Polytope of Type {4,62,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,62,4}*1984
Also Known As : {{4,62|2},{62,4|2}}. if this polytope has another name.
Group : SmallGroup(1984,1181)
Rank : 4
Schlafli Type : {4,62,4}
Number of vertices, edges, etc : 4, 124, 124, 4
Order of s0s1s2s3 : 124
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   Orientable
   Flat
   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 : {2,62,4}*992, {4,62,2}*992
   4-fold quotients : {2,62,2}*496
   8-fold quotients : {2,31,2}*248
   31-fold quotients : {4,2,4}*64
   62-fold quotients : {2,2,4}*32, {4,2,2}*32
   124-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,497)(  2,498)(  3,499)(  4,500)(  5,501)(  6,502)(  7,503)(  8,504)
(  9,505)( 10,506)( 11,507)( 12,508)( 13,509)( 14,510)( 15,511)( 16,512)
( 17,513)( 18,514)( 19,515)( 20,516)( 21,517)( 22,518)( 23,519)( 24,520)
( 25,521)( 26,522)( 27,523)( 28,524)( 29,525)( 30,526)( 31,527)( 32,528)
( 33,529)( 34,530)( 35,531)( 36,532)( 37,533)( 38,534)( 39,535)( 40,536)
( 41,537)( 42,538)( 43,539)( 44,540)( 45,541)( 46,542)( 47,543)( 48,544)
( 49,545)( 50,546)( 51,547)( 52,548)( 53,549)( 54,550)( 55,551)( 56,552)
( 57,553)( 58,554)( 59,555)( 60,556)( 61,557)( 62,558)( 63,559)( 64,560)
( 65,561)( 66,562)( 67,563)( 68,564)( 69,565)( 70,566)( 71,567)( 72,568)
( 73,569)( 74,570)( 75,571)( 76,572)( 77,573)( 78,574)( 79,575)( 80,576)
( 81,577)( 82,578)( 83,579)( 84,580)( 85,581)( 86,582)( 87,583)( 88,584)
( 89,585)( 90,586)( 91,587)( 92,588)( 93,589)( 94,590)( 95,591)( 96,592)
( 97,593)( 98,594)( 99,595)(100,596)(101,597)(102,598)(103,599)(104,600)
(105,601)(106,602)(107,603)(108,604)(109,605)(110,606)(111,607)(112,608)
(113,609)(114,610)(115,611)(116,612)(117,613)(118,614)(119,615)(120,616)
(121,617)(122,618)(123,619)(124,620)(125,683)(126,684)(127,685)(128,686)
(129,687)(130,688)(131,689)(132,690)(133,691)(134,692)(135,693)(136,694)
(137,695)(138,696)(139,697)(140,698)(141,699)(142,700)(143,701)(144,702)
(145,703)(146,704)(147,705)(148,706)(149,707)(150,708)(151,709)(152,710)
(153,711)(154,712)(155,713)(156,714)(157,715)(158,716)(159,717)(160,718)
(161,719)(162,720)(163,721)(164,722)(165,723)(166,724)(167,725)(168,726)
(169,727)(170,728)(171,729)(172,730)(173,731)(174,732)(175,733)(176,734)
(177,735)(178,736)(179,737)(180,738)(181,739)(182,740)(183,741)(184,742)
(185,743)(186,744)(187,621)(188,622)(189,623)(190,624)(191,625)(192,626)
(193,627)(194,628)(195,629)(196,630)(197,631)(198,632)(199,633)(200,634)
(201,635)(202,636)(203,637)(204,638)(205,639)(206,640)(207,641)(208,642)
(209,643)(210,644)(211,645)(212,646)(213,647)(214,648)(215,649)(216,650)
(217,651)(218,652)(219,653)(220,654)(221,655)(222,656)(223,657)(224,658)
(225,659)(226,660)(227,661)(228,662)(229,663)(230,664)(231,665)(232,666)
(233,667)(234,668)(235,669)(236,670)(237,671)(238,672)(239,673)(240,674)
(241,675)(242,676)(243,677)(244,678)(245,679)(246,680)(247,681)(248,682)
(249,745)(250,746)(251,747)(252,748)(253,749)(254,750)(255,751)(256,752)
(257,753)(258,754)(259,755)(260,756)(261,757)(262,758)(263,759)(264,760)
(265,761)(266,762)(267,763)(268,764)(269,765)(270,766)(271,767)(272,768)
(273,769)(274,770)(275,771)(276,772)(277,773)(278,774)(279,775)(280,776)
(281,777)(282,778)(283,779)(284,780)(285,781)(286,782)(287,783)(288,784)
(289,785)(290,786)(291,787)(292,788)(293,789)(294,790)(295,791)(296,792)
(297,793)(298,794)(299,795)(300,796)(301,797)(302,798)(303,799)(304,800)
(305,801)(306,802)(307,803)(308,804)(309,805)(310,806)(311,807)(312,808)
(313,809)(314,810)(315,811)(316,812)(317,813)(318,814)(319,815)(320,816)
(321,817)(322,818)(323,819)(324,820)(325,821)(326,822)(327,823)(328,824)
(329,825)(330,826)(331,827)(332,828)(333,829)(334,830)(335,831)(336,832)
(337,833)(338,834)(339,835)(340,836)(341,837)(342,838)(343,839)(344,840)
(345,841)(346,842)(347,843)(348,844)(349,845)(350,846)(351,847)(352,848)
(353,849)(354,850)(355,851)(356,852)(357,853)(358,854)(359,855)(360,856)
(361,857)(362,858)(363,859)(364,860)(365,861)(366,862)(367,863)(368,864)
(369,865)(370,866)(371,867)(372,868)(373,931)(374,932)(375,933)(376,934)
(377,935)(378,936)(379,937)(380,938)(381,939)(382,940)(383,941)(384,942)
(385,943)(386,944)(387,945)(388,946)(389,947)(390,948)(391,949)(392,950)
(393,951)(394,952)(395,953)(396,954)(397,955)(398,956)(399,957)(400,958)
(401,959)(402,960)(403,961)(404,962)(405,963)(406,964)(407,965)(408,966)
(409,967)(410,968)(411,969)(412,970)(413,971)(414,972)(415,973)(416,974)
(417,975)(418,976)(419,977)(420,978)(421,979)(422,980)(423,981)(424,982)
(425,983)(426,984)(427,985)(428,986)(429,987)(430,988)(431,989)(432,990)
(433,991)(434,992)(435,869)(436,870)(437,871)(438,872)(439,873)(440,874)
(441,875)(442,876)(443,877)(444,878)(445,879)(446,880)(447,881)(448,882)
(449,883)(450,884)(451,885)(452,886)(453,887)(454,888)(455,889)(456,890)
(457,891)(458,892)(459,893)(460,894)(461,895)(462,896)(463,897)(464,898)
(465,899)(466,900)(467,901)(468,902)(469,903)(470,904)(471,905)(472,906)
(473,907)(474,908)(475,909)(476,910)(477,911)(478,912)(479,913)(480,914)
(481,915)(482,916)(483,917)(484,918)(485,919)(486,920)(487,921)(488,922)
(489,923)(490,924)(491,925)(492,926)(493,927)(494,928)(495,929)(496,930);;
s1 := (  1,125)(  2,155)(  3,154)(  4,153)(  5,152)(  6,151)(  7,150)(  8,149)
(  9,148)( 10,147)( 11,146)( 12,145)( 13,144)( 14,143)( 15,142)( 16,141)
( 17,140)( 18,139)( 19,138)( 20,137)( 21,136)( 22,135)( 23,134)( 24,133)
( 25,132)( 26,131)( 27,130)( 28,129)( 29,128)( 30,127)( 31,126)( 32,156)
( 33,186)( 34,185)( 35,184)( 36,183)( 37,182)( 38,181)( 39,180)( 40,179)
( 41,178)( 42,177)( 43,176)( 44,175)( 45,174)( 46,173)( 47,172)( 48,171)
( 49,170)( 50,169)( 51,168)( 52,167)( 53,166)( 54,165)( 55,164)( 56,163)
( 57,162)( 58,161)( 59,160)( 60,159)( 61,158)( 62,157)( 63,187)( 64,217)
( 65,216)( 66,215)( 67,214)( 68,213)( 69,212)( 70,211)( 71,210)( 72,209)
( 73,208)( 74,207)( 75,206)( 76,205)( 77,204)( 78,203)( 79,202)( 80,201)
( 81,200)( 82,199)( 83,198)( 84,197)( 85,196)( 86,195)( 87,194)( 88,193)
( 89,192)( 90,191)( 91,190)( 92,189)( 93,188)( 94,218)( 95,248)( 96,247)
( 97,246)( 98,245)( 99,244)(100,243)(101,242)(102,241)(103,240)(104,239)
(105,238)(106,237)(107,236)(108,235)(109,234)(110,233)(111,232)(112,231)
(113,230)(114,229)(115,228)(116,227)(117,226)(118,225)(119,224)(120,223)
(121,222)(122,221)(123,220)(124,219)(249,373)(250,403)(251,402)(252,401)
(253,400)(254,399)(255,398)(256,397)(257,396)(258,395)(259,394)(260,393)
(261,392)(262,391)(263,390)(264,389)(265,388)(266,387)(267,386)(268,385)
(269,384)(270,383)(271,382)(272,381)(273,380)(274,379)(275,378)(276,377)
(277,376)(278,375)(279,374)(280,404)(281,434)(282,433)(283,432)(284,431)
(285,430)(286,429)(287,428)(288,427)(289,426)(290,425)(291,424)(292,423)
(293,422)(294,421)(295,420)(296,419)(297,418)(298,417)(299,416)(300,415)
(301,414)(302,413)(303,412)(304,411)(305,410)(306,409)(307,408)(308,407)
(309,406)(310,405)(311,435)(312,465)(313,464)(314,463)(315,462)(316,461)
(317,460)(318,459)(319,458)(320,457)(321,456)(322,455)(323,454)(324,453)
(325,452)(326,451)(327,450)(328,449)(329,448)(330,447)(331,446)(332,445)
(333,444)(334,443)(335,442)(336,441)(337,440)(338,439)(339,438)(340,437)
(341,436)(342,466)(343,496)(344,495)(345,494)(346,493)(347,492)(348,491)
(349,490)(350,489)(351,488)(352,487)(353,486)(354,485)(355,484)(356,483)
(357,482)(358,481)(359,480)(360,479)(361,478)(362,477)(363,476)(364,475)
(365,474)(366,473)(367,472)(368,471)(369,470)(370,469)(371,468)(372,467)
(497,621)(498,651)(499,650)(500,649)(501,648)(502,647)(503,646)(504,645)
(505,644)(506,643)(507,642)(508,641)(509,640)(510,639)(511,638)(512,637)
(513,636)(514,635)(515,634)(516,633)(517,632)(518,631)(519,630)(520,629)
(521,628)(522,627)(523,626)(524,625)(525,624)(526,623)(527,622)(528,652)
(529,682)(530,681)(531,680)(532,679)(533,678)(534,677)(535,676)(536,675)
(537,674)(538,673)(539,672)(540,671)(541,670)(542,669)(543,668)(544,667)
(545,666)(546,665)(547,664)(548,663)(549,662)(550,661)(551,660)(552,659)
(553,658)(554,657)(555,656)(556,655)(557,654)(558,653)(559,683)(560,713)
(561,712)(562,711)(563,710)(564,709)(565,708)(566,707)(567,706)(568,705)
(569,704)(570,703)(571,702)(572,701)(573,700)(574,699)(575,698)(576,697)
(577,696)(578,695)(579,694)(580,693)(581,692)(582,691)(583,690)(584,689)
(585,688)(586,687)(587,686)(588,685)(589,684)(590,714)(591,744)(592,743)
(593,742)(594,741)(595,740)(596,739)(597,738)(598,737)(599,736)(600,735)
(601,734)(602,733)(603,732)(604,731)(605,730)(606,729)(607,728)(608,727)
(609,726)(610,725)(611,724)(612,723)(613,722)(614,721)(615,720)(616,719)
(617,718)(618,717)(619,716)(620,715)(745,869)(746,899)(747,898)(748,897)
(749,896)(750,895)(751,894)(752,893)(753,892)(754,891)(755,890)(756,889)
(757,888)(758,887)(759,886)(760,885)(761,884)(762,883)(763,882)(764,881)
(765,880)(766,879)(767,878)(768,877)(769,876)(770,875)(771,874)(772,873)
(773,872)(774,871)(775,870)(776,900)(777,930)(778,929)(779,928)(780,927)
(781,926)(782,925)(783,924)(784,923)(785,922)(786,921)(787,920)(788,919)
(789,918)(790,917)(791,916)(792,915)(793,914)(794,913)(795,912)(796,911)
(797,910)(798,909)(799,908)(800,907)(801,906)(802,905)(803,904)(804,903)
(805,902)(806,901)(807,931)(808,961)(809,960)(810,959)(811,958)(812,957)
(813,956)(814,955)(815,954)(816,953)(817,952)(818,951)(819,950)(820,949)
(821,948)(822,947)(823,946)(824,945)(825,944)(826,943)(827,942)(828,941)
(829,940)(830,939)(831,938)(832,937)(833,936)(834,935)(835,934)(836,933)
(837,932)(838,962)(839,992)(840,991)(841,990)(842,989)(843,988)(844,987)
(845,986)(846,985)(847,984)(848,983)(849,982)(850,981)(851,980)(852,979)
(853,978)(854,977)(855,976)(856,975)(857,974)(858,973)(859,972)(860,971)
(861,970)(862,969)(863,968)(864,967)(865,966)(866,965)(867,964)(868,963);;
s2 := (  1,126)(  2,125)(  3,155)(  4,154)(  5,153)(  6,152)(  7,151)(  8,150)
(  9,149)( 10,148)( 11,147)( 12,146)( 13,145)( 14,144)( 15,143)( 16,142)
( 17,141)( 18,140)( 19,139)( 20,138)( 21,137)( 22,136)( 23,135)( 24,134)
( 25,133)( 26,132)( 27,131)( 28,130)( 29,129)( 30,128)( 31,127)( 32,157)
( 33,156)( 34,186)( 35,185)( 36,184)( 37,183)( 38,182)( 39,181)( 40,180)
( 41,179)( 42,178)( 43,177)( 44,176)( 45,175)( 46,174)( 47,173)( 48,172)
( 49,171)( 50,170)( 51,169)( 52,168)( 53,167)( 54,166)( 55,165)( 56,164)
( 57,163)( 58,162)( 59,161)( 60,160)( 61,159)( 62,158)( 63,188)( 64,187)
( 65,217)( 66,216)( 67,215)( 68,214)( 69,213)( 70,212)( 71,211)( 72,210)
( 73,209)( 74,208)( 75,207)( 76,206)( 77,205)( 78,204)( 79,203)( 80,202)
( 81,201)( 82,200)( 83,199)( 84,198)( 85,197)( 86,196)( 87,195)( 88,194)
( 89,193)( 90,192)( 91,191)( 92,190)( 93,189)( 94,219)( 95,218)( 96,248)
( 97,247)( 98,246)( 99,245)(100,244)(101,243)(102,242)(103,241)(104,240)
(105,239)(106,238)(107,237)(108,236)(109,235)(110,234)(111,233)(112,232)
(113,231)(114,230)(115,229)(116,228)(117,227)(118,226)(119,225)(120,224)
(121,223)(122,222)(123,221)(124,220)(249,405)(250,404)(251,434)(252,433)
(253,432)(254,431)(255,430)(256,429)(257,428)(258,427)(259,426)(260,425)
(261,424)(262,423)(263,422)(264,421)(265,420)(266,419)(267,418)(268,417)
(269,416)(270,415)(271,414)(272,413)(273,412)(274,411)(275,410)(276,409)
(277,408)(278,407)(279,406)(280,374)(281,373)(282,403)(283,402)(284,401)
(285,400)(286,399)(287,398)(288,397)(289,396)(290,395)(291,394)(292,393)
(293,392)(294,391)(295,390)(296,389)(297,388)(298,387)(299,386)(300,385)
(301,384)(302,383)(303,382)(304,381)(305,380)(306,379)(307,378)(308,377)
(309,376)(310,375)(311,467)(312,466)(313,496)(314,495)(315,494)(316,493)
(317,492)(318,491)(319,490)(320,489)(321,488)(322,487)(323,486)(324,485)
(325,484)(326,483)(327,482)(328,481)(329,480)(330,479)(331,478)(332,477)
(333,476)(334,475)(335,474)(336,473)(337,472)(338,471)(339,470)(340,469)
(341,468)(342,436)(343,435)(344,465)(345,464)(346,463)(347,462)(348,461)
(349,460)(350,459)(351,458)(352,457)(353,456)(354,455)(355,454)(356,453)
(357,452)(358,451)(359,450)(360,449)(361,448)(362,447)(363,446)(364,445)
(365,444)(366,443)(367,442)(368,441)(369,440)(370,439)(371,438)(372,437)
(497,684)(498,683)(499,713)(500,712)(501,711)(502,710)(503,709)(504,708)
(505,707)(506,706)(507,705)(508,704)(509,703)(510,702)(511,701)(512,700)
(513,699)(514,698)(515,697)(516,696)(517,695)(518,694)(519,693)(520,692)
(521,691)(522,690)(523,689)(524,688)(525,687)(526,686)(527,685)(528,715)
(529,714)(530,744)(531,743)(532,742)(533,741)(534,740)(535,739)(536,738)
(537,737)(538,736)(539,735)(540,734)(541,733)(542,732)(543,731)(544,730)
(545,729)(546,728)(547,727)(548,726)(549,725)(550,724)(551,723)(552,722)
(553,721)(554,720)(555,719)(556,718)(557,717)(558,716)(559,622)(560,621)
(561,651)(562,650)(563,649)(564,648)(565,647)(566,646)(567,645)(568,644)
(569,643)(570,642)(571,641)(572,640)(573,639)(574,638)(575,637)(576,636)
(577,635)(578,634)(579,633)(580,632)(581,631)(582,630)(583,629)(584,628)
(585,627)(586,626)(587,625)(588,624)(589,623)(590,653)(591,652)(592,682)
(593,681)(594,680)(595,679)(596,678)(597,677)(598,676)(599,675)(600,674)
(601,673)(602,672)(603,671)(604,670)(605,669)(606,668)(607,667)(608,666)
(609,665)(610,664)(611,663)(612,662)(613,661)(614,660)(615,659)(616,658)
(617,657)(618,656)(619,655)(620,654)(745,963)(746,962)(747,992)(748,991)
(749,990)(750,989)(751,988)(752,987)(753,986)(754,985)(755,984)(756,983)
(757,982)(758,981)(759,980)(760,979)(761,978)(762,977)(763,976)(764,975)
(765,974)(766,973)(767,972)(768,971)(769,970)(770,969)(771,968)(772,967)
(773,966)(774,965)(775,964)(776,932)(777,931)(778,961)(779,960)(780,959)
(781,958)(782,957)(783,956)(784,955)(785,954)(786,953)(787,952)(788,951)
(789,950)(790,949)(791,948)(792,947)(793,946)(794,945)(795,944)(796,943)
(797,942)(798,941)(799,940)(800,939)(801,938)(802,937)(803,936)(804,935)
(805,934)(806,933)(807,901)(808,900)(809,930)(810,929)(811,928)(812,927)
(813,926)(814,925)(815,924)(816,923)(817,922)(818,921)(819,920)(820,919)
(821,918)(822,917)(823,916)(824,915)(825,914)(826,913)(827,912)(828,911)
(829,910)(830,909)(831,908)(832,907)(833,906)(834,905)(835,904)(836,903)
(837,902)(838,870)(839,869)(840,899)(841,898)(842,897)(843,896)(844,895)
(845,894)(846,893)(847,892)(848,891)(849,890)(850,889)(851,888)(852,887)
(853,886)(854,885)(855,884)(856,883)(857,882)(858,881)(859,880)(860,879)
(861,878)(862,877)(863,876)(864,875)(865,874)(866,873)(867,872)(868,871);;
s3 := (  1,249)(  2,250)(  3,251)(  4,252)(  5,253)(  6,254)(  7,255)(  8,256)
(  9,257)( 10,258)( 11,259)( 12,260)( 13,261)( 14,262)( 15,263)( 16,264)
( 17,265)( 18,266)( 19,267)( 20,268)( 21,269)( 22,270)( 23,271)( 24,272)
( 25,273)( 26,274)( 27,275)( 28,276)( 29,277)( 30,278)( 31,279)( 32,280)
( 33,281)( 34,282)( 35,283)( 36,284)( 37,285)( 38,286)( 39,287)( 40,288)
( 41,289)( 42,290)( 43,291)( 44,292)( 45,293)( 46,294)( 47,295)( 48,296)
( 49,297)( 50,298)( 51,299)( 52,300)( 53,301)( 54,302)( 55,303)( 56,304)
( 57,305)( 58,306)( 59,307)( 60,308)( 61,309)( 62,310)( 63,311)( 64,312)
( 65,313)( 66,314)( 67,315)( 68,316)( 69,317)( 70,318)( 71,319)( 72,320)
( 73,321)( 74,322)( 75,323)( 76,324)( 77,325)( 78,326)( 79,327)( 80,328)
( 81,329)( 82,330)( 83,331)( 84,332)( 85,333)( 86,334)( 87,335)( 88,336)
( 89,337)( 90,338)( 91,339)( 92,340)( 93,341)( 94,342)( 95,343)( 96,344)
( 97,345)( 98,346)( 99,347)(100,348)(101,349)(102,350)(103,351)(104,352)
(105,353)(106,354)(107,355)(108,356)(109,357)(110,358)(111,359)(112,360)
(113,361)(114,362)(115,363)(116,364)(117,365)(118,366)(119,367)(120,368)
(121,369)(122,370)(123,371)(124,372)(125,373)(126,374)(127,375)(128,376)
(129,377)(130,378)(131,379)(132,380)(133,381)(134,382)(135,383)(136,384)
(137,385)(138,386)(139,387)(140,388)(141,389)(142,390)(143,391)(144,392)
(145,393)(146,394)(147,395)(148,396)(149,397)(150,398)(151,399)(152,400)
(153,401)(154,402)(155,403)(156,404)(157,405)(158,406)(159,407)(160,408)
(161,409)(162,410)(163,411)(164,412)(165,413)(166,414)(167,415)(168,416)
(169,417)(170,418)(171,419)(172,420)(173,421)(174,422)(175,423)(176,424)
(177,425)(178,426)(179,427)(180,428)(181,429)(182,430)(183,431)(184,432)
(185,433)(186,434)(187,435)(188,436)(189,437)(190,438)(191,439)(192,440)
(193,441)(194,442)(195,443)(196,444)(197,445)(198,446)(199,447)(200,448)
(201,449)(202,450)(203,451)(204,452)(205,453)(206,454)(207,455)(208,456)
(209,457)(210,458)(211,459)(212,460)(213,461)(214,462)(215,463)(216,464)
(217,465)(218,466)(219,467)(220,468)(221,469)(222,470)(223,471)(224,472)
(225,473)(226,474)(227,475)(228,476)(229,477)(230,478)(231,479)(232,480)
(233,481)(234,482)(235,483)(236,484)(237,485)(238,486)(239,487)(240,488)
(241,489)(242,490)(243,491)(244,492)(245,493)(246,494)(247,495)(248,496)
(497,745)(498,746)(499,747)(500,748)(501,749)(502,750)(503,751)(504,752)
(505,753)(506,754)(507,755)(508,756)(509,757)(510,758)(511,759)(512,760)
(513,761)(514,762)(515,763)(516,764)(517,765)(518,766)(519,767)(520,768)
(521,769)(522,770)(523,771)(524,772)(525,773)(526,774)(527,775)(528,776)
(529,777)(530,778)(531,779)(532,780)(533,781)(534,782)(535,783)(536,784)
(537,785)(538,786)(539,787)(540,788)(541,789)(542,790)(543,791)(544,792)
(545,793)(546,794)(547,795)(548,796)(549,797)(550,798)(551,799)(552,800)
(553,801)(554,802)(555,803)(556,804)(557,805)(558,806)(559,807)(560,808)
(561,809)(562,810)(563,811)(564,812)(565,813)(566,814)(567,815)(568,816)
(569,817)(570,818)(571,819)(572,820)(573,821)(574,822)(575,823)(576,824)
(577,825)(578,826)(579,827)(580,828)(581,829)(582,830)(583,831)(584,832)
(585,833)(586,834)(587,835)(588,836)(589,837)(590,838)(591,839)(592,840)
(593,841)(594,842)(595,843)(596,844)(597,845)(598,846)(599,847)(600,848)
(601,849)(602,850)(603,851)(604,852)(605,853)(606,854)(607,855)(608,856)
(609,857)(610,858)(611,859)(612,860)(613,861)(614,862)(615,863)(616,864)
(617,865)(618,866)(619,867)(620,868)(621,869)(622,870)(623,871)(624,872)
(625,873)(626,874)(627,875)(628,876)(629,877)(630,878)(631,879)(632,880)
(633,881)(634,882)(635,883)(636,884)(637,885)(638,886)(639,887)(640,888)
(641,889)(642,890)(643,891)(644,892)(645,893)(646,894)(647,895)(648,896)
(649,897)(650,898)(651,899)(652,900)(653,901)(654,902)(655,903)(656,904)
(657,905)(658,906)(659,907)(660,908)(661,909)(662,910)(663,911)(664,912)
(665,913)(666,914)(667,915)(668,916)(669,917)(670,918)(671,919)(672,920)
(673,921)(674,922)(675,923)(676,924)(677,925)(678,926)(679,927)(680,928)
(681,929)(682,930)(683,931)(684,932)(685,933)(686,934)(687,935)(688,936)
(689,937)(690,938)(691,939)(692,940)(693,941)(694,942)(695,943)(696,944)
(697,945)(698,946)(699,947)(700,948)(701,949)(702,950)(703,951)(704,952)
(705,953)(706,954)(707,955)(708,956)(709,957)(710,958)(711,959)(712,960)
(713,961)(714,962)(715,963)(716,964)(717,965)(718,966)(719,967)(720,968)
(721,969)(722,970)(723,971)(724,972)(725,973)(726,974)(727,975)(728,976)
(729,977)(730,978)(731,979)(732,980)(733,981)(734,982)(735,983)(736,984)
(737,985)(738,986)(739,987)(740,988)(741,989)(742,990)(743,991)(744,992);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, 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)!(  1,497)(  2,498)(  3,499)(  4,500)(  5,501)(  6,502)(  7,503)
(  8,504)(  9,505)( 10,506)( 11,507)( 12,508)( 13,509)( 14,510)( 15,511)
( 16,512)( 17,513)( 18,514)( 19,515)( 20,516)( 21,517)( 22,518)( 23,519)
( 24,520)( 25,521)( 26,522)( 27,523)( 28,524)( 29,525)( 30,526)( 31,527)
( 32,528)( 33,529)( 34,530)( 35,531)( 36,532)( 37,533)( 38,534)( 39,535)
( 40,536)( 41,537)( 42,538)( 43,539)( 44,540)( 45,541)( 46,542)( 47,543)
( 48,544)( 49,545)( 50,546)( 51,547)( 52,548)( 53,549)( 54,550)( 55,551)
( 56,552)( 57,553)( 58,554)( 59,555)( 60,556)( 61,557)( 62,558)( 63,559)
( 64,560)( 65,561)( 66,562)( 67,563)( 68,564)( 69,565)( 70,566)( 71,567)
( 72,568)( 73,569)( 74,570)( 75,571)( 76,572)( 77,573)( 78,574)( 79,575)
( 80,576)( 81,577)( 82,578)( 83,579)( 84,580)( 85,581)( 86,582)( 87,583)
( 88,584)( 89,585)( 90,586)( 91,587)( 92,588)( 93,589)( 94,590)( 95,591)
( 96,592)( 97,593)( 98,594)( 99,595)(100,596)(101,597)(102,598)(103,599)
(104,600)(105,601)(106,602)(107,603)(108,604)(109,605)(110,606)(111,607)
(112,608)(113,609)(114,610)(115,611)(116,612)(117,613)(118,614)(119,615)
(120,616)(121,617)(122,618)(123,619)(124,620)(125,683)(126,684)(127,685)
(128,686)(129,687)(130,688)(131,689)(132,690)(133,691)(134,692)(135,693)
(136,694)(137,695)(138,696)(139,697)(140,698)(141,699)(142,700)(143,701)
(144,702)(145,703)(146,704)(147,705)(148,706)(149,707)(150,708)(151,709)
(152,710)(153,711)(154,712)(155,713)(156,714)(157,715)(158,716)(159,717)
(160,718)(161,719)(162,720)(163,721)(164,722)(165,723)(166,724)(167,725)
(168,726)(169,727)(170,728)(171,729)(172,730)(173,731)(174,732)(175,733)
(176,734)(177,735)(178,736)(179,737)(180,738)(181,739)(182,740)(183,741)
(184,742)(185,743)(186,744)(187,621)(188,622)(189,623)(190,624)(191,625)
(192,626)(193,627)(194,628)(195,629)(196,630)(197,631)(198,632)(199,633)
(200,634)(201,635)(202,636)(203,637)(204,638)(205,639)(206,640)(207,641)
(208,642)(209,643)(210,644)(211,645)(212,646)(213,647)(214,648)(215,649)
(216,650)(217,651)(218,652)(219,653)(220,654)(221,655)(222,656)(223,657)
(224,658)(225,659)(226,660)(227,661)(228,662)(229,663)(230,664)(231,665)
(232,666)(233,667)(234,668)(235,669)(236,670)(237,671)(238,672)(239,673)
(240,674)(241,675)(242,676)(243,677)(244,678)(245,679)(246,680)(247,681)
(248,682)(249,745)(250,746)(251,747)(252,748)(253,749)(254,750)(255,751)
(256,752)(257,753)(258,754)(259,755)(260,756)(261,757)(262,758)(263,759)
(264,760)(265,761)(266,762)(267,763)(268,764)(269,765)(270,766)(271,767)
(272,768)(273,769)(274,770)(275,771)(276,772)(277,773)(278,774)(279,775)
(280,776)(281,777)(282,778)(283,779)(284,780)(285,781)(286,782)(287,783)
(288,784)(289,785)(290,786)(291,787)(292,788)(293,789)(294,790)(295,791)
(296,792)(297,793)(298,794)(299,795)(300,796)(301,797)(302,798)(303,799)
(304,800)(305,801)(306,802)(307,803)(308,804)(309,805)(310,806)(311,807)
(312,808)(313,809)(314,810)(315,811)(316,812)(317,813)(318,814)(319,815)
(320,816)(321,817)(322,818)(323,819)(324,820)(325,821)(326,822)(327,823)
(328,824)(329,825)(330,826)(331,827)(332,828)(333,829)(334,830)(335,831)
(336,832)(337,833)(338,834)(339,835)(340,836)(341,837)(342,838)(343,839)
(344,840)(345,841)(346,842)(347,843)(348,844)(349,845)(350,846)(351,847)
(352,848)(353,849)(354,850)(355,851)(356,852)(357,853)(358,854)(359,855)
(360,856)(361,857)(362,858)(363,859)(364,860)(365,861)(366,862)(367,863)
(368,864)(369,865)(370,866)(371,867)(372,868)(373,931)(374,932)(375,933)
(376,934)(377,935)(378,936)(379,937)(380,938)(381,939)(382,940)(383,941)
(384,942)(385,943)(386,944)(387,945)(388,946)(389,947)(390,948)(391,949)
(392,950)(393,951)(394,952)(395,953)(396,954)(397,955)(398,956)(399,957)
(400,958)(401,959)(402,960)(403,961)(404,962)(405,963)(406,964)(407,965)
(408,966)(409,967)(410,968)(411,969)(412,970)(413,971)(414,972)(415,973)
(416,974)(417,975)(418,976)(419,977)(420,978)(421,979)(422,980)(423,981)
(424,982)(425,983)(426,984)(427,985)(428,986)(429,987)(430,988)(431,989)
(432,990)(433,991)(434,992)(435,869)(436,870)(437,871)(438,872)(439,873)
(440,874)(441,875)(442,876)(443,877)(444,878)(445,879)(446,880)(447,881)
(448,882)(449,883)(450,884)(451,885)(452,886)(453,887)(454,888)(455,889)
(456,890)(457,891)(458,892)(459,893)(460,894)(461,895)(462,896)(463,897)
(464,898)(465,899)(466,900)(467,901)(468,902)(469,903)(470,904)(471,905)
(472,906)(473,907)(474,908)(475,909)(476,910)(477,911)(478,912)(479,913)
(480,914)(481,915)(482,916)(483,917)(484,918)(485,919)(486,920)(487,921)
(488,922)(489,923)(490,924)(491,925)(492,926)(493,927)(494,928)(495,929)
(496,930);
s1 := Sym(992)!(  1,125)(  2,155)(  3,154)(  4,153)(  5,152)(  6,151)(  7,150)
(  8,149)(  9,148)( 10,147)( 11,146)( 12,145)( 13,144)( 14,143)( 15,142)
( 16,141)( 17,140)( 18,139)( 19,138)( 20,137)( 21,136)( 22,135)( 23,134)
( 24,133)( 25,132)( 26,131)( 27,130)( 28,129)( 29,128)( 30,127)( 31,126)
( 32,156)( 33,186)( 34,185)( 35,184)( 36,183)( 37,182)( 38,181)( 39,180)
( 40,179)( 41,178)( 42,177)( 43,176)( 44,175)( 45,174)( 46,173)( 47,172)
( 48,171)( 49,170)( 50,169)( 51,168)( 52,167)( 53,166)( 54,165)( 55,164)
( 56,163)( 57,162)( 58,161)( 59,160)( 60,159)( 61,158)( 62,157)( 63,187)
( 64,217)( 65,216)( 66,215)( 67,214)( 68,213)( 69,212)( 70,211)( 71,210)
( 72,209)( 73,208)( 74,207)( 75,206)( 76,205)( 77,204)( 78,203)( 79,202)
( 80,201)( 81,200)( 82,199)( 83,198)( 84,197)( 85,196)( 86,195)( 87,194)
( 88,193)( 89,192)( 90,191)( 91,190)( 92,189)( 93,188)( 94,218)( 95,248)
( 96,247)( 97,246)( 98,245)( 99,244)(100,243)(101,242)(102,241)(103,240)
(104,239)(105,238)(106,237)(107,236)(108,235)(109,234)(110,233)(111,232)
(112,231)(113,230)(114,229)(115,228)(116,227)(117,226)(118,225)(119,224)
(120,223)(121,222)(122,221)(123,220)(124,219)(249,373)(250,403)(251,402)
(252,401)(253,400)(254,399)(255,398)(256,397)(257,396)(258,395)(259,394)
(260,393)(261,392)(262,391)(263,390)(264,389)(265,388)(266,387)(267,386)
(268,385)(269,384)(270,383)(271,382)(272,381)(273,380)(274,379)(275,378)
(276,377)(277,376)(278,375)(279,374)(280,404)(281,434)(282,433)(283,432)
(284,431)(285,430)(286,429)(287,428)(288,427)(289,426)(290,425)(291,424)
(292,423)(293,422)(294,421)(295,420)(296,419)(297,418)(298,417)(299,416)
(300,415)(301,414)(302,413)(303,412)(304,411)(305,410)(306,409)(307,408)
(308,407)(309,406)(310,405)(311,435)(312,465)(313,464)(314,463)(315,462)
(316,461)(317,460)(318,459)(319,458)(320,457)(321,456)(322,455)(323,454)
(324,453)(325,452)(326,451)(327,450)(328,449)(329,448)(330,447)(331,446)
(332,445)(333,444)(334,443)(335,442)(336,441)(337,440)(338,439)(339,438)
(340,437)(341,436)(342,466)(343,496)(344,495)(345,494)(346,493)(347,492)
(348,491)(349,490)(350,489)(351,488)(352,487)(353,486)(354,485)(355,484)
(356,483)(357,482)(358,481)(359,480)(360,479)(361,478)(362,477)(363,476)
(364,475)(365,474)(366,473)(367,472)(368,471)(369,470)(370,469)(371,468)
(372,467)(497,621)(498,651)(499,650)(500,649)(501,648)(502,647)(503,646)
(504,645)(505,644)(506,643)(507,642)(508,641)(509,640)(510,639)(511,638)
(512,637)(513,636)(514,635)(515,634)(516,633)(517,632)(518,631)(519,630)
(520,629)(521,628)(522,627)(523,626)(524,625)(525,624)(526,623)(527,622)
(528,652)(529,682)(530,681)(531,680)(532,679)(533,678)(534,677)(535,676)
(536,675)(537,674)(538,673)(539,672)(540,671)(541,670)(542,669)(543,668)
(544,667)(545,666)(546,665)(547,664)(548,663)(549,662)(550,661)(551,660)
(552,659)(553,658)(554,657)(555,656)(556,655)(557,654)(558,653)(559,683)
(560,713)(561,712)(562,711)(563,710)(564,709)(565,708)(566,707)(567,706)
(568,705)(569,704)(570,703)(571,702)(572,701)(573,700)(574,699)(575,698)
(576,697)(577,696)(578,695)(579,694)(580,693)(581,692)(582,691)(583,690)
(584,689)(585,688)(586,687)(587,686)(588,685)(589,684)(590,714)(591,744)
(592,743)(593,742)(594,741)(595,740)(596,739)(597,738)(598,737)(599,736)
(600,735)(601,734)(602,733)(603,732)(604,731)(605,730)(606,729)(607,728)
(608,727)(609,726)(610,725)(611,724)(612,723)(613,722)(614,721)(615,720)
(616,719)(617,718)(618,717)(619,716)(620,715)(745,869)(746,899)(747,898)
(748,897)(749,896)(750,895)(751,894)(752,893)(753,892)(754,891)(755,890)
(756,889)(757,888)(758,887)(759,886)(760,885)(761,884)(762,883)(763,882)
(764,881)(765,880)(766,879)(767,878)(768,877)(769,876)(770,875)(771,874)
(772,873)(773,872)(774,871)(775,870)(776,900)(777,930)(778,929)(779,928)
(780,927)(781,926)(782,925)(783,924)(784,923)(785,922)(786,921)(787,920)
(788,919)(789,918)(790,917)(791,916)(792,915)(793,914)(794,913)(795,912)
(796,911)(797,910)(798,909)(799,908)(800,907)(801,906)(802,905)(803,904)
(804,903)(805,902)(806,901)(807,931)(808,961)(809,960)(810,959)(811,958)
(812,957)(813,956)(814,955)(815,954)(816,953)(817,952)(818,951)(819,950)
(820,949)(821,948)(822,947)(823,946)(824,945)(825,944)(826,943)(827,942)
(828,941)(829,940)(830,939)(831,938)(832,937)(833,936)(834,935)(835,934)
(836,933)(837,932)(838,962)(839,992)(840,991)(841,990)(842,989)(843,988)
(844,987)(845,986)(846,985)(847,984)(848,983)(849,982)(850,981)(851,980)
(852,979)(853,978)(854,977)(855,976)(856,975)(857,974)(858,973)(859,972)
(860,971)(861,970)(862,969)(863,968)(864,967)(865,966)(866,965)(867,964)
(868,963);
s2 := Sym(992)!(  1,126)(  2,125)(  3,155)(  4,154)(  5,153)(  6,152)(  7,151)
(  8,150)(  9,149)( 10,148)( 11,147)( 12,146)( 13,145)( 14,144)( 15,143)
( 16,142)( 17,141)( 18,140)( 19,139)( 20,138)( 21,137)( 22,136)( 23,135)
( 24,134)( 25,133)( 26,132)( 27,131)( 28,130)( 29,129)( 30,128)( 31,127)
( 32,157)( 33,156)( 34,186)( 35,185)( 36,184)( 37,183)( 38,182)( 39,181)
( 40,180)( 41,179)( 42,178)( 43,177)( 44,176)( 45,175)( 46,174)( 47,173)
( 48,172)( 49,171)( 50,170)( 51,169)( 52,168)( 53,167)( 54,166)( 55,165)
( 56,164)( 57,163)( 58,162)( 59,161)( 60,160)( 61,159)( 62,158)( 63,188)
( 64,187)( 65,217)( 66,216)( 67,215)( 68,214)( 69,213)( 70,212)( 71,211)
( 72,210)( 73,209)( 74,208)( 75,207)( 76,206)( 77,205)( 78,204)( 79,203)
( 80,202)( 81,201)( 82,200)( 83,199)( 84,198)( 85,197)( 86,196)( 87,195)
( 88,194)( 89,193)( 90,192)( 91,191)( 92,190)( 93,189)( 94,219)( 95,218)
( 96,248)( 97,247)( 98,246)( 99,245)(100,244)(101,243)(102,242)(103,241)
(104,240)(105,239)(106,238)(107,237)(108,236)(109,235)(110,234)(111,233)
(112,232)(113,231)(114,230)(115,229)(116,228)(117,227)(118,226)(119,225)
(120,224)(121,223)(122,222)(123,221)(124,220)(249,405)(250,404)(251,434)
(252,433)(253,432)(254,431)(255,430)(256,429)(257,428)(258,427)(259,426)
(260,425)(261,424)(262,423)(263,422)(264,421)(265,420)(266,419)(267,418)
(268,417)(269,416)(270,415)(271,414)(272,413)(273,412)(274,411)(275,410)
(276,409)(277,408)(278,407)(279,406)(280,374)(281,373)(282,403)(283,402)
(284,401)(285,400)(286,399)(287,398)(288,397)(289,396)(290,395)(291,394)
(292,393)(293,392)(294,391)(295,390)(296,389)(297,388)(298,387)(299,386)
(300,385)(301,384)(302,383)(303,382)(304,381)(305,380)(306,379)(307,378)
(308,377)(309,376)(310,375)(311,467)(312,466)(313,496)(314,495)(315,494)
(316,493)(317,492)(318,491)(319,490)(320,489)(321,488)(322,487)(323,486)
(324,485)(325,484)(326,483)(327,482)(328,481)(329,480)(330,479)(331,478)
(332,477)(333,476)(334,475)(335,474)(336,473)(337,472)(338,471)(339,470)
(340,469)(341,468)(342,436)(343,435)(344,465)(345,464)(346,463)(347,462)
(348,461)(349,460)(350,459)(351,458)(352,457)(353,456)(354,455)(355,454)
(356,453)(357,452)(358,451)(359,450)(360,449)(361,448)(362,447)(363,446)
(364,445)(365,444)(366,443)(367,442)(368,441)(369,440)(370,439)(371,438)
(372,437)(497,684)(498,683)(499,713)(500,712)(501,711)(502,710)(503,709)
(504,708)(505,707)(506,706)(507,705)(508,704)(509,703)(510,702)(511,701)
(512,700)(513,699)(514,698)(515,697)(516,696)(517,695)(518,694)(519,693)
(520,692)(521,691)(522,690)(523,689)(524,688)(525,687)(526,686)(527,685)
(528,715)(529,714)(530,744)(531,743)(532,742)(533,741)(534,740)(535,739)
(536,738)(537,737)(538,736)(539,735)(540,734)(541,733)(542,732)(543,731)
(544,730)(545,729)(546,728)(547,727)(548,726)(549,725)(550,724)(551,723)
(552,722)(553,721)(554,720)(555,719)(556,718)(557,717)(558,716)(559,622)
(560,621)(561,651)(562,650)(563,649)(564,648)(565,647)(566,646)(567,645)
(568,644)(569,643)(570,642)(571,641)(572,640)(573,639)(574,638)(575,637)
(576,636)(577,635)(578,634)(579,633)(580,632)(581,631)(582,630)(583,629)
(584,628)(585,627)(586,626)(587,625)(588,624)(589,623)(590,653)(591,652)
(592,682)(593,681)(594,680)(595,679)(596,678)(597,677)(598,676)(599,675)
(600,674)(601,673)(602,672)(603,671)(604,670)(605,669)(606,668)(607,667)
(608,666)(609,665)(610,664)(611,663)(612,662)(613,661)(614,660)(615,659)
(616,658)(617,657)(618,656)(619,655)(620,654)(745,963)(746,962)(747,992)
(748,991)(749,990)(750,989)(751,988)(752,987)(753,986)(754,985)(755,984)
(756,983)(757,982)(758,981)(759,980)(760,979)(761,978)(762,977)(763,976)
(764,975)(765,974)(766,973)(767,972)(768,971)(769,970)(770,969)(771,968)
(772,967)(773,966)(774,965)(775,964)(776,932)(777,931)(778,961)(779,960)
(780,959)(781,958)(782,957)(783,956)(784,955)(785,954)(786,953)(787,952)
(788,951)(789,950)(790,949)(791,948)(792,947)(793,946)(794,945)(795,944)
(796,943)(797,942)(798,941)(799,940)(800,939)(801,938)(802,937)(803,936)
(804,935)(805,934)(806,933)(807,901)(808,900)(809,930)(810,929)(811,928)
(812,927)(813,926)(814,925)(815,924)(816,923)(817,922)(818,921)(819,920)
(820,919)(821,918)(822,917)(823,916)(824,915)(825,914)(826,913)(827,912)
(828,911)(829,910)(830,909)(831,908)(832,907)(833,906)(834,905)(835,904)
(836,903)(837,902)(838,870)(839,869)(840,899)(841,898)(842,897)(843,896)
(844,895)(845,894)(846,893)(847,892)(848,891)(849,890)(850,889)(851,888)
(852,887)(853,886)(854,885)(855,884)(856,883)(857,882)(858,881)(859,880)
(860,879)(861,878)(862,877)(863,876)(864,875)(865,874)(866,873)(867,872)
(868,871);
s3 := Sym(992)!(  1,249)(  2,250)(  3,251)(  4,252)(  5,253)(  6,254)(  7,255)
(  8,256)(  9,257)( 10,258)( 11,259)( 12,260)( 13,261)( 14,262)( 15,263)
( 16,264)( 17,265)( 18,266)( 19,267)( 20,268)( 21,269)( 22,270)( 23,271)
( 24,272)( 25,273)( 26,274)( 27,275)( 28,276)( 29,277)( 30,278)( 31,279)
( 32,280)( 33,281)( 34,282)( 35,283)( 36,284)( 37,285)( 38,286)( 39,287)
( 40,288)( 41,289)( 42,290)( 43,291)( 44,292)( 45,293)( 46,294)( 47,295)
( 48,296)( 49,297)( 50,298)( 51,299)( 52,300)( 53,301)( 54,302)( 55,303)
( 56,304)( 57,305)( 58,306)( 59,307)( 60,308)( 61,309)( 62,310)( 63,311)
( 64,312)( 65,313)( 66,314)( 67,315)( 68,316)( 69,317)( 70,318)( 71,319)
( 72,320)( 73,321)( 74,322)( 75,323)( 76,324)( 77,325)( 78,326)( 79,327)
( 80,328)( 81,329)( 82,330)( 83,331)( 84,332)( 85,333)( 86,334)( 87,335)
( 88,336)( 89,337)( 90,338)( 91,339)( 92,340)( 93,341)( 94,342)( 95,343)
( 96,344)( 97,345)( 98,346)( 99,347)(100,348)(101,349)(102,350)(103,351)
(104,352)(105,353)(106,354)(107,355)(108,356)(109,357)(110,358)(111,359)
(112,360)(113,361)(114,362)(115,363)(116,364)(117,365)(118,366)(119,367)
(120,368)(121,369)(122,370)(123,371)(124,372)(125,373)(126,374)(127,375)
(128,376)(129,377)(130,378)(131,379)(132,380)(133,381)(134,382)(135,383)
(136,384)(137,385)(138,386)(139,387)(140,388)(141,389)(142,390)(143,391)
(144,392)(145,393)(146,394)(147,395)(148,396)(149,397)(150,398)(151,399)
(152,400)(153,401)(154,402)(155,403)(156,404)(157,405)(158,406)(159,407)
(160,408)(161,409)(162,410)(163,411)(164,412)(165,413)(166,414)(167,415)
(168,416)(169,417)(170,418)(171,419)(172,420)(173,421)(174,422)(175,423)
(176,424)(177,425)(178,426)(179,427)(180,428)(181,429)(182,430)(183,431)
(184,432)(185,433)(186,434)(187,435)(188,436)(189,437)(190,438)(191,439)
(192,440)(193,441)(194,442)(195,443)(196,444)(197,445)(198,446)(199,447)
(200,448)(201,449)(202,450)(203,451)(204,452)(205,453)(206,454)(207,455)
(208,456)(209,457)(210,458)(211,459)(212,460)(213,461)(214,462)(215,463)
(216,464)(217,465)(218,466)(219,467)(220,468)(221,469)(222,470)(223,471)
(224,472)(225,473)(226,474)(227,475)(228,476)(229,477)(230,478)(231,479)
(232,480)(233,481)(234,482)(235,483)(236,484)(237,485)(238,486)(239,487)
(240,488)(241,489)(242,490)(243,491)(244,492)(245,493)(246,494)(247,495)
(248,496)(497,745)(498,746)(499,747)(500,748)(501,749)(502,750)(503,751)
(504,752)(505,753)(506,754)(507,755)(508,756)(509,757)(510,758)(511,759)
(512,760)(513,761)(514,762)(515,763)(516,764)(517,765)(518,766)(519,767)
(520,768)(521,769)(522,770)(523,771)(524,772)(525,773)(526,774)(527,775)
(528,776)(529,777)(530,778)(531,779)(532,780)(533,781)(534,782)(535,783)
(536,784)(537,785)(538,786)(539,787)(540,788)(541,789)(542,790)(543,791)
(544,792)(545,793)(546,794)(547,795)(548,796)(549,797)(550,798)(551,799)
(552,800)(553,801)(554,802)(555,803)(556,804)(557,805)(558,806)(559,807)
(560,808)(561,809)(562,810)(563,811)(564,812)(565,813)(566,814)(567,815)
(568,816)(569,817)(570,818)(571,819)(572,820)(573,821)(574,822)(575,823)
(576,824)(577,825)(578,826)(579,827)(580,828)(581,829)(582,830)(583,831)
(584,832)(585,833)(586,834)(587,835)(588,836)(589,837)(590,838)(591,839)
(592,840)(593,841)(594,842)(595,843)(596,844)(597,845)(598,846)(599,847)
(600,848)(601,849)(602,850)(603,851)(604,852)(605,853)(606,854)(607,855)
(608,856)(609,857)(610,858)(611,859)(612,860)(613,861)(614,862)(615,863)
(616,864)(617,865)(618,866)(619,867)(620,868)(621,869)(622,870)(623,871)
(624,872)(625,873)(626,874)(627,875)(628,876)(629,877)(630,878)(631,879)
(632,880)(633,881)(634,882)(635,883)(636,884)(637,885)(638,886)(639,887)
(640,888)(641,889)(642,890)(643,891)(644,892)(645,893)(646,894)(647,895)
(648,896)(649,897)(650,898)(651,899)(652,900)(653,901)(654,902)(655,903)
(656,904)(657,905)(658,906)(659,907)(660,908)(661,909)(662,910)(663,911)
(664,912)(665,913)(666,914)(667,915)(668,916)(669,917)(670,918)(671,919)
(672,920)(673,921)(674,922)(675,923)(676,924)(677,925)(678,926)(679,927)
(680,928)(681,929)(682,930)(683,931)(684,932)(685,933)(686,934)(687,935)
(688,936)(689,937)(690,938)(691,939)(692,940)(693,941)(694,942)(695,943)
(696,944)(697,945)(698,946)(699,947)(700,948)(701,949)(702,950)(703,951)
(704,952)(705,953)(706,954)(707,955)(708,956)(709,957)(710,958)(711,959)
(712,960)(713,961)(714,962)(715,963)(716,964)(717,965)(718,966)(719,967)
(720,968)(721,969)(722,970)(723,971)(724,972)(725,973)(726,974)(727,975)
(728,976)(729,977)(730,978)(731,979)(732,980)(733,981)(734,982)(735,983)
(736,984)(737,985)(738,986)(739,987)(740,988)(741,989)(742,990)(743,991)
(744,992);
poly := sub<Sym(992)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
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