Polytope of Type {16,62}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,62}*1984
Also Known As : {16,62|2}. if this polytope has another name.
Group : SmallGroup(1984,968)
Rank : 3
Schlafli Type : {16,62}
Number of vertices, edges, etc : 16, 496, 62
Order of s₀s₁s₂ : 496
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
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 : {8,62}*992
   4-fold quotients : {4,62}*496
   8-fold quotients : {2,62}*248
   16-fold quotients : {2,31}*124
   31-fold quotients : {16,2}*64
   62-fold quotients : {8,2}*32
   124-fold quotients : {4,2}*16
   248-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 63, 94)( 64, 95)( 65, 96)( 66, 97)( 67, 98)( 68, 99)( 69,100)( 70,101)
( 71,102)( 72,103)( 73,104)( 74,105)( 75,106)( 76,107)( 77,108)( 78,109)
( 79,110)( 80,111)( 81,112)( 82,113)( 83,114)( 84,115)( 85,116)( 86,117)
( 87,118)( 88,119)( 89,120)( 90,121)( 91,122)( 92,123)( 93,124)(125,187)
(126,188)(127,189)(128,190)(129,191)(130,192)(131,193)(132,194)(133,195)
(134,196)(135,197)(136,198)(137,199)(138,200)(139,201)(140,202)(141,203)
(142,204)(143,205)(144,206)(145,207)(146,208)(147,209)(148,210)(149,211)
(150,212)(151,213)(152,214)(153,215)(154,216)(155,217)(156,218)(157,219)
(158,220)(159,221)(160,222)(161,223)(162,224)(163,225)(164,226)(165,227)
(166,228)(167,229)(168,230)(169,231)(170,232)(171,233)(172,234)(173,235)
(174,236)(175,237)(176,238)(177,239)(178,240)(179,241)(180,242)(181,243)
(182,244)(183,245)(184,246)(185,247)(186,248)(311,342)(312,343)(313,344)
(314,345)(315,346)(316,347)(317,348)(318,349)(319,350)(320,351)(321,352)
(322,353)(323,354)(324,355)(325,356)(326,357)(327,358)(328,359)(329,360)
(330,361)(331,362)(332,363)(333,364)(334,365)(335,366)(336,367)(337,368)
(338,369)(339,370)(340,371)(341,372)(373,435)(374,436)(375,437)(376,438)
(377,439)(378,440)(379,441)(380,442)(381,443)(382,444)(383,445)(384,446)
(385,447)(386,448)(387,449)(388,450)(389,451)(390,452)(391,453)(392,454)
(393,455)(394,456)(395,457)(396,458)(397,459)(398,460)(399,461)(400,462)
(401,463)(402,464)(403,465)(404,466)(405,467)(406,468)(407,469)(408,470)
(409,471)(410,472)(411,473)(412,474)(413,475)(414,476)(415,477)(416,478)
(417,479)(418,480)(419,481)(420,482)(421,483)(422,484)(423,485)(424,486)
(425,487)(426,488)(427,489)(428,490)(429,491)(430,492)(431,493)(432,494)
(433,495)(434,496)(497,621)(498,622)(499,623)(500,624)(501,625)(502,626)
(503,627)(504,628)(505,629)(506,630)(507,631)(508,632)(509,633)(510,634)
(511,635)(512,636)(513,637)(514,638)(515,639)(516,640)(517,641)(518,642)
(519,643)(520,644)(521,645)(522,646)(523,647)(524,648)(525,649)(526,650)
(527,651)(528,652)(529,653)(530,654)(531,655)(532,656)(533,657)(534,658)
(535,659)(536,660)(537,661)(538,662)(539,663)(540,664)(541,665)(542,666)
(543,667)(544,668)(545,669)(546,670)(547,671)(548,672)(549,673)(550,674)
(551,675)(552,676)(553,677)(554,678)(555,679)(556,680)(557,681)(558,682)
(559,714)(560,715)(561,716)(562,717)(563,718)(564,719)(565,720)(566,721)
(567,722)(568,723)(569,724)(570,725)(571,726)(572,727)(573,728)(574,729)
(575,730)(576,731)(577,732)(578,733)(579,734)(580,735)(581,736)(582,737)
(583,738)(584,739)(585,740)(586,741)(587,742)(588,743)(589,744)(590,683)
(591,684)(592,685)(593,686)(594,687)(595,688)(596,689)(597,690)(598,691)
(599,692)(600,693)(601,694)(602,695)(603,696)(604,697)(605,698)(606,699)
(607,700)(608,701)(609,702)(610,703)(611,704)(612,705)(613,706)(614,707)
(615,708)(616,709)(617,710)(618,711)(619,712)(620,713)(745,869)(746,870)
(747,871)(748,872)(749,873)(750,874)(751,875)(752,876)(753,877)(754,878)
(755,879)(756,880)(757,881)(758,882)(759,883)(760,884)(761,885)(762,886)
(763,887)(764,888)(765,889)(766,890)(767,891)(768,892)(769,893)(770,894)
(771,895)(772,896)(773,897)(774,898)(775,899)(776,900)(777,901)(778,902)
(779,903)(780,904)(781,905)(782,906)(783,907)(784,908)(785,909)(786,910)
(787,911)(788,912)(789,913)(790,914)(791,915)(792,916)(793,917)(794,918)
(795,919)(796,920)(797,921)(798,922)(799,923)(800,924)(801,925)(802,926)
(803,927)(804,928)(805,929)(806,930)(807,962)(808,963)(809,964)(810,965)
(811,966)(812,967)(813,968)(814,969)(815,970)(816,971)(817,972)(818,973)
(819,974)(820,975)(821,976)(822,977)(823,978)(824,979)(825,980)(826,981)
(827,982)(828,983)(829,984)(830,985)(831,986)(832,987)(833,988)(834,989)
(835,990)(836,991)(837,992)(838,931)(839,932)(840,933)(841,934)(842,935)
(843,936)(844,937)(845,938)(846,939)(847,940)(848,941)(849,942)(850,943)
(851,944)(852,945)(853,946)(854,947)(855,948)(856,949)(857,950)(858,951)
(859,952)(860,953)(861,954)(862,955)(863,956)(864,957)(865,958)(866,959)
(867,960)(868,961);;
s1 := (  1,745)(  2,775)(  3,774)(  4,773)(  5,772)(  6,771)(  7,770)(  8,769)
(  9,768)( 10,767)( 11,766)( 12,765)( 13,764)( 14,763)( 15,762)( 16,761)
( 17,760)( 18,759)( 19,758)( 20,757)( 21,756)( 22,755)( 23,754)( 24,753)
( 25,752)( 26,751)( 27,750)( 28,749)( 29,748)( 30,747)( 31,746)( 32,776)
( 33,806)( 34,805)( 35,804)( 36,803)( 37,802)( 38,801)( 39,800)( 40,799)
( 41,798)( 42,797)( 43,796)( 44,795)( 45,794)( 46,793)( 47,792)( 48,791)
( 49,790)( 50,789)( 51,788)( 52,787)( 53,786)( 54,785)( 55,784)( 56,783)
( 57,782)( 58,781)( 59,780)( 60,779)( 61,778)( 62,777)( 63,838)( 64,868)
( 65,867)( 66,866)( 67,865)( 68,864)( 69,863)( 70,862)( 71,861)( 72,860)
( 73,859)( 74,858)( 75,857)( 76,856)( 77,855)( 78,854)( 79,853)( 80,852)
( 81,851)( 82,850)( 83,849)( 84,848)( 85,847)( 86,846)( 87,845)( 88,844)
( 89,843)( 90,842)( 91,841)( 92,840)( 93,839)( 94,807)( 95,837)( 96,836)
( 97,835)( 98,834)( 99,833)(100,832)(101,831)(102,830)(103,829)(104,828)
(105,827)(106,826)(107,825)(108,824)(109,823)(110,822)(111,821)(112,820)
(113,819)(114,818)(115,817)(116,816)(117,815)(118,814)(119,813)(120,812)
(121,811)(122,810)(123,809)(124,808)(125,931)(126,961)(127,960)(128,959)
(129,958)(130,957)(131,956)(132,955)(133,954)(134,953)(135,952)(136,951)
(137,950)(138,949)(139,948)(140,947)(141,946)(142,945)(143,944)(144,943)
(145,942)(146,941)(147,940)(148,939)(149,938)(150,937)(151,936)(152,935)
(153,934)(154,933)(155,932)(156,962)(157,992)(158,991)(159,990)(160,989)
(161,988)(162,987)(163,986)(164,985)(165,984)(166,983)(167,982)(168,981)
(169,980)(170,979)(171,978)(172,977)(173,976)(174,975)(175,974)(176,973)
(177,972)(178,971)(179,970)(180,969)(181,968)(182,967)(183,966)(184,965)
(185,964)(186,963)(187,869)(188,899)(189,898)(190,897)(191,896)(192,895)
(193,894)(194,893)(195,892)(196,891)(197,890)(198,889)(199,888)(200,887)
(201,886)(202,885)(203,884)(204,883)(205,882)(206,881)(207,880)(208,879)
(209,878)(210,877)(211,876)(212,875)(213,874)(214,873)(215,872)(216,871)
(217,870)(218,900)(219,930)(220,929)(221,928)(222,927)(223,926)(224,925)
(225,924)(226,923)(227,922)(228,921)(229,920)(230,919)(231,918)(232,917)
(233,916)(234,915)(235,914)(236,913)(237,912)(238,911)(239,910)(240,909)
(241,908)(242,907)(243,906)(244,905)(245,904)(246,903)(247,902)(248,901)
(249,497)(250,527)(251,526)(252,525)(253,524)(254,523)(255,522)(256,521)
(257,520)(258,519)(259,518)(260,517)(261,516)(262,515)(263,514)(264,513)
(265,512)(266,511)(267,510)(268,509)(269,508)(270,507)(271,506)(272,505)
(273,504)(274,503)(275,502)(276,501)(277,500)(278,499)(279,498)(280,528)
(281,558)(282,557)(283,556)(284,555)(285,554)(286,553)(287,552)(288,551)
(289,550)(290,549)(291,548)(292,547)(293,546)(294,545)(295,544)(296,543)
(297,542)(298,541)(299,540)(300,539)(301,538)(302,537)(303,536)(304,535)
(305,534)(306,533)(307,532)(308,531)(309,530)(310,529)(311,590)(312,620)
(313,619)(314,618)(315,617)(316,616)(317,615)(318,614)(319,613)(320,612)
(321,611)(322,610)(323,609)(324,608)(325,607)(326,606)(327,605)(328,604)
(329,603)(330,602)(331,601)(332,600)(333,599)(334,598)(335,597)(336,596)
(337,595)(338,594)(339,593)(340,592)(341,591)(342,559)(343,589)(344,588)
(345,587)(346,586)(347,585)(348,584)(349,583)(350,582)(351,581)(352,580)
(353,579)(354,578)(355,577)(356,576)(357,575)(358,574)(359,573)(360,572)
(361,571)(362,570)(363,569)(364,568)(365,567)(366,566)(367,565)(368,564)
(369,563)(370,562)(371,561)(372,560)(373,683)(374,713)(375,712)(376,711)
(377,710)(378,709)(379,708)(380,707)(381,706)(382,705)(383,704)(384,703)
(385,702)(386,701)(387,700)(388,699)(389,698)(390,697)(391,696)(392,695)
(393,694)(394,693)(395,692)(396,691)(397,690)(398,689)(399,688)(400,687)
(401,686)(402,685)(403,684)(404,714)(405,744)(406,743)(407,742)(408,741)
(409,740)(410,739)(411,738)(412,737)(413,736)(414,735)(415,734)(416,733)
(417,732)(418,731)(419,730)(420,729)(421,728)(422,727)(423,726)(424,725)
(425,724)(426,723)(427,722)(428,721)(429,720)(430,719)(431,718)(432,717)
(433,716)(434,715)(435,621)(436,651)(437,650)(438,649)(439,648)(440,647)
(441,646)(442,645)(443,644)(444,643)(445,642)(446,641)(447,640)(448,639)
(449,638)(450,637)(451,636)(452,635)(453,634)(454,633)(455,632)(456,631)
(457,630)(458,629)(459,628)(460,627)(461,626)(462,625)(463,624)(464,623)
(465,622)(466,652)(467,682)(468,681)(469,680)(470,679)(471,678)(472,677)
(473,676)(474,675)(475,674)(476,673)(477,672)(478,671)(479,670)(480,669)
(481,668)(482,667)(483,666)(484,665)(485,664)(486,663)(487,662)(488,661)
(489,660)(490,659)(491,658)(492,657)(493,656)(494,655)(495,654)(496,653);;
s2 := (  1,250)(  2,249)(  3,279)(  4,278)(  5,277)(  6,276)(  7,275)(  8,274)
(  9,273)( 10,272)( 11,271)( 12,270)( 13,269)( 14,268)( 15,267)( 16,266)
( 17,265)( 18,264)( 19,263)( 20,262)( 21,261)( 22,260)( 23,259)( 24,258)
( 25,257)( 26,256)( 27,255)( 28,254)( 29,253)( 30,252)( 31,251)( 32,281)
( 33,280)( 34,310)( 35,309)( 36,308)( 37,307)( 38,306)( 39,305)( 40,304)
( 41,303)( 42,302)( 43,301)( 44,300)( 45,299)( 46,298)( 47,297)( 48,296)
( 49,295)( 50,294)( 51,293)( 52,292)( 53,291)( 54,290)( 55,289)( 56,288)
( 57,287)( 58,286)( 59,285)( 60,284)( 61,283)( 62,282)( 63,312)( 64,311)
( 65,341)( 66,340)( 67,339)( 68,338)( 69,337)( 70,336)( 71,335)( 72,334)
( 73,333)( 74,332)( 75,331)( 76,330)( 77,329)( 78,328)( 79,327)( 80,326)
( 81,325)( 82,324)( 83,323)( 84,322)( 85,321)( 86,320)( 87,319)( 88,318)
( 89,317)( 90,316)( 91,315)( 92,314)( 93,313)( 94,343)( 95,342)( 96,372)
( 97,371)( 98,370)( 99,369)(100,368)(101,367)(102,366)(103,365)(104,364)
(105,363)(106,362)(107,361)(108,360)(109,359)(110,358)(111,357)(112,356)
(113,355)(114,354)(115,353)(116,352)(117,351)(118,350)(119,349)(120,348)
(121,347)(122,346)(123,345)(124,344)(125,374)(126,373)(127,403)(128,402)
(129,401)(130,400)(131,399)(132,398)(133,397)(134,396)(135,395)(136,394)
(137,393)(138,392)(139,391)(140,390)(141,389)(142,388)(143,387)(144,386)
(145,385)(146,384)(147,383)(148,382)(149,381)(150,380)(151,379)(152,378)
(153,377)(154,376)(155,375)(156,405)(157,404)(158,434)(159,433)(160,432)
(161,431)(162,430)(163,429)(164,428)(165,427)(166,426)(167,425)(168,424)
(169,423)(170,422)(171,421)(172,420)(173,419)(174,418)(175,417)(176,416)
(177,415)(178,414)(179,413)(180,412)(181,411)(182,410)(183,409)(184,408)
(185,407)(186,406)(187,436)(188,435)(189,465)(190,464)(191,463)(192,462)
(193,461)(194,460)(195,459)(196,458)(197,457)(198,456)(199,455)(200,454)
(201,453)(202,452)(203,451)(204,450)(205,449)(206,448)(207,447)(208,446)
(209,445)(210,444)(211,443)(212,442)(213,441)(214,440)(215,439)(216,438)
(217,437)(218,467)(219,466)(220,496)(221,495)(222,494)(223,493)(224,492)
(225,491)(226,490)(227,489)(228,488)(229,487)(230,486)(231,485)(232,484)
(233,483)(234,482)(235,481)(236,480)(237,479)(238,478)(239,477)(240,476)
(241,475)(242,474)(243,473)(244,472)(245,471)(246,470)(247,469)(248,468)
(497,746)(498,745)(499,775)(500,774)(501,773)(502,772)(503,771)(504,770)
(505,769)(506,768)(507,767)(508,766)(509,765)(510,764)(511,763)(512,762)
(513,761)(514,760)(515,759)(516,758)(517,757)(518,756)(519,755)(520,754)
(521,753)(522,752)(523,751)(524,750)(525,749)(526,748)(527,747)(528,777)
(529,776)(530,806)(531,805)(532,804)(533,803)(534,802)(535,801)(536,800)
(537,799)(538,798)(539,797)(540,796)(541,795)(542,794)(543,793)(544,792)
(545,791)(546,790)(547,789)(548,788)(549,787)(550,786)(551,785)(552,784)
(553,783)(554,782)(555,781)(556,780)(557,779)(558,778)(559,808)(560,807)
(561,837)(562,836)(563,835)(564,834)(565,833)(566,832)(567,831)(568,830)
(569,829)(570,828)(571,827)(572,826)(573,825)(574,824)(575,823)(576,822)
(577,821)(578,820)(579,819)(580,818)(581,817)(582,816)(583,815)(584,814)
(585,813)(586,812)(587,811)(588,810)(589,809)(590,839)(591,838)(592,868)
(593,867)(594,866)(595,865)(596,864)(597,863)(598,862)(599,861)(600,860)
(601,859)(602,858)(603,857)(604,856)(605,855)(606,854)(607,853)(608,852)
(609,851)(610,850)(611,849)(612,848)(613,847)(614,846)(615,845)(616,844)
(617,843)(618,842)(619,841)(620,840)(621,870)(622,869)(623,899)(624,898)
(625,897)(626,896)(627,895)(628,894)(629,893)(630,892)(631,891)(632,890)
(633,889)(634,888)(635,887)(636,886)(637,885)(638,884)(639,883)(640,882)
(641,881)(642,880)(643,879)(644,878)(645,877)(646,876)(647,875)(648,874)
(649,873)(650,872)(651,871)(652,901)(653,900)(654,930)(655,929)(656,928)
(657,927)(658,926)(659,925)(660,924)(661,923)(662,922)(663,921)(664,920)
(665,919)(666,918)(667,917)(668,916)(669,915)(670,914)(671,913)(672,912)
(673,911)(674,910)(675,909)(676,908)(677,907)(678,906)(679,905)(680,904)
(681,903)(682,902)(683,932)(684,931)(685,961)(686,960)(687,959)(688,958)
(689,957)(690,956)(691,955)(692,954)(693,953)(694,952)(695,951)(696,950)
(697,949)(698,948)(699,947)(700,946)(701,945)(702,944)(703,943)(704,942)
(705,941)(706,940)(707,939)(708,938)(709,937)(710,936)(711,935)(712,934)
(713,933)(714,963)(715,962)(716,992)(717,991)(718,990)(719,989)(720,988)
(721,987)(722,986)(723,985)(724,984)(725,983)(726,982)(727,981)(728,980)
(729,979)(730,978)(731,977)(732,976)(733,975)(734,974)(735,973)(736,972)
(737,971)(738,970)(739,969)(740,968)(741,967)(742,966)(743,965)(744,964);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(992)!( 63, 94)( 64, 95)( 65, 96)( 66, 97)( 67, 98)( 68, 99)( 69,100)
( 70,101)( 71,102)( 72,103)( 73,104)( 74,105)( 75,106)( 76,107)( 77,108)
( 78,109)( 79,110)( 80,111)( 81,112)( 82,113)( 83,114)( 84,115)( 85,116)
( 86,117)( 87,118)( 88,119)( 89,120)( 90,121)( 91,122)( 92,123)( 93,124)
(125,187)(126,188)(127,189)(128,190)(129,191)(130,192)(131,193)(132,194)
(133,195)(134,196)(135,197)(136,198)(137,199)(138,200)(139,201)(140,202)
(141,203)(142,204)(143,205)(144,206)(145,207)(146,208)(147,209)(148,210)
(149,211)(150,212)(151,213)(152,214)(153,215)(154,216)(155,217)(156,218)
(157,219)(158,220)(159,221)(160,222)(161,223)(162,224)(163,225)(164,226)
(165,227)(166,228)(167,229)(168,230)(169,231)(170,232)(171,233)(172,234)
(173,235)(174,236)(175,237)(176,238)(177,239)(178,240)(179,241)(180,242)
(181,243)(182,244)(183,245)(184,246)(185,247)(186,248)(311,342)(312,343)
(313,344)(314,345)(315,346)(316,347)(317,348)(318,349)(319,350)(320,351)
(321,352)(322,353)(323,354)(324,355)(325,356)(326,357)(327,358)(328,359)
(329,360)(330,361)(331,362)(332,363)(333,364)(334,365)(335,366)(336,367)
(337,368)(338,369)(339,370)(340,371)(341,372)(373,435)(374,436)(375,437)
(376,438)(377,439)(378,440)(379,441)(380,442)(381,443)(382,444)(383,445)
(384,446)(385,447)(386,448)(387,449)(388,450)(389,451)(390,452)(391,453)
(392,454)(393,455)(394,456)(395,457)(396,458)(397,459)(398,460)(399,461)
(400,462)(401,463)(402,464)(403,465)(404,466)(405,467)(406,468)(407,469)
(408,470)(409,471)(410,472)(411,473)(412,474)(413,475)(414,476)(415,477)
(416,478)(417,479)(418,480)(419,481)(420,482)(421,483)(422,484)(423,485)
(424,486)(425,487)(426,488)(427,489)(428,490)(429,491)(430,492)(431,493)
(432,494)(433,495)(434,496)(497,621)(498,622)(499,623)(500,624)(501,625)
(502,626)(503,627)(504,628)(505,629)(506,630)(507,631)(508,632)(509,633)
(510,634)(511,635)(512,636)(513,637)(514,638)(515,639)(516,640)(517,641)
(518,642)(519,643)(520,644)(521,645)(522,646)(523,647)(524,648)(525,649)
(526,650)(527,651)(528,652)(529,653)(530,654)(531,655)(532,656)(533,657)
(534,658)(535,659)(536,660)(537,661)(538,662)(539,663)(540,664)(541,665)
(542,666)(543,667)(544,668)(545,669)(546,670)(547,671)(548,672)(549,673)
(550,674)(551,675)(552,676)(553,677)(554,678)(555,679)(556,680)(557,681)
(558,682)(559,714)(560,715)(561,716)(562,717)(563,718)(564,719)(565,720)
(566,721)(567,722)(568,723)(569,724)(570,725)(571,726)(572,727)(573,728)
(574,729)(575,730)(576,731)(577,732)(578,733)(579,734)(580,735)(581,736)
(582,737)(583,738)(584,739)(585,740)(586,741)(587,742)(588,743)(589,744)
(590,683)(591,684)(592,685)(593,686)(594,687)(595,688)(596,689)(597,690)
(598,691)(599,692)(600,693)(601,694)(602,695)(603,696)(604,697)(605,698)
(606,699)(607,700)(608,701)(609,702)(610,703)(611,704)(612,705)(613,706)
(614,707)(615,708)(616,709)(617,710)(618,711)(619,712)(620,713)(745,869)
(746,870)(747,871)(748,872)(749,873)(750,874)(751,875)(752,876)(753,877)
(754,878)(755,879)(756,880)(757,881)(758,882)(759,883)(760,884)(761,885)
(762,886)(763,887)(764,888)(765,889)(766,890)(767,891)(768,892)(769,893)
(770,894)(771,895)(772,896)(773,897)(774,898)(775,899)(776,900)(777,901)
(778,902)(779,903)(780,904)(781,905)(782,906)(783,907)(784,908)(785,909)
(786,910)(787,911)(788,912)(789,913)(790,914)(791,915)(792,916)(793,917)
(794,918)(795,919)(796,920)(797,921)(798,922)(799,923)(800,924)(801,925)
(802,926)(803,927)(804,928)(805,929)(806,930)(807,962)(808,963)(809,964)
(810,965)(811,966)(812,967)(813,968)(814,969)(815,970)(816,971)(817,972)
(818,973)(819,974)(820,975)(821,976)(822,977)(823,978)(824,979)(825,980)
(826,981)(827,982)(828,983)(829,984)(830,985)(831,986)(832,987)(833,988)
(834,989)(835,990)(836,991)(837,992)(838,931)(839,932)(840,933)(841,934)
(842,935)(843,936)(844,937)(845,938)(846,939)(847,940)(848,941)(849,942)
(850,943)(851,944)(852,945)(853,946)(854,947)(855,948)(856,949)(857,950)
(858,951)(859,952)(860,953)(861,954)(862,955)(863,956)(864,957)(865,958)
(866,959)(867,960)(868,961);
s1 := Sym(992)!(  1,745)(  2,775)(  3,774)(  4,773)(  5,772)(  6,771)(  7,770)
(  8,769)(  9,768)( 10,767)( 11,766)( 12,765)( 13,764)( 14,763)( 15,762)
( 16,761)( 17,760)( 18,759)( 19,758)( 20,757)( 21,756)( 22,755)( 23,754)
( 24,753)( 25,752)( 26,751)( 27,750)( 28,749)( 29,748)( 30,747)( 31,746)
( 32,776)( 33,806)( 34,805)( 35,804)( 36,803)( 37,802)( 38,801)( 39,800)
( 40,799)( 41,798)( 42,797)( 43,796)( 44,795)( 45,794)( 46,793)( 47,792)
( 48,791)( 49,790)( 50,789)( 51,788)( 52,787)( 53,786)( 54,785)( 55,784)
( 56,783)( 57,782)( 58,781)( 59,780)( 60,779)( 61,778)( 62,777)( 63,838)
( 64,868)( 65,867)( 66,866)( 67,865)( 68,864)( 69,863)( 70,862)( 71,861)
( 72,860)( 73,859)( 74,858)( 75,857)( 76,856)( 77,855)( 78,854)( 79,853)
( 80,852)( 81,851)( 82,850)( 83,849)( 84,848)( 85,847)( 86,846)( 87,845)
( 88,844)( 89,843)( 90,842)( 91,841)( 92,840)( 93,839)( 94,807)( 95,837)
( 96,836)( 97,835)( 98,834)( 99,833)(100,832)(101,831)(102,830)(103,829)
(104,828)(105,827)(106,826)(107,825)(108,824)(109,823)(110,822)(111,821)
(112,820)(113,819)(114,818)(115,817)(116,816)(117,815)(118,814)(119,813)
(120,812)(121,811)(122,810)(123,809)(124,808)(125,931)(126,961)(127,960)
(128,959)(129,958)(130,957)(131,956)(132,955)(133,954)(134,953)(135,952)
(136,951)(137,950)(138,949)(139,948)(140,947)(141,946)(142,945)(143,944)
(144,943)(145,942)(146,941)(147,940)(148,939)(149,938)(150,937)(151,936)
(152,935)(153,934)(154,933)(155,932)(156,962)(157,992)(158,991)(159,990)
(160,989)(161,988)(162,987)(163,986)(164,985)(165,984)(166,983)(167,982)
(168,981)(169,980)(170,979)(171,978)(172,977)(173,976)(174,975)(175,974)
(176,973)(177,972)(178,971)(179,970)(180,969)(181,968)(182,967)(183,966)
(184,965)(185,964)(186,963)(187,869)(188,899)(189,898)(190,897)(191,896)
(192,895)(193,894)(194,893)(195,892)(196,891)(197,890)(198,889)(199,888)
(200,887)(201,886)(202,885)(203,884)(204,883)(205,882)(206,881)(207,880)
(208,879)(209,878)(210,877)(211,876)(212,875)(213,874)(214,873)(215,872)
(216,871)(217,870)(218,900)(219,930)(220,929)(221,928)(222,927)(223,926)
(224,925)(225,924)(226,923)(227,922)(228,921)(229,920)(230,919)(231,918)
(232,917)(233,916)(234,915)(235,914)(236,913)(237,912)(238,911)(239,910)
(240,909)(241,908)(242,907)(243,906)(244,905)(245,904)(246,903)(247,902)
(248,901)(249,497)(250,527)(251,526)(252,525)(253,524)(254,523)(255,522)
(256,521)(257,520)(258,519)(259,518)(260,517)(261,516)(262,515)(263,514)
(264,513)(265,512)(266,511)(267,510)(268,509)(269,508)(270,507)(271,506)
(272,505)(273,504)(274,503)(275,502)(276,501)(277,500)(278,499)(279,498)
(280,528)(281,558)(282,557)(283,556)(284,555)(285,554)(286,553)(287,552)
(288,551)(289,550)(290,549)(291,548)(292,547)(293,546)(294,545)(295,544)
(296,543)(297,542)(298,541)(299,540)(300,539)(301,538)(302,537)(303,536)
(304,535)(305,534)(306,533)(307,532)(308,531)(309,530)(310,529)(311,590)
(312,620)(313,619)(314,618)(315,617)(316,616)(317,615)(318,614)(319,613)
(320,612)(321,611)(322,610)(323,609)(324,608)(325,607)(326,606)(327,605)
(328,604)(329,603)(330,602)(331,601)(332,600)(333,599)(334,598)(335,597)
(336,596)(337,595)(338,594)(339,593)(340,592)(341,591)(342,559)(343,589)
(344,588)(345,587)(346,586)(347,585)(348,584)(349,583)(350,582)(351,581)
(352,580)(353,579)(354,578)(355,577)(356,576)(357,575)(358,574)(359,573)
(360,572)(361,571)(362,570)(363,569)(364,568)(365,567)(366,566)(367,565)
(368,564)(369,563)(370,562)(371,561)(372,560)(373,683)(374,713)(375,712)
(376,711)(377,710)(378,709)(379,708)(380,707)(381,706)(382,705)(383,704)
(384,703)(385,702)(386,701)(387,700)(388,699)(389,698)(390,697)(391,696)
(392,695)(393,694)(394,693)(395,692)(396,691)(397,690)(398,689)(399,688)
(400,687)(401,686)(402,685)(403,684)(404,714)(405,744)(406,743)(407,742)
(408,741)(409,740)(410,739)(411,738)(412,737)(413,736)(414,735)(415,734)
(416,733)(417,732)(418,731)(419,730)(420,729)(421,728)(422,727)(423,726)
(424,725)(425,724)(426,723)(427,722)(428,721)(429,720)(430,719)(431,718)
(432,717)(433,716)(434,715)(435,621)(436,651)(437,650)(438,649)(439,648)
(440,647)(441,646)(442,645)(443,644)(444,643)(445,642)(446,641)(447,640)
(448,639)(449,638)(450,637)(451,636)(452,635)(453,634)(454,633)(455,632)
(456,631)(457,630)(458,629)(459,628)(460,627)(461,626)(462,625)(463,624)
(464,623)(465,622)(466,652)(467,682)(468,681)(469,680)(470,679)(471,678)
(472,677)(473,676)(474,675)(475,674)(476,673)(477,672)(478,671)(479,670)
(480,669)(481,668)(482,667)(483,666)(484,665)(485,664)(486,663)(487,662)
(488,661)(489,660)(490,659)(491,658)(492,657)(493,656)(494,655)(495,654)
(496,653);
s2 := Sym(992)!(  1,250)(  2,249)(  3,279)(  4,278)(  5,277)(  6,276)(  7,275)
(  8,274)(  9,273)( 10,272)( 11,271)( 12,270)( 13,269)( 14,268)( 15,267)
( 16,266)( 17,265)( 18,264)( 19,263)( 20,262)( 21,261)( 22,260)( 23,259)
( 24,258)( 25,257)( 26,256)( 27,255)( 28,254)( 29,253)( 30,252)( 31,251)
( 32,281)( 33,280)( 34,310)( 35,309)( 36,308)( 37,307)( 38,306)( 39,305)
( 40,304)( 41,303)( 42,302)( 43,301)( 44,300)( 45,299)( 46,298)( 47,297)
( 48,296)( 49,295)( 50,294)( 51,293)( 52,292)( 53,291)( 54,290)( 55,289)
( 56,288)( 57,287)( 58,286)( 59,285)( 60,284)( 61,283)( 62,282)( 63,312)
( 64,311)( 65,341)( 66,340)( 67,339)( 68,338)( 69,337)( 70,336)( 71,335)
( 72,334)( 73,333)( 74,332)( 75,331)( 76,330)( 77,329)( 78,328)( 79,327)
( 80,326)( 81,325)( 82,324)( 83,323)( 84,322)( 85,321)( 86,320)( 87,319)
( 88,318)( 89,317)( 90,316)( 91,315)( 92,314)( 93,313)( 94,343)( 95,342)
( 96,372)( 97,371)( 98,370)( 99,369)(100,368)(101,367)(102,366)(103,365)
(104,364)(105,363)(106,362)(107,361)(108,360)(109,359)(110,358)(111,357)
(112,356)(113,355)(114,354)(115,353)(116,352)(117,351)(118,350)(119,349)
(120,348)(121,347)(122,346)(123,345)(124,344)(125,374)(126,373)(127,403)
(128,402)(129,401)(130,400)(131,399)(132,398)(133,397)(134,396)(135,395)
(136,394)(137,393)(138,392)(139,391)(140,390)(141,389)(142,388)(143,387)
(144,386)(145,385)(146,384)(147,383)(148,382)(149,381)(150,380)(151,379)
(152,378)(153,377)(154,376)(155,375)(156,405)(157,404)(158,434)(159,433)
(160,432)(161,431)(162,430)(163,429)(164,428)(165,427)(166,426)(167,425)
(168,424)(169,423)(170,422)(171,421)(172,420)(173,419)(174,418)(175,417)
(176,416)(177,415)(178,414)(179,413)(180,412)(181,411)(182,410)(183,409)
(184,408)(185,407)(186,406)(187,436)(188,435)(189,465)(190,464)(191,463)
(192,462)(193,461)(194,460)(195,459)(196,458)(197,457)(198,456)(199,455)
(200,454)(201,453)(202,452)(203,451)(204,450)(205,449)(206,448)(207,447)
(208,446)(209,445)(210,444)(211,443)(212,442)(213,441)(214,440)(215,439)
(216,438)(217,437)(218,467)(219,466)(220,496)(221,495)(222,494)(223,493)
(224,492)(225,491)(226,490)(227,489)(228,488)(229,487)(230,486)(231,485)
(232,484)(233,483)(234,482)(235,481)(236,480)(237,479)(238,478)(239,477)
(240,476)(241,475)(242,474)(243,473)(244,472)(245,471)(246,470)(247,469)
(248,468)(497,746)(498,745)(499,775)(500,774)(501,773)(502,772)(503,771)
(504,770)(505,769)(506,768)(507,767)(508,766)(509,765)(510,764)(511,763)
(512,762)(513,761)(514,760)(515,759)(516,758)(517,757)(518,756)(519,755)
(520,754)(521,753)(522,752)(523,751)(524,750)(525,749)(526,748)(527,747)
(528,777)(529,776)(530,806)(531,805)(532,804)(533,803)(534,802)(535,801)
(536,800)(537,799)(538,798)(539,797)(540,796)(541,795)(542,794)(543,793)
(544,792)(545,791)(546,790)(547,789)(548,788)(549,787)(550,786)(551,785)
(552,784)(553,783)(554,782)(555,781)(556,780)(557,779)(558,778)(559,808)
(560,807)(561,837)(562,836)(563,835)(564,834)(565,833)(566,832)(567,831)
(568,830)(569,829)(570,828)(571,827)(572,826)(573,825)(574,824)(575,823)
(576,822)(577,821)(578,820)(579,819)(580,818)(581,817)(582,816)(583,815)
(584,814)(585,813)(586,812)(587,811)(588,810)(589,809)(590,839)(591,838)
(592,868)(593,867)(594,866)(595,865)(596,864)(597,863)(598,862)(599,861)
(600,860)(601,859)(602,858)(603,857)(604,856)(605,855)(606,854)(607,853)
(608,852)(609,851)(610,850)(611,849)(612,848)(613,847)(614,846)(615,845)
(616,844)(617,843)(618,842)(619,841)(620,840)(621,870)(622,869)(623,899)
(624,898)(625,897)(626,896)(627,895)(628,894)(629,893)(630,892)(631,891)
(632,890)(633,889)(634,888)(635,887)(636,886)(637,885)(638,884)(639,883)
(640,882)(641,881)(642,880)(643,879)(644,878)(645,877)(646,876)(647,875)
(648,874)(649,873)(650,872)(651,871)(652,901)(653,900)(654,930)(655,929)
(656,928)(657,927)(658,926)(659,925)(660,924)(661,923)(662,922)(663,921)
(664,920)(665,919)(666,918)(667,917)(668,916)(669,915)(670,914)(671,913)
(672,912)(673,911)(674,910)(675,909)(676,908)(677,907)(678,906)(679,905)
(680,904)(681,903)(682,902)(683,932)(684,931)(685,961)(686,960)(687,959)
(688,958)(689,957)(690,956)(691,955)(692,954)(693,953)(694,952)(695,951)
(696,950)(697,949)(698,948)(699,947)(700,946)(701,945)(702,944)(703,943)
(704,942)(705,941)(706,940)(707,939)(708,938)(709,937)(710,936)(711,935)
(712,934)(713,933)(714,963)(715,962)(716,992)(717,991)(718,990)(719,989)
(720,988)(721,987)(722,986)(723,985)(724,984)(725,983)(726,982)(727,981)
(728,980)(729,979)(730,978)(731,977)(732,976)(733,975)(734,974)(735,973)
(736,972)(737,971)(738,970)(739,969)(740,968)(741,967)(742,966)(743,965)
(744,964);
poly := sub<Sym(992)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope