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.
Irregular Quotients (of which this is a minimal cover):
None.
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