Polytope of Type {746}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {746}*1492
Also Known As : 746-gon, {746}. if this polytope has another name.
Group : SmallGroup(1492,4)
Rank : 2
Schlafli Type : {746}
Number of vertices, edges, etc : 746, 746
Order of s₀s₁ : 746
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 : {373}*746
   373-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope