Polytope of Type {710}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {710}*1420
Also Known As : 710-gon, {710}. if this polytope has another name.
Group : SmallGroup(1420,14)
Rank : 2
Schlafli Type : {710}
Number of vertices, edges, etc : 710, 710
Order of s0s1 : 710
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 : {355}*710
5-fold quotients : {142}*284
10-fold quotients : {71}*142
71-fold quotients : {10}*20
142-fold quotients : {5}*10
355-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, 71)( 3, 70)( 4, 69)( 5, 68)( 6, 67)( 7, 66)( 8, 65)( 9, 64)( 10, 63)( 11, 62)( 12, 61)( 13, 60)( 14, 59)( 15, 58)( 16, 57)( 17, 56)( 18, 55)( 19, 54)( 20, 53)( 21, 52)( 22, 51)( 23, 50)( 24, 49)( 25, 48)( 26, 47)( 27, 46)( 28, 45)( 29, 44)( 30, 43)( 31, 42)( 32, 41)( 33, 40)( 34, 39)( 35, 38)( 36, 37)( 72,285)( 73,355)( 74,354)( 75,353)( 76,352)( 77,351)( 78,350)( 79,349)( 80,348)( 81,347)( 82,346)( 83,345)( 84,344)( 85,343)( 86,342)( 87,341)( 88,340)( 89,339)( 90,338)( 91,337)( 92,336)( 93,335)( 94,334)( 95,333)( 96,332)( 97,331)( 98,330)( 99,329)(100,328)(101,327)(102,326)(103,325)(104,324)(105,323)(106,322)(107,321)(108,320)(109,319)(110,318)(111,317)(112,316)(113,315)(114,314)(115,313)(116,312)(117,311)(118,310)(119,309)(120,308)(121,307)(122,306)(123,305)(124,304)(125,303)(126,302)(127,301)(128,300)(129,299)(130,298)(131,297)(132,296)(133,295)(134,294)(135,293)(136,292)(137,291)(138,290)(139,289)(140,288)(141,287)(142,286)(143,214)(144,284)(145,283)(146,282)(147,281)(148,280)(149,279)(150,278)(151,277)(152,276)(153,275)(154,274)(155,273)(156,272)(157,271)(158,270)(159,269)(160,268)(161,267)(162,266)(163,265)(164,264)(165,263)(166,262)(167,261)(168,260)(169,259)(170,258)(171,257)(172,256)(173,255)(174,254)(175,253)(176,252)(177,251)(178,250)(179,249)(180,248)(181,247)(182,246)(183,245)(184,244)(185,243)(186,242)(187,241)(188,240)(189,239)(190,238)(191,237)(192,236)(193,235)(194,234)(195,233)(196,232)(197,231)(198,230)(199,229)(200,228)(201,227)(202,226)(203,225)(204,224)(205,223)(206,222)(207,221)(208,220)(209,219)(210,218)(211,217)(212,216)(213,215)(357,426)(358,425)(359,424)(360,423)(361,422)(362,421)(363,420)(364,419)(365,418)(366,417)(367,416)(368,415)(369,414)(370,413)(371,412)(372,411)(373,410)(374,409)(375,408)(376,407)(377,406)(378,405)(379,404)(380,403)(381,402)(382,401)(383,400)(384,399)(385,398)(386,397)(387,396)(388,395)(389,394)(390,393)(391,392)(427,640)(428,710)(429,709)(430,708)(431,707)(432,706)(433,705)(434,704)(435,703)(436,702)(437,701)(438,700)(439,699)(440,698)(441,697)(442,696)(443,695)(444,694)(445,693)(446,692)(447,691)(448,690)(449,689)(450,688)(451,687)(452,686)(453,685)(454,684)(455,683)(456,682)(457,681)(458,680)(459,679)(460,678)(461,677)(462,676)(463,675)(464,674)(465,673)(466,672)(467,671)(468,670)(469,669)(470,668)(471,667)(472,666)(473,665)(474,664)(475,663)(476,662)(477,661)(478,660)(479,659)(480,658)(481,657)(482,656)(483,655)(484,654)(485,653)(486,652)(487,651)(488,650)(489,649)(490,648)(491,647)(492,646)(493,645)(494,644)(495,643)(496,642)(497,641)(498,569)(499,639)(500,638)(501,637)(502,636)(503,635)(504,634)(505,633)(506,632)(507,631)(508,630)(509,629)(510,628)(511,627)(512,626)(513,625)(514,624)(515,623)(516,622)(517,621)(518,620)(519,619)(520,618)(521,617)(522,616)(523,615)(524,614)(525,613)(526,612)(527,611)(528,610)(529,609)(530,608)(531,607)(532,606)(533,605)(534,604)(535,603)(536,602)(537,601)(538,600)(539,599)(540,598)(541,597)(542,596)(543,595)(544,594)(545,593)(546,592)(547,591)(548,590)(549,589)(550,588)(551,587)(552,586)(553,585)(554,584)(555,583)(556,582)(557,581)(558,580)(559,579)(560,578)(561,577)(562,576)(563,575)(564,574)(565,573)(566,572)(567,571)(568,570);;
s1 := ( 1,428)( 2,427)( 3,497)( 4,496)( 5,495)( 6,494)( 7,493)( 8,492)( 9,491)( 10,490)( 11,489)( 12,488)( 13,487)( 14,486)( 15,485)( 16,484)( 17,483)( 18,482)( 19,481)( 20,480)( 21,479)( 22,478)( 23,477)( 24,476)( 25,475)( 26,474)( 27,473)( 28,472)( 29,471)( 30,470)( 31,469)( 32,468)( 33,467)( 34,466)( 35,465)( 36,464)( 37,463)( 38,462)( 39,461)( 40,460)( 41,459)( 42,458)( 43,457)( 44,456)( 45,455)( 46,454)( 47,453)( 48,452)( 49,451)( 50,450)( 51,449)( 52,448)( 53,447)( 54,446)( 55,445)( 56,444)( 57,443)( 58,442)( 59,441)( 60,440)( 61,439)( 62,438)( 63,437)( 64,436)( 65,435)( 66,434)( 67,433)( 68,432)( 69,431)( 70,430)( 71,429)( 72,357)( 73,356)( 74,426)( 75,425)( 76,424)( 77,423)( 78,422)( 79,421)( 80,420)( 81,419)( 82,418)( 83,417)( 84,416)( 85,415)( 86,414)( 87,413)( 88,412)( 89,411)( 90,410)( 91,409)( 92,408)( 93,407)( 94,406)( 95,405)( 96,404)( 97,403)( 98,402)( 99,401)(100,400)(101,399)(102,398)(103,397)(104,396)(105,395)(106,394)(107,393)(108,392)(109,391)(110,390)(111,389)(112,388)(113,387)(114,386)(115,385)(116,384)(117,383)(118,382)(119,381)(120,380)(121,379)(122,378)(123,377)(124,376)(125,375)(126,374)(127,373)(128,372)(129,371)(130,370)(131,369)(132,368)(133,367)(134,366)(135,365)(136,364)(137,363)(138,362)(139,361)(140,360)(141,359)(142,358)(143,641)(144,640)(145,710)(146,709)(147,708)(148,707)(149,706)(150,705)(151,704)(152,703)(153,702)(154,701)(155,700)(156,699)(157,698)(158,697)(159,696)(160,695)(161,694)(162,693)(163,692)(164,691)(165,690)(166,689)(167,688)(168,687)(169,686)(170,685)(171,684)(172,683)(173,682)(174,681)(175,680)(176,679)(177,678)(178,677)(179,676)(180,675)(181,674)(182,673)(183,672)(184,671)(185,670)(186,669)(187,668)(188,667)(189,666)(190,665)(191,664)(192,663)(193,662)(194,661)(195,660)(196,659)(197,658)(198,657)(199,656)(200,655)(201,654)(202,653)(203,652)(204,651)(205,650)(206,649)(207,648)(208,647)(209,646)(210,645)(211,644)(212,643)(213,642)(214,570)(215,569)(216,639)(217,638)(218,637)(219,636)(220,635)(221,634)(222,633)(223,632)(224,631)(225,630)(226,629)(227,628)(228,627)(229,626)(230,625)(231,624)(232,623)(233,622)(234,621)(235,620)(236,619)(237,618)(238,617)(239,616)(240,615)(241,614)(242,613)(243,612)(244,611)(245,610)(246,609)(247,608)(248,607)(249,606)(250,605)(251,604)(252,603)(253,602)(254,601)(255,600)(256,599)(257,598)(258,597)(259,596)(260,595)(261,594)(262,593)(263,592)(264,591)(265,590)(266,589)(267,588)(268,587)(269,586)(270,585)(271,584)(272,583)(273,582)(274,581)(275,580)(276,579)(277,578)(278,577)(279,576)(280,575)(281,574)(282,573)(283,572)(284,571)(285,499)(286,498)(287,568)(288,567)(289,566)(290,565)(291,564)(292,563)(293,562)(294,561)(295,560)(296,559)(297,558)(298,557)(299,556)(300,555)(301,554)(302,553)(303,552)(304,551)(305,550)(306,549)(307,548)(308,547)(309,546)(310,545)(311,544)(312,543)(313,542)(314,541)(315,540)(316,539)(317,538)(318,537)(319,536)(320,535)(321,534)(322,533)(323,532)(324,531)(325,530)(326,529)(327,528)(328,527)(329,526)(330,525)(331,524)(332,523)(333,522)(334,521)(335,520)(336,519)(337,518)(338,517)(339,516)(340,515)(341,514)(342,513)(343,512)(344,511)(345,510)(346,509)(347,508)(348,507)(349,506)(350,505)(351,504)(352,503)(353,502)(354,501)(355,500);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(710)!( 2, 71)( 3, 70)( 4, 69)( 5, 68)( 6, 67)( 7, 66)( 8, 65)( 9, 64)( 10, 63)( 11, 62)( 12, 61)( 13, 60)( 14, 59)( 15, 58)( 16, 57)( 17, 56)( 18, 55)( 19, 54)( 20, 53)( 21, 52)( 22, 51)( 23, 50)( 24, 49)( 25, 48)( 26, 47)( 27, 46)( 28, 45)( 29, 44)( 30, 43)( 31, 42)( 32, 41)( 33, 40)( 34, 39)( 35, 38)( 36, 37)( 72,285)( 73,355)( 74,354)( 75,353)( 76,352)( 77,351)( 78,350)( 79,349)( 80,348)( 81,347)( 82,346)( 83,345)( 84,344)( 85,343)( 86,342)( 87,341)( 88,340)( 89,339)( 90,338)( 91,337)( 92,336)( 93,335)( 94,334)( 95,333)( 96,332)( 97,331)( 98,330)( 99,329)(100,328)(101,327)(102,326)(103,325)(104,324)(105,323)(106,322)(107,321)(108,320)(109,319)(110,318)(111,317)(112,316)(113,315)(114,314)(115,313)(116,312)(117,311)(118,310)(119,309)(120,308)(121,307)(122,306)(123,305)(124,304)(125,303)(126,302)(127,301)(128,300)(129,299)(130,298)(131,297)(132,296)(133,295)(134,294)(135,293)(136,292)(137,291)(138,290)(139,289)(140,288)(141,287)(142,286)(143,214)(144,284)(145,283)(146,282)(147,281)(148,280)(149,279)(150,278)(151,277)(152,276)(153,275)(154,274)(155,273)(156,272)(157,271)(158,270)(159,269)(160,268)(161,267)(162,266)(163,265)(164,264)(165,263)(166,262)(167,261)(168,260)(169,259)(170,258)(171,257)(172,256)(173,255)(174,254)(175,253)(176,252)(177,251)(178,250)(179,249)(180,248)(181,247)(182,246)(183,245)(184,244)(185,243)(186,242)(187,241)(188,240)(189,239)(190,238)(191,237)(192,236)(193,235)(194,234)(195,233)(196,232)(197,231)(198,230)(199,229)(200,228)(201,227)(202,226)(203,225)(204,224)(205,223)(206,222)(207,221)(208,220)(209,219)(210,218)(211,217)(212,216)(213,215)(357,426)(358,425)(359,424)(360,423)(361,422)(362,421)(363,420)(364,419)(365,418)(366,417)(367,416)(368,415)(369,414)(370,413)(371,412)(372,411)(373,410)(374,409)(375,408)(376,407)(377,406)(378,405)(379,404)(380,403)(381,402)(382,401)(383,400)(384,399)(385,398)(386,397)(387,396)(388,395)(389,394)(390,393)(391,392)(427,640)(428,710)(429,709)(430,708)(431,707)(432,706)(433,705)(434,704)(435,703)(436,702)(437,701)(438,700)(439,699)(440,698)(441,697)(442,696)(443,695)(444,694)(445,693)(446,692)(447,691)(448,690)(449,689)(450,688)(451,687)(452,686)(453,685)(454,684)(455,683)(456,682)(457,681)(458,680)(459,679)(460,678)(461,677)(462,676)(463,675)(464,674)(465,673)(466,672)(467,671)(468,670)(469,669)(470,668)(471,667)(472,666)(473,665)(474,664)(475,663)(476,662)(477,661)(478,660)(479,659)(480,658)(481,657)(482,656)(483,655)(484,654)(485,653)(486,652)(487,651)(488,650)(489,649)(490,648)(491,647)(492,646)(493,645)(494,644)(495,643)(496,642)(497,641)(498,569)(499,639)(500,638)(501,637)(502,636)(503,635)(504,634)(505,633)(506,632)(507,631)(508,630)(509,629)(510,628)(511,627)(512,626)(513,625)(514,624)(515,623)(516,622)(517,621)(518,620)(519,619)(520,618)(521,617)(522,616)(523,615)(524,614)(525,613)(526,612)(527,611)(528,610)(529,609)(530,608)(531,607)(532,606)(533,605)(534,604)(535,603)(536,602)(537,601)(538,600)(539,599)(540,598)(541,597)(542,596)(543,595)(544,594)(545,593)(546,592)(547,591)(548,590)(549,589)(550,588)(551,587)(552,586)(553,585)(554,584)(555,583)(556,582)(557,581)(558,580)(559,579)(560,578)(561,577)(562,576)(563,575)(564,574)(565,573)(566,572)(567,571)(568,570);
s1 := Sym(710)!( 1,428)( 2,427)( 3,497)( 4,496)( 5,495)( 6,494)( 7,493)( 8,492)( 9,491)( 10,490)( 11,489)( 12,488)( 13,487)( 14,486)( 15,485)( 16,484)( 17,483)( 18,482)( 19,481)( 20,480)( 21,479)( 22,478)( 23,477)( 24,476)( 25,475)( 26,474)( 27,473)( 28,472)( 29,471)( 30,470)( 31,469)( 32,468)( 33,467)( 34,466)( 35,465)( 36,464)( 37,463)( 38,462)( 39,461)( 40,460)( 41,459)( 42,458)( 43,457)( 44,456)( 45,455)( 46,454)( 47,453)( 48,452)( 49,451)( 50,450)( 51,449)( 52,448)( 53,447)( 54,446)( 55,445)( 56,444)( 57,443)( 58,442)( 59,441)( 60,440)( 61,439)( 62,438)( 63,437)( 64,436)( 65,435)( 66,434)( 67,433)( 68,432)( 69,431)( 70,430)( 71,429)( 72,357)( 73,356)( 74,426)( 75,425)( 76,424)( 77,423)( 78,422)( 79,421)( 80,420)( 81,419)( 82,418)( 83,417)( 84,416)( 85,415)( 86,414)( 87,413)( 88,412)( 89,411)( 90,410)( 91,409)( 92,408)( 93,407)( 94,406)( 95,405)( 96,404)( 97,403)( 98,402)( 99,401)(100,400)(101,399)(102,398)(103,397)(104,396)(105,395)(106,394)(107,393)(108,392)(109,391)(110,390)(111,389)(112,388)(113,387)(114,386)(115,385)(116,384)(117,383)(118,382)(119,381)(120,380)(121,379)(122,378)(123,377)(124,376)(125,375)(126,374)(127,373)(128,372)(129,371)(130,370)(131,369)(132,368)(133,367)(134,366)(135,365)(136,364)(137,363)(138,362)(139,361)(140,360)(141,359)(142,358)(143,641)(144,640)(145,710)(146,709)(147,708)(148,707)(149,706)(150,705)(151,704)(152,703)(153,702)(154,701)(155,700)(156,699)(157,698)(158,697)(159,696)(160,695)(161,694)(162,693)(163,692)(164,691)(165,690)(166,689)(167,688)(168,687)(169,686)(170,685)(171,684)(172,683)(173,682)(174,681)(175,680)(176,679)(177,678)(178,677)(179,676)(180,675)(181,674)(182,673)(183,672)(184,671)(185,670)(186,669)(187,668)(188,667)(189,666)(190,665)(191,664)(192,663)(193,662)(194,661)(195,660)(196,659)(197,658)(198,657)(199,656)(200,655)(201,654)(202,653)(203,652)(204,651)(205,650)(206,649)(207,648)(208,647)(209,646)(210,645)(211,644)(212,643)(213,642)(214,570)(215,569)(216,639)(217,638)(218,637)(219,636)(220,635)(221,634)(222,633)(223,632)(224,631)(225,630)(226,629)(227,628)(228,627)(229,626)(230,625)(231,624)(232,623)(233,622)(234,621)(235,620)(236,619)(237,618)(238,617)(239,616)(240,615)(241,614)(242,613)(243,612)(244,611)(245,610)(246,609)(247,608)(248,607)(249,606)(250,605)(251,604)(252,603)(253,602)(254,601)(255,600)(256,599)(257,598)(258,597)(259,596)(260,595)(261,594)(262,593)(263,592)(264,591)(265,590)(266,589)(267,588)(268,587)(269,586)(270,585)(271,584)(272,583)(273,582)(274,581)(275,580)(276,579)(277,578)(278,577)(279,576)(280,575)(281,574)(282,573)(283,572)(284,571)(285,499)(286,498)(287,568)(288,567)(289,566)(290,565)(291,564)(292,563)(293,562)(294,561)(295,560)(296,559)(297,558)(298,557)(299,556)(300,555)(301,554)(302,553)(303,552)(304,551)(305,550)(306,549)(307,548)(308,547)(309,546)(310,545)(311,544)(312,543)(313,542)(314,541)(315,540)(316,539)(317,538)(318,537)(319,536)(320,535)(321,534)(322,533)(323,532)(324,531)(325,530)(326,529)(327,528)(328,527)(329,526)(330,525)(331,524)(332,523)(333,522)(334,521)(335,520)(336,519)(337,518)(338,517)(339,516)(340,515)(341,514)(342,513)(343,512)(344,511)(345,510)(346,509)(347,508)(348,507)(349,506)(350,505)(351,504)(352,503)(353,502)(354,501)(355,500);
poly := sub<Sym(710)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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