Polytope of Type {614}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {614}*1228
Also Known As : 614-gon, {614}. if this polytope has another name.
Group : SmallGroup(1228,3)
Rank : 2
Schlafli Type : {614}
Number of vertices, edges, etc : 614, 614
Order of s₀s₁ : 614
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 : {307}*614
   307-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope