Polytope of Type {662}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {662}*1324
Also Known As : 662-gon, {662}. if this polytope has another name.
Group : SmallGroup(1324,3)
Rank : 2
Schlafli Type : {662}
Number of vertices, edges, etc : 662, 662
Order of s₀s₁ : 662
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 : {331}*662
   331-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope