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.
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