(186,353)(187,352)(188,351)(189,350)(190,349)(191,348)(192,347)
(193,346)(194,345)(195,344)(196,343)(197,342)(198,341)(199,340)(200,339)
(201,338);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(402)!( 2, 67)( 3, 66)( 4, 65)( 5, 64)( 6, 63)( 7, 62)( 8, 61)
( 9, 60)( 10, 59)( 11, 58)( 12, 57)( 13, 56)( 14, 55)( 15, 54)( 16, 53)
( 17, 52)( 18, 51)( 19, 50)( 20, 49)( 21, 48)( 22, 47)( 23, 46)( 24, 45)
( 25, 44)( 26, 43)( 27, 42)( 28, 41)( 29, 40)( 30, 39)( 31, 38)( 32, 37)
( 33, 36)( 34, 35)( 68,135)( 69,201)( 70,200)( 71,199)( 72,198)( 73,197)
( 74,196)( 75,195)( 76,194)( 77,193)( 78,192)( 79,191)( 80,190)( 81,189)
( 82,188)( 83,187)( 84,186)( 85,185)( 86,184)( 87,183)( 88,182)( 89,181)
( 90,180)( 91,179)( 92,178)( 93,177)( 94,176)( 95,175)( 96,174)( 97,173)
( 98,172)( 99,171)(100,170)(101,169)(102,168)(103,167)(104,166)(105,165)
(106,164)(107,163)(108,162)(109,161)(110,160)(111,159)(112,158)(113,157)
(114,156)(115,155)(116,154)(117,153)(118,152)(119,151)(120,150)(121,149)
(122,148)(123,147)(124,146)(125,145)(126,144)(127,143)(128,142)(129,141)
(130,140)(131,139)(132,138)(133,137)(134,136)(203,268)(204,267)(205,266)
(206,265)(207,264)(208,263)(209,262)(210,261)(211,260)(212,259)(213,258)
(214,257)(215,256)(216,255)(217,254)(218,253)(219,252)(220,251)(221,250)
(222,249)(223,248)(224,247)(225,246)(226,245)(227,244)(228,243)(229,242)
(230,241)(231,240)(232,239)(233,238)(234,237)(235,236)(269,336)(270,402)
(271,401)(272,400)(273,399)(274,398)(275,397)(276,396)(277,395)(278,394)
(279,393)(280,392)(281,391)(282,390)(283,389)(284,388)(285,387)(286,386)
(287,385)(288,384)(289,383)(290,382)(291,381)(292,380)(293,379)(294,378)
(295,377)(296,376)(297,375)(298,374)(299,373)(300,372)(301,371)(302,370)
(303,369)(304,368)(305,367)(306,366)(307,365)(308,364)(309,363)(310,362)
(311,361)(312,360)(313,359)(314,358)(315,357)(316,356)(317,355)(318,354)
(319,353)(320,352)(321,351)(322,350)(323,349)(324,348)(325,347)(326,346)
(327,345)(328,344)(329,343)(330,342)(331,341)(332,340)(333,339)(334,338)
(335,337);
s1 := Sym(402)!( 1,270)( 2,269)( 3,335)( 4,334)( 5,333)( 6,332)( 7,331)
( 8,330)( 9,329)( 10,328)( 11,327)( 12,326)( 13,325)( 14,324)( 15,323)
( 16,322)( 17,321)( 18,320)( 19,319)( 20,318)( 21,317)( 22,316)( 23,315)
( 24,314)( 25,313)( 26,312)( 27,311)( 28,310)( 29,309)( 30,308)( 31,307)
( 32,306)( 33,305)( 34,304)( 35,303)( 36,302)( 37,301)( 38,300)( 39,299)
( 40,298)( 41,297)( 42,296)( 43,295)( 44,294)( 45,293)( 46,292)( 47,291)
( 48,290)( 49,289)( 50,288)( 51,287)( 52,286)( 53,285)( 54,284)( 55,283)
( 56,282)( 57,281)( 58,280)( 59,279)( 60,278)( 61,277)( 62,276)( 63,275)
( 64,274)( 65,273)( 66,272)( 67,271)( 68,203)( 69,202)( 70,268)( 71,267)
( 72,266)( 73,265)( 74,264)( 75,263)( 76,262)( 77,261)( 78,260)( 79,259)
( 80,258)( 81,257)( 82,256)( 83,255)( 84,254)( 85,253)( 86,252)( 87,251)
( 88,250)( 89,249)( 90,248)( 91,247)( 92,246)( 93,245)( 94,244)( 95,243)
( 96,242)( 97,241)( 98,240)( 99,239)(100,238)(101,237)(102,236)(103,235)
(104,234)(105,233)(106,232)(107,231)(108,230)(109,229)(110,228)(111,227)
(112,226)(113,225)(114,224)(115,223)(116,222)(117,221)(118,220)(119,219)
(120,218)(121,217)(122,216)(123,215)(124,214)(125,213)(126,212)(127,211)
(128,210)(129,209)(130,208)(131,207)(132,206)(133,205)(134,204)(135,337)
(136,336)(137,402)(138,401)(139,400)(140,399)(141,398)(142,397)(143,396)
(144,395)(145,394)(146,393)(147,392)(148,391)(149,390)(150,389)(151,388)
(152,387)(153,386)(154,385)(155,384)(156,383)(157,382)(158,381)(159,380)
(160,379)(161,378)(162,377)(163,376)(164,375)(165,374)(166,373)(167,372)
(168,371)(169,370)(170,369)(171,368)(172,367)(173,366)(174,365)(175,364)
(176,363)(177,362)(178,361)(179,360)(180,359)(181,358)(182,357)(183,356)
(184,355)(185,354)(186,353)(187,352)(188,351)(189,350)(190,349)(191,348)
(192,347)(193,346)(194,345)(195,344)(196,343)(197,342)(198,341)(199,340)
(200,339)(201,338);
poly := sub<Sym(402)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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