Polytope of Type {4,27,4}

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