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.
Irregular Quotients (of which this is a minimal cover):
None.
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