Polytope of Type {642}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {642}*1284
Also Known As : 642-gon, {642}. if this polytope has another name.
Group : SmallGroup(1284,9)
Rank : 2
Schlafli Type : {642}
Number of vertices, edges, etc : 642, 642
Order of s0s1 : 642
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {321}*642
3-fold quotients : {214}*428
6-fold quotients : {107}*214
107-fold quotients : {6}*12
214-fold quotients : {3}*6
321-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
None in this atlas.
Irregular Quotients (of which this is a minimal cover):
None.
Permutation Representation (GAP) :
s0 := ( 2,107)( 3,106)( 4,105)( 5,104)( 6,103)( 7,102)( 8,101)( 9,100)( 10, 99)( 11, 98)( 12, 97)( 13, 96)( 14, 95)( 15, 94)( 16, 93)( 17, 92)( 18, 91)( 19, 90)( 20, 89)( 21, 88)( 22, 87)( 23, 86)( 24, 85)( 25, 84)( 26, 83)( 27, 82)( 28, 81)( 29, 80)( 30, 79)( 31, 78)( 32, 77)( 33, 76)( 34, 75)( 35, 74)( 36, 73)( 37, 72)( 38, 71)( 39, 70)( 40, 69)( 41, 68)( 42, 67)( 43, 66)( 44, 65)( 45, 64)( 46, 63)( 47, 62)( 48, 61)( 49, 60)( 50, 59)( 51, 58)( 52, 57)( 53, 56)( 54, 55)(108,215)(109,321)(110,320)(111,319)(112,318)(113,317)(114,316)(115,315)(116,314)(117,313)(118,312)(119,311)(120,310)(121,309)(122,308)(123,307)(124,306)(125,305)(126,304)(127,303)(128,302)(129,301)(130,300)(131,299)(132,298)(133,297)(134,296)(135,295)(136,294)(137,293)(138,292)(139,291)(140,290)(141,289)(142,288)(143,287)(144,286)(145,285)(146,284)(147,283)(148,282)(149,281)(150,280)(151,279)(152,278)(153,277)(154,276)(155,275)(156,274)(157,273)(158,272)(159,271)(160,270)(161,269)(162,268)(163,267)(164,266)(165,265)(166,264)(167,263)(168,262)(169,261)(170,260)(171,259)(172,258)(173,257)(174,256)(175,255)(176,254)(177,253)(178,252)(179,251)(180,250)(181,249)(182,248)(183,247)(184,246)(185,245)(186,244)(187,243)(188,242)(189,241)(190,240)(191,239)(192,238)(193,237)(194,236)(195,235)(196,234)(197,233)(198,232)(199,231)(200,230)(201,229)(202,228)(203,227)(204,226)(205,225)(206,224)(207,223)(208,222)(209,221)(210,220)(211,219)(212,218)(213,217)(214,216)(323,428)(324,427)(325,426)(326,425)(327,424)(328,423)(329,422)(330,421)(331,420)(332,419)(333,418)(334,417)(335,416)(336,415)(337,414)(338,413)(339,412)(340,411)(341,410)(342,409)(343,408)(344,407)(345,406)(346,405)(347,404)(348,403)(349,402)(350,401)(351,400)(352,399)(353,398)(354,397)(355,396)(356,395)(357,394)(358,393)(359,392)(360,391)(361,390)(362,389)(363,388)(364,387)(365,386)(366,385)(367,384)(368,383)(369,382)(370,381)(371,380)(372,379)(373,378)(374,377)(375,376)(429,536)(430,642)(431,641)(432,640)(433,639)(434,638)(435,637)(436,636)(437,635)(438,634)(439,633)(440,632)(441,631)(442,630)(443,629)(444,628)(445,627)(446,626)(447,625)(448,624)(449,623)(450,622)(451,621)(452,620)(453,619)(454,618)(455,617)(456,616)(457,615)(458,614)(459,613)(460,612)(461,611)(462,610)(463,609)(464,608)(465,607)(466,606)(467,605)(468,604)(469,603)(470,602)(471,601)(472,600)(473,599)(474,598)(475,597)(476,596)(477,595)(478,594)(479,593)(480,592)(481,591)(482,590)(483,589)(484,588)(485,587)(486,586)(487,585)(488,584)(489,583)(490,582)(491,581)(492,580)(493,579)(494,578)(495,577)(496,576)(497,575)(498,574)(499,573)(500,572)(501,571)(502,570)(503,569)(504,568)(505,567)(506,566)(507,565)(508,564)(509,563)(510,562)(511,561)(512,560)(513,559)(514,558)(515,557)(516,556)(517,555)(518,554)(519,553)(520,552)(521,551)(522,550)(523,549)(524,548)(525,547)(526,546)(527,545)(528,544)(529,543)(530,542)(531,541)(532,540)(533,539)(534,538)(535,537);;
s1 := ( 1,430)( 2,429)( 3,535)( 4,534)( 5,533)( 6,532)( 7,531)( 8,530)( 9,529)( 10,528)( 11,527)( 12,526)( 13,525)( 14,524)( 15,523)( 16,522)( 17,521)( 18,520)( 19,519)( 20,518)( 21,517)( 22,516)( 23,515)( 24,514)( 25,513)( 26,512)( 27,511)( 28,510)( 29,509)( 30,508)( 31,507)( 32,506)( 33,505)( 34,504)( 35,503)( 36,502)( 37,501)( 38,500)( 39,499)( 40,498)( 41,497)( 42,496)( 43,495)( 44,494)( 45,493)( 46,492)( 47,491)( 48,490)( 49,489)( 50,488)( 51,487)( 52,486)( 53,485)( 54,484)( 55,483)( 56,482)( 57,481)( 58,480)( 59,479)( 60,478)( 61,477)( 62,476)( 63,475)( 64,474)( 65,473)( 66,472)( 67,471)( 68,470)( 69,469)( 70,468)( 71,467)( 72,466)( 73,465)( 74,464)( 75,463)( 76,462)( 77,461)( 78,460)( 79,459)( 80,458)( 81,457)( 82,456)( 83,455)( 84,454)( 85,453)( 86,452)( 87,451)( 88,450)( 89,449)( 90,448)( 91,447)( 92,446)( 93,445)( 94,444)( 95,443)( 96,442)( 97,441)( 98,440)( 99,439)(100,438)(101,437)(102,436)(103,435)(104,434)(105,433)(106,432)(107,431)(108,323)(109,322)(110,428)(111,427)(112,426)(113,425)(114,424)(115,423)(116,422)(117,421)(118,420)(119,419)(120,418)(121,417)(122,416)(123,415)(124,414)(125,413)(126,412)(127,411)(128,410)(129,409)(130,408)(131,407)(132,406)(133,405)(134,404)(135,403)(136,402)(137,401)(138,400)(139,399)(140,398)(141,397)(142,396)(143,395)(144,394)(145,393)(146,392)(147,391)(148,390)(149,389)(150,388)(151,387)(152,386)(153,385)(154,384)(155,383)(156,382)(157,381)(158,380)(159,379)(160,378)(161,377)(162,376)(163,375)(164,374)(165,373)(166,372)(167,371)(168,370)(169,369)(170,368)(171,367)(172,366)(173,365)(174,364)(175,363)(176,362)(177,361)(178,360)(179,359)(180,358)(181,357)(182,356)(183,355)(184,354)(185,353)(186,352)(187,351)(188,350)(189,349)(190,348)(191,347)(192,346)(193,345)(194,344)(195,343)(196,342)(197,341)(198,340)(199,339)(200,338)(201,337)(202,336)(203,335)(204,334)(205,333)(206,332)(207,331)(208,330)(209,329)(210,328)(211,327)(212,326)(213,325)(214,324)(215,537)(216,536)(217,642)(218,641)(219,640)(220,639)(221,638)(222,637)(223,636)(224,635)(225,634)(226,633)(227,632)(228,631)(229,630)(230,629)(231,628)(232,627)(233,626)(234,625)(235,624)(236,623)(237,622)(238,621)(239,620)(240,619)(241,618)(242,617)(243,616)(244,615)(245,614)(246,613)(247,612)(248,611)(249,610)(250,609)(251,608)(252,607)(253,606)(254,605)(255,604)(256,603)(257,602)(258,601)(259,600)(260,599)(261,598)(262,597)(263,596)(264,595)(265,594)(266,593)(267,592)(268,591)(269,590)(270,589)(271,588)(272,587)(273,586)(274,585)(275,584)(276,583)(277,582)(278,581)(279,580)(280,579)(281,578)(282,577)(283,576)(284,575)(285,574)(286,573)(287,572)(288,571)(289,570)(290,569)(291,568)(292,567)(293,566)(294,565)(295,564)(296,563)(297,562)(298,561)(299,560)(300,559)(301,558)(302,557)(303,556)(304,555)(305,554)(306,553)(307,552)(308,551)(309,550)(310,549)(311,548)(312,547)(313,546)(314,545)(315,544)(316,543)(317,542)(318,541)(319,540)(320,539)(321,538);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(642)!( 2,107)( 3,106)( 4,105)( 5,104)( 6,103)( 7,102)( 8,101)( 9,100)( 10, 99)( 11, 98)( 12, 97)( 13, 96)( 14, 95)( 15, 94)( 16, 93)( 17, 92)( 18, 91)( 19, 90)( 20, 89)( 21, 88)( 22, 87)( 23, 86)( 24, 85)( 25, 84)( 26, 83)( 27, 82)( 28, 81)( 29, 80)( 30, 79)( 31, 78)( 32, 77)( 33, 76)( 34, 75)( 35, 74)( 36, 73)( 37, 72)( 38, 71)( 39, 70)( 40, 69)( 41, 68)( 42, 67)( 43, 66)( 44, 65)( 45, 64)( 46, 63)( 47, 62)( 48, 61)( 49, 60)( 50, 59)( 51, 58)( 52, 57)( 53, 56)( 54, 55)(108,215)(109,321)(110,320)(111,319)(112,318)(113,317)(114,316)(115,315)(116,314)(117,313)(118,312)(119,311)(120,310)(121,309)(122,308)(123,307)(124,306)(125,305)(126,304)(127,303)(128,302)(129,301)(130,300)(131,299)(132,298)(133,297)(134,296)(135,295)(136,294)(137,293)(138,292)(139,291)(140,290)(141,289)(142,288)(143,287)(144,286)(145,285)(146,284)(147,283)(148,282)(149,281)(150,280)(151,279)(152,278)(153,277)(154,276)(155,275)(156,274)(157,273)(158,272)(159,271)(160,270)(161,269)(162,268)(163,267)(164,266)(165,265)(166,264)(167,263)(168,262)(169,261)(170,260)(171,259)(172,258)(173,257)(174,256)(175,255)(176,254)(177,253)(178,252)(179,251)(180,250)(181,249)(182,248)(183,247)(184,246)(185,245)(186,244)(187,243)(188,242)(189,241)(190,240)(191,239)(192,238)(193,237)(194,236)(195,235)(196,234)(197,233)(198,232)(199,231)(200,230)(201,229)(202,228)(203,227)(204,226)(205,225)(206,224)(207,223)(208,222)(209,221)(210,220)(211,219)(212,218)(213,217)(214,216)(323,428)(324,427)(325,426)(326,425)(327,424)(328,423)(329,422)(330,421)(331,420)(332,419)(333,418)(334,417)(335,416)(336,415)(337,414)(338,413)(339,412)(340,411)(341,410)(342,409)(343,408)(344,407)(345,406)(346,405)(347,404)(348,403)(349,402)(350,401)(351,400)(352,399)(353,398)(354,397)(355,396)(356,395)(357,394)(358,393)(359,392)(360,391)(361,390)(362,389)(363,388)(364,387)(365,386)(366,385)(367,384)(368,383)(369,382)(370,381)(371,380)(372,379)(373,378)(374,377)(375,376)(429,536)(430,642)(431,641)(432,640)(433,639)(434,638)(435,637)(436,636)(437,635)(438,634)(439,633)(440,632)(441,631)(442,630)(443,629)(444,628)(445,627)(446,626)(447,625)(448,624)(449,623)(450,622)(451,621)(452,620)(453,619)(454,618)(455,617)(456,616)(457,615)(458,614)(459,613)(460,612)(461,611)(462,610)(463,609)(464,608)(465,607)(466,606)(467,605)(468,604)(469,603)(470,602)(471,601)(472,600)(473,599)(474,598)(475,597)(476,596)(477,595)(478,594)(479,593)(480,592)(481,591)(482,590)(483,589)(484,588)(485,587)(486,586)(487,585)(488,584)(489,583)(490,582)(491,581)(492,580)(493,579)(494,578)(495,577)(496,576)(497,575)(498,574)(499,573)(500,572)(501,571)(502,570)(503,569)(504,568)(505,567)(506,566)(507,565)(508,564)(509,563)(510,562)(511,561)(512,560)(513,559)(514,558)(515,557)(516,556)(517,555)(518,554)(519,553)(520,552)(521,551)(522,550)(523,549)(524,548)(525,547)(526,546)(527,545)(528,544)(529,543)(530,542)(531,541)(532,540)(533,539)(534,538)(535,537);
s1 := Sym(642)!( 1,430)( 2,429)( 3,535)( 4,534)( 5,533)( 6,532)( 7,531)( 8,530)( 9,529)( 10,528)( 11,527)( 12,526)( 13,525)( 14,524)( 15,523)( 16,522)( 17,521)( 18,520)( 19,519)( 20,518)( 21,517)( 22,516)( 23,515)( 24,514)( 25,513)( 26,512)( 27,511)( 28,510)( 29,509)( 30,508)( 31,507)( 32,506)( 33,505)( 34,504)( 35,503)( 36,502)( 37,501)( 38,500)( 39,499)( 40,498)( 41,497)( 42,496)( 43,495)( 44,494)( 45,493)( 46,492)( 47,491)( 48,490)( 49,489)( 50,488)( 51,487)( 52,486)( 53,485)( 54,484)( 55,483)( 56,482)( 57,481)( 58,480)( 59,479)( 60,478)( 61,477)( 62,476)( 63,475)( 64,474)( 65,473)( 66,472)( 67,471)( 68,470)( 69,469)( 70,468)( 71,467)( 72,466)( 73,465)( 74,464)( 75,463)( 76,462)( 77,461)( 78,460)( 79,459)( 80,458)( 81,457)( 82,456)( 83,455)( 84,454)( 85,453)( 86,452)( 87,451)( 88,450)( 89,449)( 90,448)( 91,447)( 92,446)( 93,445)( 94,444)( 95,443)( 96,442)( 97,441)( 98,440)( 99,439)(100,438)(101,437)(102,436)(103,435)(104,434)(105,433)(106,432)(107,431)(108,323)(109,322)(110,428)(111,427)(112,426)(113,425)(114,424)(115,423)(116,422)(117,421)(118,420)(119,419)(120,418)(121,417)(122,416)(123,415)(124,414)(125,413)(126,412)(127,411)(128,410)(129,409)(130,408)(131,407)(132,406)(133,405)(134,404)(135,403)(136,402)(137,401)(138,400)(139,399)(140,398)(141,397)(142,396)(143,395)(144,394)(145,393)(146,392)(147,391)(148,390)(149,389)(150,388)(151,387)(152,386)(153,385)(154,384)(155,383)(156,382)(157,381)(158,380)(159,379)(160,378)(161,377)(162,376)(163,375)(164,374)(165,373)(166,372)(167,371)(168,370)(169,369)(170,368)(171,367)(172,366)(173,365)(174,364)(175,363)(176,362)(177,361)(178,360)(179,359)(180,358)(181,357)(182,356)(183,355)(184,354)(185,353)(186,352)(187,351)(188,350)(189,349)(190,348)(191,347)(192,346)(193,345)(194,344)(195,343)(196,342)(197,341)(198,340)(199,339)(200,338)(201,337)(202,336)(203,335)(204,334)(205,333)(206,332)(207,331)(208,330)(209,329)(210,328)(211,327)(212,326)(213,325)(214,324)(215,537)(216,536)(217,642)(218,641)(219,640)(220,639)(221,638)(222,637)(223,636)(224,635)(225,634)(226,633)(227,632)(228,631)(229,630)(230,629)(231,628)(232,627)(233,626)(234,625)(235,624)(236,623)(237,622)(238,621)(239,620)(240,619)(241,618)(242,617)(243,616)(244,615)(245,614)(246,613)(247,612)(248,611)(249,610)(250,609)(251,608)(252,607)(253,606)(254,605)(255,604)(256,603)(257,602)(258,601)(259,600)(260,599)(261,598)(262,597)(263,596)(264,595)(265,594)(266,593)(267,592)(268,591)(269,590)(270,589)(271,588)(272,587)(273,586)(274,585)(275,584)(276,583)(277,582)(278,581)(279,580)(280,579)(281,578)(282,577)(283,576)(284,575)(285,574)(286,573)(287,572)(288,571)(289,570)(290,569)(291,568)(292,567)(293,566)(294,565)(295,564)(296,563)(297,562)(298,561)(299,560)(300,559)(301,558)(302,557)(303,556)(304,555)(305,554)(306,553)(307,552)(308,551)(309,550)(310,549)(311,548)(312,547)(313,546)(314,545)(315,544)(316,543)(317,542)(318,541)(319,540)(320,539)(321,538);
poly := sub<Sym(642)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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