Polytope of Type {8,28,4}

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

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