Polytope of Type {622}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {622}*1244
Also Known As : 622-gon, {622}. if this polytope has another name.
Group : SmallGroup(1244,3)
Rank : 2
Schlafli Type : {622}
Number of vertices, edges, etc : 622, 622
Order of s₀s₁ : 622
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 : {311}*622
   311-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope