Polytope of Type {758}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {758}*1516
Also Known As : 758-gon, {758}. if this polytope has another name.
Group : SmallGroup(1516,3)
Rank : 2
Schlafli Type : {758}
Number of vertices, edges, etc : 758, 758
Order of s₀s₁ : 758
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 : {379}*758
   379-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2,379)(  3,378)(  4,377)(  5,376)(  6,375)(  7,374)(  8,373)(  9,372)
( 10,371)( 11,370)( 12,369)( 13,368)( 14,367)( 15,366)( 16,365)( 17,364)
( 18,363)( 19,362)( 20,361)( 21,360)( 22,359)( 23,358)( 24,357)( 25,356)
( 26,355)( 27,354)( 28,353)( 29,352)( 30,351)( 31,350)( 32,349)( 33,348)
( 34,347)( 35,346)( 36,345)( 37,344)( 38,343)( 39,342)( 40,341)( 41,340)
( 42,339)( 43,338)( 44,337)( 45,336)( 46,335)( 47,334)( 48,333)( 49,332)
( 50,331)( 51,330)( 52,329)( 53,328)( 54,327)( 55,326)( 56,325)( 57,324)
( 58,323)( 59,322)( 60,321)( 61,320)( 62,319)( 63,318)( 64,317)( 65,316)
( 66,315)( 67,314)( 68,313)( 69,312)( 70,311)( 71,310)( 72,309)( 73,308)
( 74,307)( 75,306)( 76,305)( 77,304)( 78,303)( 79,302)( 80,301)( 81,300)
( 82,299)( 83,298)( 84,297)( 85,296)( 86,295)( 87,294)( 88,293)( 89,292)
( 90,291)( 91,290)( 92,289)( 93,288)( 94,287)( 95,286)( 96,285)( 97,284)
( 98,283)( 99,282)(100,281)(101,280)(102,279)(103,278)(104,277)(105,276)
(106,275)(107,274)(108,273)(109,272)(110,271)(111,270)(112,269)(113,268)
(114,267)(115,266)(116,265)(117,264)(118,263)(119,262)(120,261)(121,260)
(122,259)(123,258)(124,257)(125,256)(126,255)(127,254)(128,253)(129,252)
(130,251)(131,250)(132,249)(133,248)(134,247)(135,246)(136,245)(137,244)
(138,243)(139,242)(140,241)(141,240)(142,239)(143,238)(144,237)(145,236)
(146,235)(147,234)(148,233)(149,232)(150,231)(151,230)(152,229)(153,228)
(154,227)(155,226)(156,225)(157,224)(158,223)(159,222)(160,221)(161,220)
(162,219)(163,218)(164,217)(165,216)(166,215)(167,214)(168,213)(169,212)
(170,211)(171,210)(172,209)(173,208)(174,207)(175,206)(176,205)(177,204)
(178,203)(179,202)(180,201)(181,200)(182,199)(183,198)(184,197)(185,196)
(186,195)(187,194)(188,193)(189,192)(190,191)(381,758)(382,757)(383,756)
(384,755)(385,754)(386,753)(387,752)(388,751)(389,750)(390,749)(391,748)
(392,747)(393,746)(394,745)(395,744)(396,743)(397,742)(398,741)(399,740)
(400,739)(401,738)(402,737)(403,736)(404,735)(405,734)(406,733)(407,732)
(408,731)(409,730)(410,729)(411,728)(412,727)(413,726)(414,725)(415,724)
(416,723)(417,722)(418,721)(419,720)(420,719)(421,718)(422,717)(423,716)
(424,715)(425,714)(426,713)(427,712)(428,711)(429,710)(430,709)(431,708)
(432,707)(433,706)(434,705)(435,704)(436,703)(437,702)(438,701)(439,700)
(440,699)(441,698)(442,697)(443,696)(444,695)(445,694)(446,693)(447,692)
(448,691)(449,690)(450,689)(451,688)(452,687)(453,686)(454,685)(455,684)
(456,683)(457,682)(458,681)(459,680)(460,679)(461,678)(462,677)(463,676)
(464,675)(465,674)(466,673)(467,672)(468,671)(469,670)(470,669)(471,668)
(472,667)(473,666)(474,665)(475,664)(476,663)(477,662)(478,661)(479,660)
(480,659)(481,658)(482,657)(483,656)(484,655)(485,654)(486,653)(487,652)
(488,651)(489,650)(490,649)(491,648)(492,647)(493,646)(494,645)(495,644)
(496,643)(497,642)(498,641)(499,640)(500,639)(501,638)(502,637)(503,636)
(504,635)(505,634)(506,633)(507,632)(508,631)(509,630)(510,629)(511,628)
(512,627)(513,626)(514,625)(515,624)(516,623)(517,622)(518,621)(519,620)
(520,619)(521,618)(522,617)(523,616)(524,615)(525,614)(526,613)(527,612)
(528,611)(529,610)(530,609)(531,608)(532,607)(533,606)(534,605)(535,604)
(536,603)(537,602)(538,601)(539,600)(540,599)(541,598)(542,597)(543,596)
(544,595)(545,594)(546,593)(547,592)(548,591)(549,590)(550,589)(551,588)
(552,587)(553,586)(554,585)(555,584)(556,583)(557,582)(558,581)(559,580)
(560,579)(561,578)(562,577)(563,576)(564,575)(565,574)(566,573)(567,572)
(568,571)(569,570);;
s1 := (  1,381)(  2,380)(  3,758)(  4,757)(  5,756)(  6,755)(  7,754)(  8,753)
(  9,752)( 10,751)( 11,750)( 12,749)( 13,748)( 14,747)( 15,746)( 16,745)
( 17,744)( 18,743)( 19,742)( 20,741)( 21,740)( 22,739)( 23,738)( 24,737)
( 25,736)( 26,735)( 27,734)( 28,733)( 29,732)( 30,731)( 31,730)( 32,729)
( 33,728)( 34,727)( 35,726)( 36,725)( 37,724)( 38,723)( 39,722)( 40,721)
( 41,720)( 42,719)( 43,718)( 44,717)( 45,716)( 46,715)( 47,714)( 48,713)
( 49,712)( 50,711)( 51,710)( 52,709)( 53,708)( 54,707)( 55,706)( 56,705)
( 57,704)( 58,703)( 59,702)( 60,701)( 61,700)( 62,699)( 63,698)( 64,697)
( 65,696)( 66,695)( 67,694)( 68,693)( 69,692)( 70,691)( 71,690)( 72,689)
( 73,688)( 74,687)( 75,686)( 76,685)( 77,684)( 78,683)( 79,682)( 80,681)
( 81,680)( 82,679)( 83,678)( 84,677)( 85,676)( 86,675)( 87,674)( 88,673)
( 89,672)( 90,671)( 91,670)( 92,669)( 93,668)( 94,667)( 95,666)( 96,665)
( 97,664)( 98,663)( 99,662)(100,661)(101,660)(102,659)(103,658)(104,657)
(105,656)(106,655)(107,654)(108,653)(109,652)(110,651)(111,650)(112,649)
(113,648)(114,647)(115,646)(116,645)(117,644)(118,643)(119,642)(120,641)
(121,640)(122,639)(123,638)(124,637)(125,636)(126,635)(127,634)(128,633)
(129,632)(130,631)(131,630)(132,629)(133,628)(134,627)(135,626)(136,625)
(137,624)(138,623)(139,622)(140,621)(141,620)(142,619)(143,618)(144,617)
(145,616)(146,615)(147,614)(148,613)(149,612)(150,611)(151,610)(152,609)
(153,608)(154,607)(155,606)(156,605)(157,604)(158,603)(159,602)(160,601)
(161,600)(162,599)(163,598)(164,597)(165,596)(166,595)(167,594)(168,593)
(169,592)(170,591)(171,590)(172,589)(173,588)(174,587)(175,586)(176,585)
(177,584)(178,583)(179,582)(180,581)(181,580)(182,579)(183,578)(184,577)
(185,576)(186,575)(187,574)(188,573)(189,572)(190,571)(191,570)(192,569)
(193,568)(194,567)(195,566)(196,565)(197,564)(198,563)(199,562)(200,561)
(201,560)(202,559)(203,558)(204,557)(205,556)(206,555)(207,554)(208,553)
(209,552)(210,551)(211,550)(212,549)(213,548)(214,547)(215,546)(216,545)
(217,544)(218,543)(219,542)(220,541)(221,540)(222,539)(223,538)(224,537)
(225,536)(226,535)(227,534)(228,533)(229,532)(230,531)(231,530)(232,529)
(233,528)(234,527)(235,526)(236,525)(237,524)(238,523)(239,522)(240,521)
(241,520)(242,519)(243,518)(244,517)(245,516)(246,515)(247,514)(248,513)
(249,512)(250,511)(251,510)(252,509)(253,508)(254,507)(255,506)(256,505)
(257,504)(258,503)(259,502)(260,501)(261,500)(262,499)(263,498)(264,497)
(265,496)(266,495)(267,494)(268,493)(269,492)(270,491)(271,490)(272,489)
(273,488)(274,487)(275,486)(276,485)(277,484)(278,483)(279,482)(280,481)
(281,480)(282,479)(283,478)(284,477)(285,476)(286,475)(287,474)(288,473)
(289,472)(290,471)(291,470)(292,469)(293,468)(294,467)(295,466)(296,465)
(297,464)(298,463)(299,462)(300,461)(301,460)(302,459)(303,458)(304,457)
(305,456)(306,455)(307,454)(308,453)(309,452)(310,451)(311,450)(312,449)
(313,448)(314,447)(315,446)(316,445)(317,444)(318,443)(319,442)(320,441)
(321,440)(322,439)(323,438)(324,437)(325,436)(326,435)(327,434)(328,433)
(329,432)(330,431)(331,430)(332,429)(333,428)(334,427)(335,426)(336,425)
(337,424)(338,423)(339,422)(340,421)(341,420)(342,419)(343,418)(344,417)
(345,416)(346,415)(347,414)(348,413)(349,412)(350,411)(351,410)(352,409)
(353,408)(354,407)(355,406)(356,405)(357,404)(358,403)(359,402)(360,401)
(361,400)(362,399)(363,398)(364,397)(365,396)(366,395)(367,394)(368,393)
(369,392)(370,391)(371,390)(372,389)(373,388)(374,387)(375,386)(376,385)
(377,384)(378,383)(379,382);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(758)!(  2,379)(  3,378)(  4,377)(  5,376)(  6,375)(  7,374)(  8,373)
(  9,372)( 10,371)( 11,370)( 12,369)( 13,368)( 14,367)( 15,366)( 16,365)
( 17,364)( 18,363)( 19,362)( 20,361)( 21,360)( 22,359)( 23,358)( 24,357)
( 25,356)( 26,355)( 27,354)( 28,353)( 29,352)( 30,351)( 31,350)( 32,349)
( 33,348)( 34,347)( 35,346)( 36,345)( 37,344)( 38,343)( 39,342)( 40,341)
( 41,340)( 42,339)( 43,338)( 44,337)( 45,336)( 46,335)( 47,334)( 48,333)
( 49,332)( 50,331)( 51,330)( 52,329)( 53,328)( 54,327)( 55,326)( 56,325)
( 57,324)( 58,323)( 59,322)( 60,321)( 61,320)( 62,319)( 63,318)( 64,317)
( 65,316)( 66,315)( 67,314)( 68,313)( 69,312)( 70,311)( 71,310)( 72,309)
( 73,308)( 74,307)( 75,306)( 76,305)( 77,304)( 78,303)( 79,302)( 80,301)
( 81,300)( 82,299)( 83,298)( 84,297)( 85,296)( 86,295)( 87,294)( 88,293)
( 89,292)( 90,291)( 91,290)( 92,289)( 93,288)( 94,287)( 95,286)( 96,285)
( 97,284)( 98,283)( 99,282)(100,281)(101,280)(102,279)(103,278)(104,277)
(105,276)(106,275)(107,274)(108,273)(109,272)(110,271)(111,270)(112,269)
(113,268)(114,267)(115,266)(116,265)(117,264)(118,263)(119,262)(120,261)
(121,260)(122,259)(123,258)(124,257)(125,256)(126,255)(127,254)(128,253)
(129,252)(130,251)(131,250)(132,249)(133,248)(134,247)(135,246)(136,245)
(137,244)(138,243)(139,242)(140,241)(141,240)(142,239)(143,238)(144,237)
(145,236)(146,235)(147,234)(148,233)(149,232)(150,231)(151,230)(152,229)
(153,228)(154,227)(155,226)(156,225)(157,224)(158,223)(159,222)(160,221)
(161,220)(162,219)(163,218)(164,217)(165,216)(166,215)(167,214)(168,213)
(169,212)(170,211)(171,210)(172,209)(173,208)(174,207)(175,206)(176,205)
(177,204)(178,203)(179,202)(180,201)(181,200)(182,199)(183,198)(184,197)
(185,196)(186,195)(187,194)(188,193)(189,192)(190,191)(381,758)(382,757)
(383,756)(384,755)(385,754)(386,753)(387,752)(388,751)(389,750)(390,749)
(391,748)(392,747)(393,746)(394,745)(395,744)(396,743)(397,742)(398,741)
(399,740)(400,739)(401,738)(402,737)(403,736)(404,735)(405,734)(406,733)
(407,732)(408,731)(409,730)(410,729)(411,728)(412,727)(413,726)(414,725)
(415,724)(416,723)(417,722)(418,721)(419,720)(420,719)(421,718)(422,717)
(423,716)(424,715)(425,714)(426,713)(427,712)(428,711)(429,710)(430,709)
(431,708)(432,707)(433,706)(434,705)(435,704)(436,703)(437,702)(438,701)
(439,700)(440,699)(441,698)(442,697)(443,696)(444,695)(445,694)(446,693)
(447,692)(448,691)(449,690)(450,689)(451,688)(452,687)(453,686)(454,685)
(455,684)(456,683)(457,682)(458,681)(459,680)(460,679)(461,678)(462,677)
(463,676)(464,675)(465,674)(466,673)(467,672)(468,671)(469,670)(470,669)
(471,668)(472,667)(473,666)(474,665)(475,664)(476,663)(477,662)(478,661)
(479,660)(480,659)(481,658)(482,657)(483,656)(484,655)(485,654)(486,653)
(487,652)(488,651)(489,650)(490,649)(491,648)(492,647)(493,646)(494,645)
(495,644)(496,643)(497,642)(498,641)(499,640)(500,639)(501,638)(502,637)
(503,636)(504,635)(505,634)(506,633)(507,632)(508,631)(509,630)(510,629)
(511,628)(512,627)(513,626)(514,625)(515,624)(516,623)(517,622)(518,621)
(519,620)(520,619)(521,618)(522,617)(523,616)(524,615)(525,614)(526,613)
(527,612)(528,611)(529,610)(530,609)(531,608)(532,607)(533,606)(534,605)
(535,604)(536,603)(537,602)(538,601)(539,600)(540,599)(541,598)(542,597)
(543,596)(544,595)(545,594)(546,593)(547,592)(548,591)(549,590)(550,589)
(551,588)(552,587)(553,586)(554,585)(555,584)(556,583)(557,582)(558,581)
(559,580)(560,579)(561,578)(562,577)(563,576)(564,575)(565,574)(566,573)
(567,572)(568,571)(569,570);
s1 := Sym(758)!(  1,381)(  2,380)(  3,758)(  4,757)(  5,756)(  6,755)(  7,754)
(  8,753)(  9,752)( 10,751)( 11,750)( 12,749)( 13,748)( 14,747)( 15,746)
( 16,745)( 17,744)( 18,743)( 19,742)( 20,741)( 21,740)( 22,739)( 23,738)
( 24,737)( 25,736)( 26,735)( 27,734)( 28,733)( 29,732)( 30,731)( 31,730)
( 32,729)( 33,728)( 34,727)( 35,726)( 36,725)( 37,724)( 38,723)( 39,722)
( 40,721)( 41,720)( 42,719)( 43,718)( 44,717)( 45,716)( 46,715)( 47,714)
( 48,713)( 49,712)( 50,711)( 51,710)( 52,709)( 53,708)( 54,707)( 55,706)
( 56,705)( 57,704)( 58,703)( 59,702)( 60,701)( 61,700)( 62,699)( 63,698)
( 64,697)( 65,696)( 66,695)( 67,694)( 68,693)( 69,692)( 70,691)( 71,690)
( 72,689)( 73,688)( 74,687)( 75,686)( 76,685)( 77,684)( 78,683)( 79,682)
( 80,681)( 81,680)( 82,679)( 83,678)( 84,677)( 85,676)( 86,675)( 87,674)
( 88,673)( 89,672)( 90,671)( 91,670)( 92,669)( 93,668)( 94,667)( 95,666)
( 96,665)( 97,664)( 98,663)( 99,662)(100,661)(101,660)(102,659)(103,658)
(104,657)(105,656)(106,655)(107,654)(108,653)(109,652)(110,651)(111,650)
(112,649)(113,648)(114,647)(115,646)(116,645)(117,644)(118,643)(119,642)
(120,641)(121,640)(122,639)(123,638)(124,637)(125,636)(126,635)(127,634)
(128,633)(129,632)(130,631)(131,630)(132,629)(133,628)(134,627)(135,626)
(136,625)(137,624)(138,623)(139,622)(140,621)(141,620)(142,619)(143,618)
(144,617)(145,616)(146,615)(147,614)(148,613)(149,612)(150,611)(151,610)
(152,609)(153,608)(154,607)(155,606)(156,605)(157,604)(158,603)(159,602)
(160,601)(161,600)(162,599)(163,598)(164,597)(165,596)(166,595)(167,594)
(168,593)(169,592)(170,591)(171,590)(172,589)(173,588)(174,587)(175,586)
(176,585)(177,584)(178,583)(179,582)(180,581)(181,580)(182,579)(183,578)
(184,577)(185,576)(186,575)(187,574)(188,573)(189,572)(190,571)(191,570)
(192,569)(193,568)(194,567)(195,566)(196,565)(197,564)(198,563)(199,562)
(200,561)(201,560)(202,559)(203,558)(204,557)(205,556)(206,555)(207,554)
(208,553)(209,552)(210,551)(211,550)(212,549)(213,548)(214,547)(215,546)
(216,545)(217,544)(218,543)(219,542)(220,541)(221,540)(222,539)(223,538)
(224,537)(225,536)(226,535)(227,534)(228,533)(229,532)(230,531)(231,530)
(232,529)(233,528)(234,527)(235,526)(236,525)(237,524)(238,523)(239,522)
(240,521)(241,520)(242,519)(243,518)(244,517)(245,516)(246,515)(247,514)
(248,513)(249,512)(250,511)(251,510)(252,509)(253,508)(254,507)(255,506)
(256,505)(257,504)(258,503)(259,502)(260,501)(261,500)(262,499)(263,498)
(264,497)(265,496)(266,495)(267,494)(268,493)(269,492)(270,491)(271,490)
(272,489)(273,488)(274,487)(275,486)(276,485)(277,484)(278,483)(279,482)
(280,481)(281,480)(282,479)(283,478)(284,477)(285,476)(286,475)(287,474)
(288,473)(289,472)(290,471)(291,470)(292,469)(293,468)(294,467)(295,466)
(296,465)(297,464)(298,463)(299,462)(300,461)(301,460)(302,459)(303,458)
(304,457)(305,456)(306,455)(307,454)(308,453)(309,452)(310,451)(311,450)
(312,449)(313,448)(314,447)(315,446)(316,445)(317,444)(318,443)(319,442)
(320,441)(321,440)(322,439)(323,438)(324,437)(325,436)(326,435)(327,434)
(328,433)(329,432)(330,431)(331,430)(332,429)(333,428)(334,427)(335,426)
(336,425)(337,424)(338,423)(339,422)(340,421)(341,420)(342,419)(343,418)
(344,417)(345,416)(346,415)(347,414)(348,413)(349,412)(350,411)(351,410)
(352,409)(353,408)(354,407)(355,406)(356,405)(357,404)(358,403)(359,402)
(360,401)(361,400)(362,399)(363,398)(364,397)(365,396)(366,395)(367,394)
(368,393)(369,392)(370,391)(371,390)(372,389)(373,388)(374,387)(375,386)
(376,385)(377,384)(378,383)(379,382);
poly := sub<Sym(758)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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