Polytope of Type {650}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {650}*1300
Also Known As : 650-gon, {650}. if this polytope has another name.
Group : SmallGroup(1300,14)
Rank : 2
Schlafli Type : {650}
Number of vertices, edges, etc : 650, 650
Order of s₀s₁ : 650
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 : {325}*650
   5-fold quotients : {130}*260
   10-fold quotients : {65}*130
   13-fold quotients : {50}*100
   25-fold quotients : {26}*52
   26-fold quotients : {25}*50
   50-fold quotients : {13}*26
   65-fold quotients : {10}*20
   130-fold quotients : {5}*10
   325-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope