Polytope of Type {570}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {570}*1140
Also Known As : 570-gon, {570}. if this polytope has another name.
Group : SmallGroup(1140,40)
Rank : 2
Schlafli Type : {570}
Number of vertices, edges, etc : 570, 570
Order of s₀s₁ : 570
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 : {285}*570
   3-fold quotients : {190}*380
   5-fold quotients : {114}*228
   6-fold quotients : {95}*190
   10-fold quotients : {57}*114
   15-fold quotients : {38}*76
   19-fold quotients : {30}*60
   30-fold quotients : {19}*38
   38-fold quotients : {15}*30
   57-fold quotients : {10}*20
   95-fold quotients : {6}*12
   114-fold quotients : {5}*10
   190-fold quotients : {3}*6
   285-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 19)(  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 14)(  8, 13)(  9, 12)
( 10, 11)( 20, 77)( 21, 95)( 22, 94)( 23, 93)( 24, 92)( 25, 91)( 26, 90)
( 27, 89)( 28, 88)( 29, 87)( 30, 86)( 31, 85)( 32, 84)( 33, 83)( 34, 82)
( 35, 81)( 36, 80)( 37, 79)( 38, 78)( 39, 58)( 40, 76)( 41, 75)( 42, 74)
( 43, 73)( 44, 72)( 45, 71)( 46, 70)( 47, 69)( 48, 68)( 49, 67)( 50, 66)
( 51, 65)( 52, 64)( 53, 63)( 54, 62)( 55, 61)( 56, 60)( 57, 59)( 96,191)
( 97,209)( 98,208)( 99,207)(100,206)(101,205)(102,204)(103,203)(104,202)
(105,201)(106,200)(107,199)(108,198)(109,197)(110,196)(111,195)(112,194)
(113,193)(114,192)(115,267)(116,285)(117,284)(118,283)(119,282)(120,281)
(121,280)(122,279)(123,278)(124,277)(125,276)(126,275)(127,274)(128,273)
(129,272)(130,271)(131,270)(132,269)(133,268)(134,248)(135,266)(136,265)
(137,264)(138,263)(139,262)(140,261)(141,260)(142,259)(143,258)(144,257)
(145,256)(146,255)(147,254)(148,253)(149,252)(150,251)(151,250)(152,249)
(153,229)(154,247)(155,246)(156,245)(157,244)(158,243)(159,242)(160,241)
(161,240)(162,239)(163,238)(164,237)(165,236)(166,235)(167,234)(168,233)
(169,232)(170,231)(171,230)(172,210)(173,228)(174,227)(175,226)(176,225)
(177,224)(178,223)(179,222)(180,221)(181,220)(182,219)(183,218)(184,217)
(185,216)(186,215)(187,214)(188,213)(189,212)(190,211)(287,304)(288,303)
(289,302)(290,301)(291,300)(292,299)(293,298)(294,297)(295,296)(305,362)
(306,380)(307,379)(308,378)(309,377)(310,376)(311,375)(312,374)(313,373)
(314,372)(315,371)(316,370)(317,369)(318,368)(319,367)(320,366)(321,365)
(322,364)(323,363)(324,343)(325,361)(326,360)(327,359)(328,358)(329,357)
(330,356)(331,355)(332,354)(333,353)(334,352)(335,351)(336,350)(337,349)
(338,348)(339,347)(340,346)(341,345)(342,344)(381,476)(382,494)(383,493)
(384,492)(385,491)(386,490)(387,489)(388,488)(389,487)(390,486)(391,485)
(392,484)(393,483)(394,482)(395,481)(396,480)(397,479)(398,478)(399,477)
(400,552)(401,570)(402,569)(403,568)(404,567)(405,566)(406,565)(407,564)
(408,563)(409,562)(410,561)(411,560)(412,559)(413,558)(414,557)(415,556)
(416,555)(417,554)(418,553)(419,533)(420,551)(421,550)(422,549)(423,548)
(424,547)(425,546)(426,545)(427,544)(428,543)(429,542)(430,541)(431,540)
(432,539)(433,538)(434,537)(435,536)(436,535)(437,534)(438,514)(439,532)
(440,531)(441,530)(442,529)(443,528)(444,527)(445,526)(446,525)(447,524)
(448,523)(449,522)(450,521)(451,520)(452,519)(453,518)(454,517)(455,516)
(456,515)(457,495)(458,513)(459,512)(460,511)(461,510)(462,509)(463,508)
(464,507)(465,506)(466,505)(467,504)(468,503)(469,502)(470,501)(471,500)
(472,499)(473,498)(474,497)(475,496);;
s1 := (  1,401)(  2,400)(  3,418)(  4,417)(  5,416)(  6,415)(  7,414)(  8,413)
(  9,412)( 10,411)( 11,410)( 12,409)( 13,408)( 14,407)( 15,406)( 16,405)
( 17,404)( 18,403)( 19,402)( 20,382)( 21,381)( 22,399)( 23,398)( 24,397)
( 25,396)( 26,395)( 27,394)( 28,393)( 29,392)( 30,391)( 31,390)( 32,389)
( 33,388)( 34,387)( 35,386)( 36,385)( 37,384)( 38,383)( 39,458)( 40,457)
( 41,475)( 42,474)( 43,473)( 44,472)( 45,471)( 46,470)( 47,469)( 48,468)
( 49,467)( 50,466)( 51,465)( 52,464)( 53,463)( 54,462)( 55,461)( 56,460)
( 57,459)( 58,439)( 59,438)( 60,456)( 61,455)( 62,454)( 63,453)( 64,452)
( 65,451)( 66,450)( 67,449)( 68,448)( 69,447)( 70,446)( 71,445)( 72,444)
( 73,443)( 74,442)( 75,441)( 76,440)( 77,420)( 78,419)( 79,437)( 80,436)
( 81,435)( 82,434)( 83,433)( 84,432)( 85,431)( 86,430)( 87,429)( 88,428)
( 89,427)( 90,426)( 91,425)( 92,424)( 93,423)( 94,422)( 95,421)( 96,306)
( 97,305)( 98,323)( 99,322)(100,321)(101,320)(102,319)(103,318)(104,317)
(105,316)(106,315)(107,314)(108,313)(109,312)(110,311)(111,310)(112,309)
(113,308)(114,307)(115,287)(116,286)(117,304)(118,303)(119,302)(120,301)
(121,300)(122,299)(123,298)(124,297)(125,296)(126,295)(127,294)(128,293)
(129,292)(130,291)(131,290)(132,289)(133,288)(134,363)(135,362)(136,380)
(137,379)(138,378)(139,377)(140,376)(141,375)(142,374)(143,373)(144,372)
(145,371)(146,370)(147,369)(148,368)(149,367)(150,366)(151,365)(152,364)
(153,344)(154,343)(155,361)(156,360)(157,359)(158,358)(159,357)(160,356)
(161,355)(162,354)(163,353)(164,352)(165,351)(166,350)(167,349)(168,348)
(169,347)(170,346)(171,345)(172,325)(173,324)(174,342)(175,341)(176,340)
(177,339)(178,338)(179,337)(180,336)(181,335)(182,334)(183,333)(184,332)
(185,331)(186,330)(187,329)(188,328)(189,327)(190,326)(191,496)(192,495)
(193,513)(194,512)(195,511)(196,510)(197,509)(198,508)(199,507)(200,506)
(201,505)(202,504)(203,503)(204,502)(205,501)(206,500)(207,499)(208,498)
(209,497)(210,477)(211,476)(212,494)(213,493)(214,492)(215,491)(216,490)
(217,489)(218,488)(219,487)(220,486)(221,485)(222,484)(223,483)(224,482)
(225,481)(226,480)(227,479)(228,478)(229,553)(230,552)(231,570)(232,569)
(233,568)(234,567)(235,566)(236,565)(237,564)(238,563)(239,562)(240,561)
(241,560)(242,559)(243,558)(244,557)(245,556)(246,555)(247,554)(248,534)
(249,533)(250,551)(251,550)(252,549)(253,548)(254,547)(255,546)(256,545)
(257,544)(258,543)(259,542)(260,541)(261,540)(262,539)(263,538)(264,537)
(265,536)(266,535)(267,515)(268,514)(269,532)(270,531)(271,530)(272,529)
(273,528)(274,527)(275,526)(276,525)(277,524)(278,523)(279,522)(280,521)
(281,520)(282,519)(283,518)(284,517)(285,516);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(570)!(  2, 19)(  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 14)(  8, 13)
(  9, 12)( 10, 11)( 20, 77)( 21, 95)( 22, 94)( 23, 93)( 24, 92)( 25, 91)
( 26, 90)( 27, 89)( 28, 88)( 29, 87)( 30, 86)( 31, 85)( 32, 84)( 33, 83)
( 34, 82)( 35, 81)( 36, 80)( 37, 79)( 38, 78)( 39, 58)( 40, 76)( 41, 75)
( 42, 74)( 43, 73)( 44, 72)( 45, 71)( 46, 70)( 47, 69)( 48, 68)( 49, 67)
( 50, 66)( 51, 65)( 52, 64)( 53, 63)( 54, 62)( 55, 61)( 56, 60)( 57, 59)
( 96,191)( 97,209)( 98,208)( 99,207)(100,206)(101,205)(102,204)(103,203)
(104,202)(105,201)(106,200)(107,199)(108,198)(109,197)(110,196)(111,195)
(112,194)(113,193)(114,192)(115,267)(116,285)(117,284)(118,283)(119,282)
(120,281)(121,280)(122,279)(123,278)(124,277)(125,276)(126,275)(127,274)
(128,273)(129,272)(130,271)(131,270)(132,269)(133,268)(134,248)(135,266)
(136,265)(137,264)(138,263)(139,262)(140,261)(141,260)(142,259)(143,258)
(144,257)(145,256)(146,255)(147,254)(148,253)(149,252)(150,251)(151,250)
(152,249)(153,229)(154,247)(155,246)(156,245)(157,244)(158,243)(159,242)
(160,241)(161,240)(162,239)(163,238)(164,237)(165,236)(166,235)(167,234)
(168,233)(169,232)(170,231)(171,230)(172,210)(173,228)(174,227)(175,226)
(176,225)(177,224)(178,223)(179,222)(180,221)(181,220)(182,219)(183,218)
(184,217)(185,216)(186,215)(187,214)(188,213)(189,212)(190,211)(287,304)
(288,303)(289,302)(290,301)(291,300)(292,299)(293,298)(294,297)(295,296)
(305,362)(306,380)(307,379)(308,378)(309,377)(310,376)(311,375)(312,374)
(313,373)(314,372)(315,371)(316,370)(317,369)(318,368)(319,367)(320,366)
(321,365)(322,364)(323,363)(324,343)(325,361)(326,360)(327,359)(328,358)
(329,357)(330,356)(331,355)(332,354)(333,353)(334,352)(335,351)(336,350)
(337,349)(338,348)(339,347)(340,346)(341,345)(342,344)(381,476)(382,494)
(383,493)(384,492)(385,491)(386,490)(387,489)(388,488)(389,487)(390,486)
(391,485)(392,484)(393,483)(394,482)(395,481)(396,480)(397,479)(398,478)
(399,477)(400,552)(401,570)(402,569)(403,568)(404,567)(405,566)(406,565)
(407,564)(408,563)(409,562)(410,561)(411,560)(412,559)(413,558)(414,557)
(415,556)(416,555)(417,554)(418,553)(419,533)(420,551)(421,550)(422,549)
(423,548)(424,547)(425,546)(426,545)(427,544)(428,543)(429,542)(430,541)
(431,540)(432,539)(433,538)(434,537)(435,536)(436,535)(437,534)(438,514)
(439,532)(440,531)(441,530)(442,529)(443,528)(444,527)(445,526)(446,525)
(447,524)(448,523)(449,522)(450,521)(451,520)(452,519)(453,518)(454,517)
(455,516)(456,515)(457,495)(458,513)(459,512)(460,511)(461,510)(462,509)
(463,508)(464,507)(465,506)(466,505)(467,504)(468,503)(469,502)(470,501)
(471,500)(472,499)(473,498)(474,497)(475,496);
s1 := Sym(570)!(  1,401)(  2,400)(  3,418)(  4,417)(  5,416)(  6,415)(  7,414)
(  8,413)(  9,412)( 10,411)( 11,410)( 12,409)( 13,408)( 14,407)( 15,406)
( 16,405)( 17,404)( 18,403)( 19,402)( 20,382)( 21,381)( 22,399)( 23,398)
( 24,397)( 25,396)( 26,395)( 27,394)( 28,393)( 29,392)( 30,391)( 31,390)
( 32,389)( 33,388)( 34,387)( 35,386)( 36,385)( 37,384)( 38,383)( 39,458)
( 40,457)( 41,475)( 42,474)( 43,473)( 44,472)( 45,471)( 46,470)( 47,469)
( 48,468)( 49,467)( 50,466)( 51,465)( 52,464)( 53,463)( 54,462)( 55,461)
( 56,460)( 57,459)( 58,439)( 59,438)( 60,456)( 61,455)( 62,454)( 63,453)
( 64,452)( 65,451)( 66,450)( 67,449)( 68,448)( 69,447)( 70,446)( 71,445)
( 72,444)( 73,443)( 74,442)( 75,441)( 76,440)( 77,420)( 78,419)( 79,437)
( 80,436)( 81,435)( 82,434)( 83,433)( 84,432)( 85,431)( 86,430)( 87,429)
( 88,428)( 89,427)( 90,426)( 91,425)( 92,424)( 93,423)( 94,422)( 95,421)
( 96,306)( 97,305)( 98,323)( 99,322)(100,321)(101,320)(102,319)(103,318)
(104,317)(105,316)(106,315)(107,314)(108,313)(109,312)(110,311)(111,310)
(112,309)(113,308)(114,307)(115,287)(116,286)(117,304)(118,303)(119,302)
(120,301)(121,300)(122,299)(123,298)(124,297)(125,296)(126,295)(127,294)
(128,293)(129,292)(130,291)(131,290)(132,289)(133,288)(134,363)(135,362)
(136,380)(137,379)(138,378)(139,377)(140,376)(141,375)(142,374)(143,373)
(144,372)(145,371)(146,370)(147,369)(148,368)(149,367)(150,366)(151,365)
(152,364)(153,344)(154,343)(155,361)(156,360)(157,359)(158,358)(159,357)
(160,356)(161,355)(162,354)(163,353)(164,352)(165,351)(166,350)(167,349)
(168,348)(169,347)(170,346)(171,345)(172,325)(173,324)(174,342)(175,341)
(176,340)(177,339)(178,338)(179,337)(180,336)(181,335)(182,334)(183,333)
(184,332)(185,331)(186,330)(187,329)(188,328)(189,327)(190,326)(191,496)
(192,495)(193,513)(194,512)(195,511)(196,510)(197,509)(198,508)(199,507)
(200,506)(201,505)(202,504)(203,503)(204,502)(205,501)(206,500)(207,499)
(208,498)(209,497)(210,477)(211,476)(212,494)(213,493)(214,492)(215,491)
(216,490)(217,489)(218,488)(219,487)(220,486)(221,485)(222,484)(223,483)
(224,482)(225,481)(226,480)(227,479)(228,478)(229,553)(230,552)(231,570)
(232,569)(233,568)(234,567)(235,566)(236,565)(237,564)(238,563)(239,562)
(240,561)(241,560)(242,559)(243,558)(244,557)(245,556)(246,555)(247,554)
(248,534)(249,533)(250,551)(251,550)(252,549)(253,548)(254,547)(255,546)
(256,545)(257,544)(258,543)(259,542)(260,541)(261,540)(262,539)(263,538)
(264,537)(265,536)(266,535)(267,515)(268,514)(269,532)(270,531)(271,530)
(272,529)(273,528)(274,527)(275,526)(276,525)(277,524)(278,523)(279,522)
(280,521)(281,520)(282,519)(283,518)(284,517)(285,516);
poly := sub<Sym(570)|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 >;

References : None.
to this polytope