Polytope of Type {4,8,30}

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

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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

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

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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;