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Polytope of Type {4,4,4,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,4,14}*1792
Also Known As : {{4,4|2},{4,4|2},{4,14|2}}. if this polytope has another name.
Group : SmallGroup(1792,336970)
Rank : 5
Schlafli Type : {4,4,4,14}
Number of vertices, edges, etc : 4, 8, 8, 28, 14
Order of s0s1s2s3s4 : 28
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,4,14}*896, {4,4,2,14}*896, {4,2,4,14}*896
   4-fold quotients : {4,4,2,7}*448, {2,2,4,14}*448, {2,4,2,14}*448, {4,2,2,14}*448
   7-fold quotients : {4,4,4,2}*256
   8-fold quotients : {2,4,2,7}*224, {4,2,2,7}*224, {2,2,2,14}*224
   14-fold quotients : {2,4,4,2}*128, {4,4,2,2}*128, {4,2,4,2}*128
   16-fold quotients : {2,2,2,7}*112
   28-fold quotients : {2,2,4,2}*64, {2,4,2,2}*64, {4,2,2,2}*64
   56-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
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)
( 57,169)( 58,170)( 59,171)( 60,172)( 61,173)( 62,174)( 63,175)( 64,176)
( 65,177)( 66,178)( 67,179)( 68,180)( 69,181)( 70,182)( 71,183)( 72,184)
( 73,185)( 74,186)( 75,187)( 76,188)( 77,189)( 78,190)( 79,191)( 80,192)
( 81,193)( 82,194)( 83,195)( 84,196)( 85,197)( 86,198)( 87,199)( 88,200)
( 89,201)( 90,202)( 91,203)( 92,204)( 93,205)( 94,206)( 95,207)( 96,208)
( 97,209)( 98,210)( 99,211)(100,212)(101,213)(102,214)(103,215)(104,216)
(105,217)(106,218)(107,219)(108,220)(109,221)(110,222)(111,223)(112,224)
(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)
(281,393)(282,394)(283,395)(284,396)(285,397)(286,398)(287,399)(288,400)
(289,401)(290,402)(291,403)(292,404)(293,405)(294,406)(295,407)(296,408)
(297,409)(298,410)(299,411)(300,412)(301,413)(302,414)(303,415)(304,416)
(305,417)(306,418)(307,419)(308,420)(309,421)(310,422)(311,423)(312,424)
(313,425)(314,426)(315,427)(316,428)(317,429)(318,430)(319,431)(320,432)
(321,433)(322,434)(323,435)(324,436)(325,437)(326,438)(327,439)(328,440)
(329,441)(330,442)(331,443)(332,444)(333,445)(334,446)(335,447)(336,448)
(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)
(505,617)(506,618)(507,619)(508,620)(509,621)(510,622)(511,623)(512,624)
(513,625)(514,626)(515,627)(516,628)(517,629)(518,630)(519,631)(520,632)
(521,633)(522,634)(523,635)(524,636)(525,637)(526,638)(527,639)(528,640)
(529,641)(530,642)(531,643)(532,644)(533,645)(534,646)(535,647)(536,648)
(537,649)(538,650)(539,651)(540,652)(541,653)(542,654)(543,655)(544,656)
(545,657)(546,658)(547,659)(548,660)(549,661)(550,662)(551,663)(552,664)
(553,665)(554,666)(555,667)(556,668)(557,669)(558,670)(559,671)(560,672)
(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)
(729,841)(730,842)(731,843)(732,844)(733,845)(734,846)(735,847)(736,848)
(737,849)(738,850)(739,851)(740,852)(741,853)(742,854)(743,855)(744,856)
(745,857)(746,858)(747,859)(748,860)(749,861)(750,862)(751,863)(752,864)
(753,865)(754,866)(755,867)(756,868)(757,869)(758,870)(759,871)(760,872)
(761,873)(762,874)(763,875)(764,876)(765,877)(766,878)(767,879)(768,880)
(769,881)(770,882)(771,883)(772,884)(773,885)(774,886)(775,887)(776,888)
(777,889)(778,890)(779,891)(780,892)(781,893)(782,894)(783,895)(784,896);;
s1 := (  1,449)(  2,450)(  3,451)(  4,452)(  5,453)(  6,454)(  7,455)(  8,456)
(  9,457)( 10,458)( 11,459)( 12,460)( 13,461)( 14,462)( 15,463)( 16,464)
( 17,465)( 18,466)( 19,467)( 20,468)( 21,469)( 22,470)( 23,471)( 24,472)
( 25,473)( 26,474)( 27,475)( 28,476)( 29,477)( 30,478)( 31,479)( 32,480)
( 33,481)( 34,482)( 35,483)( 36,484)( 37,485)( 38,486)( 39,487)( 40,488)
( 41,489)( 42,490)( 43,491)( 44,492)( 45,493)( 46,494)( 47,495)( 48,496)
( 49,497)( 50,498)( 51,499)( 52,500)( 53,501)( 54,502)( 55,503)( 56,504)
( 57,505)( 58,506)( 59,507)( 60,508)( 61,509)( 62,510)( 63,511)( 64,512)
( 65,513)( 66,514)( 67,515)( 68,516)( 69,517)( 70,518)( 71,519)( 72,520)
( 73,521)( 74,522)( 75,523)( 76,524)( 77,525)( 78,526)( 79,527)( 80,528)
( 81,529)( 82,530)( 83,531)( 84,532)( 85,533)( 86,534)( 87,535)( 88,536)
( 89,537)( 90,538)( 91,539)( 92,540)( 93,541)( 94,542)( 95,543)( 96,544)
( 97,545)( 98,546)( 99,547)(100,548)(101,549)(102,550)(103,551)(104,552)
(105,553)(106,554)(107,555)(108,556)(109,557)(110,558)(111,559)(112,560)
(113,568)(114,569)(115,570)(116,571)(117,572)(118,573)(119,574)(120,561)
(121,562)(122,563)(123,564)(124,565)(125,566)(126,567)(127,582)(128,583)
(129,584)(130,585)(131,586)(132,587)(133,588)(134,575)(135,576)(136,577)
(137,578)(138,579)(139,580)(140,581)(141,596)(142,597)(143,598)(144,599)
(145,600)(146,601)(147,602)(148,589)(149,590)(150,591)(151,592)(152,593)
(153,594)(154,595)(155,610)(156,611)(157,612)(158,613)(159,614)(160,615)
(161,616)(162,603)(163,604)(164,605)(165,606)(166,607)(167,608)(168,609)
(169,624)(170,625)(171,626)(172,627)(173,628)(174,629)(175,630)(176,617)
(177,618)(178,619)(179,620)(180,621)(181,622)(182,623)(183,638)(184,639)
(185,640)(186,641)(187,642)(188,643)(189,644)(190,631)(191,632)(192,633)
(193,634)(194,635)(195,636)(196,637)(197,652)(198,653)(199,654)(200,655)
(201,656)(202,657)(203,658)(204,645)(205,646)(206,647)(207,648)(208,649)
(209,650)(210,651)(211,666)(212,667)(213,668)(214,669)(215,670)(216,671)
(217,672)(218,659)(219,660)(220,661)(221,662)(222,663)(223,664)(224,665)
(225,680)(226,681)(227,682)(228,683)(229,684)(230,685)(231,686)(232,673)
(233,674)(234,675)(235,676)(236,677)(237,678)(238,679)(239,694)(240,695)
(241,696)(242,697)(243,698)(244,699)(245,700)(246,687)(247,688)(248,689)
(249,690)(250,691)(251,692)(252,693)(253,708)(254,709)(255,710)(256,711)
(257,712)(258,713)(259,714)(260,701)(261,702)(262,703)(263,704)(264,705)
(265,706)(266,707)(267,722)(268,723)(269,724)(270,725)(271,726)(272,727)
(273,728)(274,715)(275,716)(276,717)(277,718)(278,719)(279,720)(280,721)
(281,736)(282,737)(283,738)(284,739)(285,740)(286,741)(287,742)(288,729)
(289,730)(290,731)(291,732)(292,733)(293,734)(294,735)(295,750)(296,751)
(297,752)(298,753)(299,754)(300,755)(301,756)(302,743)(303,744)(304,745)
(305,746)(306,747)(307,748)(308,749)(309,764)(310,765)(311,766)(312,767)
(313,768)(314,769)(315,770)(316,757)(317,758)(318,759)(319,760)(320,761)
(321,762)(322,763)(323,778)(324,779)(325,780)(326,781)(327,782)(328,783)
(329,784)(330,771)(331,772)(332,773)(333,774)(334,775)(335,776)(336,777)
(337,785)(338,786)(339,787)(340,788)(341,789)(342,790)(343,791)(344,792)
(345,793)(346,794)(347,795)(348,796)(349,797)(350,798)(351,799)(352,800)
(353,801)(354,802)(355,803)(356,804)(357,805)(358,806)(359,807)(360,808)
(361,809)(362,810)(363,811)(364,812)(365,813)(366,814)(367,815)(368,816)
(369,817)(370,818)(371,819)(372,820)(373,821)(374,822)(375,823)(376,824)
(377,825)(378,826)(379,827)(380,828)(381,829)(382,830)(383,831)(384,832)
(385,833)(386,834)(387,835)(388,836)(389,837)(390,838)(391,839)(392,840)
(393,841)(394,842)(395,843)(396,844)(397,845)(398,846)(399,847)(400,848)
(401,849)(402,850)(403,851)(404,852)(405,853)(406,854)(407,855)(408,856)
(409,857)(410,858)(411,859)(412,860)(413,861)(414,862)(415,863)(416,864)
(417,865)(418,866)(419,867)(420,868)(421,869)(422,870)(423,871)(424,872)
(425,873)(426,874)(427,875)(428,876)(429,877)(430,878)(431,879)(432,880)
(433,881)(434,882)(435,883)(436,884)(437,885)(438,886)(439,887)(440,888)
(441,889)(442,890)(443,891)(444,892)(445,893)(446,894)(447,895)(448,896);;
s2 := (225,239)(226,240)(227,241)(228,242)(229,243)(230,244)(231,245)(232,246)
(233,247)(234,248)(235,249)(236,250)(237,251)(238,252)(253,267)(254,268)
(255,269)(256,270)(257,271)(258,272)(259,273)(260,274)(261,275)(262,276)
(263,277)(264,278)(265,279)(266,280)(281,295)(282,296)(283,297)(284,298)
(285,299)(286,300)(287,301)(288,302)(289,303)(290,304)(291,305)(292,306)
(293,307)(294,308)(309,323)(310,324)(311,325)(312,326)(313,327)(314,328)
(315,329)(316,330)(317,331)(318,332)(319,333)(320,334)(321,335)(322,336)
(337,351)(338,352)(339,353)(340,354)(341,355)(342,356)(343,357)(344,358)
(345,359)(346,360)(347,361)(348,362)(349,363)(350,364)(365,379)(366,380)
(367,381)(368,382)(369,383)(370,384)(371,385)(372,386)(373,387)(374,388)
(375,389)(376,390)(377,391)(378,392)(393,407)(394,408)(395,409)(396,410)
(397,411)(398,412)(399,413)(400,414)(401,415)(402,416)(403,417)(404,418)
(405,419)(406,420)(421,435)(422,436)(423,437)(424,438)(425,439)(426,440)
(427,441)(428,442)(429,443)(430,444)(431,445)(432,446)(433,447)(434,448)
(449,477)(450,478)(451,479)(452,480)(453,481)(454,482)(455,483)(456,484)
(457,485)(458,486)(459,487)(460,488)(461,489)(462,490)(463,491)(464,492)
(465,493)(466,494)(467,495)(468,496)(469,497)(470,498)(471,499)(472,500)
(473,501)(474,502)(475,503)(476,504)(505,533)(506,534)(507,535)(508,536)
(509,537)(510,538)(511,539)(512,540)(513,541)(514,542)(515,543)(516,544)
(517,545)(518,546)(519,547)(520,548)(521,549)(522,550)(523,551)(524,552)
(525,553)(526,554)(527,555)(528,556)(529,557)(530,558)(531,559)(532,560)
(561,589)(562,590)(563,591)(564,592)(565,593)(566,594)(567,595)(568,596)
(569,597)(570,598)(571,599)(572,600)(573,601)(574,602)(575,603)(576,604)
(577,605)(578,606)(579,607)(580,608)(581,609)(582,610)(583,611)(584,612)
(585,613)(586,614)(587,615)(588,616)(617,645)(618,646)(619,647)(620,648)
(621,649)(622,650)(623,651)(624,652)(625,653)(626,654)(627,655)(628,656)
(629,657)(630,658)(631,659)(632,660)(633,661)(634,662)(635,663)(636,664)
(637,665)(638,666)(639,667)(640,668)(641,669)(642,670)(643,671)(644,672)
(673,715)(674,716)(675,717)(676,718)(677,719)(678,720)(679,721)(680,722)
(681,723)(682,724)(683,725)(684,726)(685,727)(686,728)(687,701)(688,702)
(689,703)(690,704)(691,705)(692,706)(693,707)(694,708)(695,709)(696,710)
(697,711)(698,712)(699,713)(700,714)(729,771)(730,772)(731,773)(732,774)
(733,775)(734,776)(735,777)(736,778)(737,779)(738,780)(739,781)(740,782)
(741,783)(742,784)(743,757)(744,758)(745,759)(746,760)(747,761)(748,762)
(749,763)(750,764)(751,765)(752,766)(753,767)(754,768)(755,769)(756,770)
(785,827)(786,828)(787,829)(788,830)(789,831)(790,832)(791,833)(792,834)
(793,835)(794,836)(795,837)(796,838)(797,839)(798,840)(799,813)(800,814)
(801,815)(802,816)(803,817)(804,818)(805,819)(806,820)(807,821)(808,822)
(809,823)(810,824)(811,825)(812,826)(841,883)(842,884)(843,885)(844,886)
(845,887)(846,888)(847,889)(848,890)(849,891)(850,892)(851,893)(852,894)
(853,895)(854,896)(855,869)(856,870)(857,871)(858,872)(859,873)(860,874)
(861,875)(862,876)(863,877)(864,878)(865,879)(866,880)(867,881)(868,882);;
s3 := (  1,393)(  2,399)(  3,398)(  4,397)(  5,396)(  6,395)(  7,394)(  8,400)
(  9,406)( 10,405)( 11,404)( 12,403)( 13,402)( 14,401)( 15,407)( 16,413)
( 17,412)( 18,411)( 19,410)( 20,409)( 21,408)( 22,414)( 23,420)( 24,419)
( 25,418)( 26,417)( 27,416)( 28,415)( 29,421)( 30,427)( 31,426)( 32,425)
( 33,424)( 34,423)( 35,422)( 36,428)( 37,434)( 38,433)( 39,432)( 40,431)
( 41,430)( 42,429)( 43,435)( 44,441)( 45,440)( 46,439)( 47,438)( 48,437)
( 49,436)( 50,442)( 51,448)( 52,447)( 53,446)( 54,445)( 55,444)( 56,443)
( 57,337)( 58,343)( 59,342)( 60,341)( 61,340)( 62,339)( 63,338)( 64,344)
( 65,350)( 66,349)( 67,348)( 68,347)( 69,346)( 70,345)( 71,351)( 72,357)
( 73,356)( 74,355)( 75,354)( 76,353)( 77,352)( 78,358)( 79,364)( 80,363)
( 81,362)( 82,361)( 83,360)( 84,359)( 85,365)( 86,371)( 87,370)( 88,369)
( 89,368)( 90,367)( 91,366)( 92,372)( 93,378)( 94,377)( 95,376)( 96,375)
( 97,374)( 98,373)( 99,379)(100,385)(101,384)(102,383)(103,382)(104,381)
(105,380)(106,386)(107,392)(108,391)(109,390)(110,389)(111,388)(112,387)
(113,281)(114,287)(115,286)(116,285)(117,284)(118,283)(119,282)(120,288)
(121,294)(122,293)(123,292)(124,291)(125,290)(126,289)(127,295)(128,301)
(129,300)(130,299)(131,298)(132,297)(133,296)(134,302)(135,308)(136,307)
(137,306)(138,305)(139,304)(140,303)(141,309)(142,315)(143,314)(144,313)
(145,312)(146,311)(147,310)(148,316)(149,322)(150,321)(151,320)(152,319)
(153,318)(154,317)(155,323)(156,329)(157,328)(158,327)(159,326)(160,325)
(161,324)(162,330)(163,336)(164,335)(165,334)(166,333)(167,332)(168,331)
(169,225)(170,231)(171,230)(172,229)(173,228)(174,227)(175,226)(176,232)
(177,238)(178,237)(179,236)(180,235)(181,234)(182,233)(183,239)(184,245)
(185,244)(186,243)(187,242)(188,241)(189,240)(190,246)(191,252)(192,251)
(193,250)(194,249)(195,248)(196,247)(197,253)(198,259)(199,258)(200,257)
(201,256)(202,255)(203,254)(204,260)(205,266)(206,265)(207,264)(208,263)
(209,262)(210,261)(211,267)(212,273)(213,272)(214,271)(215,270)(216,269)
(217,268)(218,274)(219,280)(220,279)(221,278)(222,277)(223,276)(224,275)
(449,841)(450,847)(451,846)(452,845)(453,844)(454,843)(455,842)(456,848)
(457,854)(458,853)(459,852)(460,851)(461,850)(462,849)(463,855)(464,861)
(465,860)(466,859)(467,858)(468,857)(469,856)(470,862)(471,868)(472,867)
(473,866)(474,865)(475,864)(476,863)(477,869)(478,875)(479,874)(480,873)
(481,872)(482,871)(483,870)(484,876)(485,882)(486,881)(487,880)(488,879)
(489,878)(490,877)(491,883)(492,889)(493,888)(494,887)(495,886)(496,885)
(497,884)(498,890)(499,896)(500,895)(501,894)(502,893)(503,892)(504,891)
(505,785)(506,791)(507,790)(508,789)(509,788)(510,787)(511,786)(512,792)
(513,798)(514,797)(515,796)(516,795)(517,794)(518,793)(519,799)(520,805)
(521,804)(522,803)(523,802)(524,801)(525,800)(526,806)(527,812)(528,811)
(529,810)(530,809)(531,808)(532,807)(533,813)(534,819)(535,818)(536,817)
(537,816)(538,815)(539,814)(540,820)(541,826)(542,825)(543,824)(544,823)
(545,822)(546,821)(547,827)(548,833)(549,832)(550,831)(551,830)(552,829)
(553,828)(554,834)(555,840)(556,839)(557,838)(558,837)(559,836)(560,835)
(561,729)(562,735)(563,734)(564,733)(565,732)(566,731)(567,730)(568,736)
(569,742)(570,741)(571,740)(572,739)(573,738)(574,737)(575,743)(576,749)
(577,748)(578,747)(579,746)(580,745)(581,744)(582,750)(583,756)(584,755)
(585,754)(586,753)(587,752)(588,751)(589,757)(590,763)(591,762)(592,761)
(593,760)(594,759)(595,758)(596,764)(597,770)(598,769)(599,768)(600,767)
(601,766)(602,765)(603,771)(604,777)(605,776)(606,775)(607,774)(608,773)
(609,772)(610,778)(611,784)(612,783)(613,782)(614,781)(615,780)(616,779)
(617,673)(618,679)(619,678)(620,677)(621,676)(622,675)(623,674)(624,680)
(625,686)(626,685)(627,684)(628,683)(629,682)(630,681)(631,687)(632,693)
(633,692)(634,691)(635,690)(636,689)(637,688)(638,694)(639,700)(640,699)
(641,698)(642,697)(643,696)(644,695)(645,701)(646,707)(647,706)(648,705)
(649,704)(650,703)(651,702)(652,708)(653,714)(654,713)(655,712)(656,711)
(657,710)(658,709)(659,715)(660,721)(661,720)(662,719)(663,718)(664,717)
(665,716)(666,722)(667,728)(668,727)(669,726)(670,725)(671,724)(672,723);;
s4 := (  1, 58)(  2, 57)(  3, 63)(  4, 62)(  5, 61)(  6, 60)(  7, 59)(  8, 65)
(  9, 64)( 10, 70)( 11, 69)( 12, 68)( 13, 67)( 14, 66)( 15, 72)( 16, 71)
( 17, 77)( 18, 76)( 19, 75)( 20, 74)( 21, 73)( 22, 79)( 23, 78)( 24, 84)
( 25, 83)( 26, 82)( 27, 81)( 28, 80)( 29, 86)( 30, 85)( 31, 91)( 32, 90)
( 33, 89)( 34, 88)( 35, 87)( 36, 93)( 37, 92)( 38, 98)( 39, 97)( 40, 96)
( 41, 95)( 42, 94)( 43,100)( 44, 99)( 45,105)( 46,104)( 47,103)( 48,102)
( 49,101)( 50,107)( 51,106)( 52,112)( 53,111)( 54,110)( 55,109)( 56,108)
(113,170)(114,169)(115,175)(116,174)(117,173)(118,172)(119,171)(120,177)
(121,176)(122,182)(123,181)(124,180)(125,179)(126,178)(127,184)(128,183)
(129,189)(130,188)(131,187)(132,186)(133,185)(134,191)(135,190)(136,196)
(137,195)(138,194)(139,193)(140,192)(141,198)(142,197)(143,203)(144,202)
(145,201)(146,200)(147,199)(148,205)(149,204)(150,210)(151,209)(152,208)
(153,207)(154,206)(155,212)(156,211)(157,217)(158,216)(159,215)(160,214)
(161,213)(162,219)(163,218)(164,224)(165,223)(166,222)(167,221)(168,220)
(225,282)(226,281)(227,287)(228,286)(229,285)(230,284)(231,283)(232,289)
(233,288)(234,294)(235,293)(236,292)(237,291)(238,290)(239,296)(240,295)
(241,301)(242,300)(243,299)(244,298)(245,297)(246,303)(247,302)(248,308)
(249,307)(250,306)(251,305)(252,304)(253,310)(254,309)(255,315)(256,314)
(257,313)(258,312)(259,311)(260,317)(261,316)(262,322)(263,321)(264,320)
(265,319)(266,318)(267,324)(268,323)(269,329)(270,328)(271,327)(272,326)
(273,325)(274,331)(275,330)(276,336)(277,335)(278,334)(279,333)(280,332)
(337,394)(338,393)(339,399)(340,398)(341,397)(342,396)(343,395)(344,401)
(345,400)(346,406)(347,405)(348,404)(349,403)(350,402)(351,408)(352,407)
(353,413)(354,412)(355,411)(356,410)(357,409)(358,415)(359,414)(360,420)
(361,419)(362,418)(363,417)(364,416)(365,422)(366,421)(367,427)(368,426)
(369,425)(370,424)(371,423)(372,429)(373,428)(374,434)(375,433)(376,432)
(377,431)(378,430)(379,436)(380,435)(381,441)(382,440)(383,439)(384,438)
(385,437)(386,443)(387,442)(388,448)(389,447)(390,446)(391,445)(392,444)
(449,506)(450,505)(451,511)(452,510)(453,509)(454,508)(455,507)(456,513)
(457,512)(458,518)(459,517)(460,516)(461,515)(462,514)(463,520)(464,519)
(465,525)(466,524)(467,523)(468,522)(469,521)(470,527)(471,526)(472,532)
(473,531)(474,530)(475,529)(476,528)(477,534)(478,533)(479,539)(480,538)
(481,537)(482,536)(483,535)(484,541)(485,540)(486,546)(487,545)(488,544)
(489,543)(490,542)(491,548)(492,547)(493,553)(494,552)(495,551)(496,550)
(497,549)(498,555)(499,554)(500,560)(501,559)(502,558)(503,557)(504,556)
(561,618)(562,617)(563,623)(564,622)(565,621)(566,620)(567,619)(568,625)
(569,624)(570,630)(571,629)(572,628)(573,627)(574,626)(575,632)(576,631)
(577,637)(578,636)(579,635)(580,634)(581,633)(582,639)(583,638)(584,644)
(585,643)(586,642)(587,641)(588,640)(589,646)(590,645)(591,651)(592,650)
(593,649)(594,648)(595,647)(596,653)(597,652)(598,658)(599,657)(600,656)
(601,655)(602,654)(603,660)(604,659)(605,665)(606,664)(607,663)(608,662)
(609,661)(610,667)(611,666)(612,672)(613,671)(614,670)(615,669)(616,668)
(673,730)(674,729)(675,735)(676,734)(677,733)(678,732)(679,731)(680,737)
(681,736)(682,742)(683,741)(684,740)(685,739)(686,738)(687,744)(688,743)
(689,749)(690,748)(691,747)(692,746)(693,745)(694,751)(695,750)(696,756)
(697,755)(698,754)(699,753)(700,752)(701,758)(702,757)(703,763)(704,762)
(705,761)(706,760)(707,759)(708,765)(709,764)(710,770)(711,769)(712,768)
(713,767)(714,766)(715,772)(716,771)(717,777)(718,776)(719,775)(720,774)
(721,773)(722,779)(723,778)(724,784)(725,783)(726,782)(727,781)(728,780)
(785,842)(786,841)(787,847)(788,846)(789,845)(790,844)(791,843)(792,849)
(793,848)(794,854)(795,853)(796,852)(797,851)(798,850)(799,856)(800,855)
(801,861)(802,860)(803,859)(804,858)(805,857)(806,863)(807,862)(808,868)
(809,867)(810,866)(811,865)(812,864)(813,870)(814,869)(815,875)(816,874)
(817,873)(818,872)(819,871)(820,877)(821,876)(822,882)(823,881)(824,880)
(825,879)(826,878)(827,884)(828,883)(829,889)(830,888)(831,887)(832,886)
(833,885)(834,891)(835,890)(836,896)(837,895)(838,894)(839,893)(840,892);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
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)( 57,169)( 58,170)( 59,171)( 60,172)( 61,173)( 62,174)( 63,175)
( 64,176)( 65,177)( 66,178)( 67,179)( 68,180)( 69,181)( 70,182)( 71,183)
( 72,184)( 73,185)( 74,186)( 75,187)( 76,188)( 77,189)( 78,190)( 79,191)
( 80,192)( 81,193)( 82,194)( 83,195)( 84,196)( 85,197)( 86,198)( 87,199)
( 88,200)( 89,201)( 90,202)( 91,203)( 92,204)( 93,205)( 94,206)( 95,207)
( 96,208)( 97,209)( 98,210)( 99,211)(100,212)(101,213)(102,214)(103,215)
(104,216)(105,217)(106,218)(107,219)(108,220)(109,221)(110,222)(111,223)
(112,224)(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)(281,393)(282,394)(283,395)(284,396)(285,397)(286,398)(287,399)
(288,400)(289,401)(290,402)(291,403)(292,404)(293,405)(294,406)(295,407)
(296,408)(297,409)(298,410)(299,411)(300,412)(301,413)(302,414)(303,415)
(304,416)(305,417)(306,418)(307,419)(308,420)(309,421)(310,422)(311,423)
(312,424)(313,425)(314,426)(315,427)(316,428)(317,429)(318,430)(319,431)
(320,432)(321,433)(322,434)(323,435)(324,436)(325,437)(326,438)(327,439)
(328,440)(329,441)(330,442)(331,443)(332,444)(333,445)(334,446)(335,447)
(336,448)(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)(505,617)(506,618)(507,619)(508,620)(509,621)(510,622)(511,623)
(512,624)(513,625)(514,626)(515,627)(516,628)(517,629)(518,630)(519,631)
(520,632)(521,633)(522,634)(523,635)(524,636)(525,637)(526,638)(527,639)
(528,640)(529,641)(530,642)(531,643)(532,644)(533,645)(534,646)(535,647)
(536,648)(537,649)(538,650)(539,651)(540,652)(541,653)(542,654)(543,655)
(544,656)(545,657)(546,658)(547,659)(548,660)(549,661)(550,662)(551,663)
(552,664)(553,665)(554,666)(555,667)(556,668)(557,669)(558,670)(559,671)
(560,672)(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)(729,841)(730,842)(731,843)(732,844)(733,845)(734,846)(735,847)
(736,848)(737,849)(738,850)(739,851)(740,852)(741,853)(742,854)(743,855)
(744,856)(745,857)(746,858)(747,859)(748,860)(749,861)(750,862)(751,863)
(752,864)(753,865)(754,866)(755,867)(756,868)(757,869)(758,870)(759,871)
(760,872)(761,873)(762,874)(763,875)(764,876)(765,877)(766,878)(767,879)
(768,880)(769,881)(770,882)(771,883)(772,884)(773,885)(774,886)(775,887)
(776,888)(777,889)(778,890)(779,891)(780,892)(781,893)(782,894)(783,895)
(784,896);
s1 := Sym(896)!(  1,449)(  2,450)(  3,451)(  4,452)(  5,453)(  6,454)(  7,455)
(  8,456)(  9,457)( 10,458)( 11,459)( 12,460)( 13,461)( 14,462)( 15,463)
( 16,464)( 17,465)( 18,466)( 19,467)( 20,468)( 21,469)( 22,470)( 23,471)
( 24,472)( 25,473)( 26,474)( 27,475)( 28,476)( 29,477)( 30,478)( 31,479)
( 32,480)( 33,481)( 34,482)( 35,483)( 36,484)( 37,485)( 38,486)( 39,487)
( 40,488)( 41,489)( 42,490)( 43,491)( 44,492)( 45,493)( 46,494)( 47,495)
( 48,496)( 49,497)( 50,498)( 51,499)( 52,500)( 53,501)( 54,502)( 55,503)
( 56,504)( 57,505)( 58,506)( 59,507)( 60,508)( 61,509)( 62,510)( 63,511)
( 64,512)( 65,513)( 66,514)( 67,515)( 68,516)( 69,517)( 70,518)( 71,519)
( 72,520)( 73,521)( 74,522)( 75,523)( 76,524)( 77,525)( 78,526)( 79,527)
( 80,528)( 81,529)( 82,530)( 83,531)( 84,532)( 85,533)( 86,534)( 87,535)
( 88,536)( 89,537)( 90,538)( 91,539)( 92,540)( 93,541)( 94,542)( 95,543)
( 96,544)( 97,545)( 98,546)( 99,547)(100,548)(101,549)(102,550)(103,551)
(104,552)(105,553)(106,554)(107,555)(108,556)(109,557)(110,558)(111,559)
(112,560)(113,568)(114,569)(115,570)(116,571)(117,572)(118,573)(119,574)
(120,561)(121,562)(122,563)(123,564)(124,565)(125,566)(126,567)(127,582)
(128,583)(129,584)(130,585)(131,586)(132,587)(133,588)(134,575)(135,576)
(136,577)(137,578)(138,579)(139,580)(140,581)(141,596)(142,597)(143,598)
(144,599)(145,600)(146,601)(147,602)(148,589)(149,590)(150,591)(151,592)
(152,593)(153,594)(154,595)(155,610)(156,611)(157,612)(158,613)(159,614)
(160,615)(161,616)(162,603)(163,604)(164,605)(165,606)(166,607)(167,608)
(168,609)(169,624)(170,625)(171,626)(172,627)(173,628)(174,629)(175,630)
(176,617)(177,618)(178,619)(179,620)(180,621)(181,622)(182,623)(183,638)
(184,639)(185,640)(186,641)(187,642)(188,643)(189,644)(190,631)(191,632)
(192,633)(193,634)(194,635)(195,636)(196,637)(197,652)(198,653)(199,654)
(200,655)(201,656)(202,657)(203,658)(204,645)(205,646)(206,647)(207,648)
(208,649)(209,650)(210,651)(211,666)(212,667)(213,668)(214,669)(215,670)
(216,671)(217,672)(218,659)(219,660)(220,661)(221,662)(222,663)(223,664)
(224,665)(225,680)(226,681)(227,682)(228,683)(229,684)(230,685)(231,686)
(232,673)(233,674)(234,675)(235,676)(236,677)(237,678)(238,679)(239,694)
(240,695)(241,696)(242,697)(243,698)(244,699)(245,700)(246,687)(247,688)
(248,689)(249,690)(250,691)(251,692)(252,693)(253,708)(254,709)(255,710)
(256,711)(257,712)(258,713)(259,714)(260,701)(261,702)(262,703)(263,704)
(264,705)(265,706)(266,707)(267,722)(268,723)(269,724)(270,725)(271,726)
(272,727)(273,728)(274,715)(275,716)(276,717)(277,718)(278,719)(279,720)
(280,721)(281,736)(282,737)(283,738)(284,739)(285,740)(286,741)(287,742)
(288,729)(289,730)(290,731)(291,732)(292,733)(293,734)(294,735)(295,750)
(296,751)(297,752)(298,753)(299,754)(300,755)(301,756)(302,743)(303,744)
(304,745)(305,746)(306,747)(307,748)(308,749)(309,764)(310,765)(311,766)
(312,767)(313,768)(314,769)(315,770)(316,757)(317,758)(318,759)(319,760)
(320,761)(321,762)(322,763)(323,778)(324,779)(325,780)(326,781)(327,782)
(328,783)(329,784)(330,771)(331,772)(332,773)(333,774)(334,775)(335,776)
(336,777)(337,785)(338,786)(339,787)(340,788)(341,789)(342,790)(343,791)
(344,792)(345,793)(346,794)(347,795)(348,796)(349,797)(350,798)(351,799)
(352,800)(353,801)(354,802)(355,803)(356,804)(357,805)(358,806)(359,807)
(360,808)(361,809)(362,810)(363,811)(364,812)(365,813)(366,814)(367,815)
(368,816)(369,817)(370,818)(371,819)(372,820)(373,821)(374,822)(375,823)
(376,824)(377,825)(378,826)(379,827)(380,828)(381,829)(382,830)(383,831)
(384,832)(385,833)(386,834)(387,835)(388,836)(389,837)(390,838)(391,839)
(392,840)(393,841)(394,842)(395,843)(396,844)(397,845)(398,846)(399,847)
(400,848)(401,849)(402,850)(403,851)(404,852)(405,853)(406,854)(407,855)
(408,856)(409,857)(410,858)(411,859)(412,860)(413,861)(414,862)(415,863)
(416,864)(417,865)(418,866)(419,867)(420,868)(421,869)(422,870)(423,871)
(424,872)(425,873)(426,874)(427,875)(428,876)(429,877)(430,878)(431,879)
(432,880)(433,881)(434,882)(435,883)(436,884)(437,885)(438,886)(439,887)
(440,888)(441,889)(442,890)(443,891)(444,892)(445,893)(446,894)(447,895)
(448,896);
s2 := Sym(896)!(225,239)(226,240)(227,241)(228,242)(229,243)(230,244)(231,245)
(232,246)(233,247)(234,248)(235,249)(236,250)(237,251)(238,252)(253,267)
(254,268)(255,269)(256,270)(257,271)(258,272)(259,273)(260,274)(261,275)
(262,276)(263,277)(264,278)(265,279)(266,280)(281,295)(282,296)(283,297)
(284,298)(285,299)(286,300)(287,301)(288,302)(289,303)(290,304)(291,305)
(292,306)(293,307)(294,308)(309,323)(310,324)(311,325)(312,326)(313,327)
(314,328)(315,329)(316,330)(317,331)(318,332)(319,333)(320,334)(321,335)
(322,336)(337,351)(338,352)(339,353)(340,354)(341,355)(342,356)(343,357)
(344,358)(345,359)(346,360)(347,361)(348,362)(349,363)(350,364)(365,379)
(366,380)(367,381)(368,382)(369,383)(370,384)(371,385)(372,386)(373,387)
(374,388)(375,389)(376,390)(377,391)(378,392)(393,407)(394,408)(395,409)
(396,410)(397,411)(398,412)(399,413)(400,414)(401,415)(402,416)(403,417)
(404,418)(405,419)(406,420)(421,435)(422,436)(423,437)(424,438)(425,439)
(426,440)(427,441)(428,442)(429,443)(430,444)(431,445)(432,446)(433,447)
(434,448)(449,477)(450,478)(451,479)(452,480)(453,481)(454,482)(455,483)
(456,484)(457,485)(458,486)(459,487)(460,488)(461,489)(462,490)(463,491)
(464,492)(465,493)(466,494)(467,495)(468,496)(469,497)(470,498)(471,499)
(472,500)(473,501)(474,502)(475,503)(476,504)(505,533)(506,534)(507,535)
(508,536)(509,537)(510,538)(511,539)(512,540)(513,541)(514,542)(515,543)
(516,544)(517,545)(518,546)(519,547)(520,548)(521,549)(522,550)(523,551)
(524,552)(525,553)(526,554)(527,555)(528,556)(529,557)(530,558)(531,559)
(532,560)(561,589)(562,590)(563,591)(564,592)(565,593)(566,594)(567,595)
(568,596)(569,597)(570,598)(571,599)(572,600)(573,601)(574,602)(575,603)
(576,604)(577,605)(578,606)(579,607)(580,608)(581,609)(582,610)(583,611)
(584,612)(585,613)(586,614)(587,615)(588,616)(617,645)(618,646)(619,647)
(620,648)(621,649)(622,650)(623,651)(624,652)(625,653)(626,654)(627,655)
(628,656)(629,657)(630,658)(631,659)(632,660)(633,661)(634,662)(635,663)
(636,664)(637,665)(638,666)(639,667)(640,668)(641,669)(642,670)(643,671)
(644,672)(673,715)(674,716)(675,717)(676,718)(677,719)(678,720)(679,721)
(680,722)(681,723)(682,724)(683,725)(684,726)(685,727)(686,728)(687,701)
(688,702)(689,703)(690,704)(691,705)(692,706)(693,707)(694,708)(695,709)
(696,710)(697,711)(698,712)(699,713)(700,714)(729,771)(730,772)(731,773)
(732,774)(733,775)(734,776)(735,777)(736,778)(737,779)(738,780)(739,781)
(740,782)(741,783)(742,784)(743,757)(744,758)(745,759)(746,760)(747,761)
(748,762)(749,763)(750,764)(751,765)(752,766)(753,767)(754,768)(755,769)
(756,770)(785,827)(786,828)(787,829)(788,830)(789,831)(790,832)(791,833)
(792,834)(793,835)(794,836)(795,837)(796,838)(797,839)(798,840)(799,813)
(800,814)(801,815)(802,816)(803,817)(804,818)(805,819)(806,820)(807,821)
(808,822)(809,823)(810,824)(811,825)(812,826)(841,883)(842,884)(843,885)
(844,886)(845,887)(846,888)(847,889)(848,890)(849,891)(850,892)(851,893)
(852,894)(853,895)(854,896)(855,869)(856,870)(857,871)(858,872)(859,873)
(860,874)(861,875)(862,876)(863,877)(864,878)(865,879)(866,880)(867,881)
(868,882);
s3 := Sym(896)!(  1,393)(  2,399)(  3,398)(  4,397)(  5,396)(  6,395)(  7,394)
(  8,400)(  9,406)( 10,405)( 11,404)( 12,403)( 13,402)( 14,401)( 15,407)
( 16,413)( 17,412)( 18,411)( 19,410)( 20,409)( 21,408)( 22,414)( 23,420)
( 24,419)( 25,418)( 26,417)( 27,416)( 28,415)( 29,421)( 30,427)( 31,426)
( 32,425)( 33,424)( 34,423)( 35,422)( 36,428)( 37,434)( 38,433)( 39,432)
( 40,431)( 41,430)( 42,429)( 43,435)( 44,441)( 45,440)( 46,439)( 47,438)
( 48,437)( 49,436)( 50,442)( 51,448)( 52,447)( 53,446)( 54,445)( 55,444)
( 56,443)( 57,337)( 58,343)( 59,342)( 60,341)( 61,340)( 62,339)( 63,338)
( 64,344)( 65,350)( 66,349)( 67,348)( 68,347)( 69,346)( 70,345)( 71,351)
( 72,357)( 73,356)( 74,355)( 75,354)( 76,353)( 77,352)( 78,358)( 79,364)
( 80,363)( 81,362)( 82,361)( 83,360)( 84,359)( 85,365)( 86,371)( 87,370)
( 88,369)( 89,368)( 90,367)( 91,366)( 92,372)( 93,378)( 94,377)( 95,376)
( 96,375)( 97,374)( 98,373)( 99,379)(100,385)(101,384)(102,383)(103,382)
(104,381)(105,380)(106,386)(107,392)(108,391)(109,390)(110,389)(111,388)
(112,387)(113,281)(114,287)(115,286)(116,285)(117,284)(118,283)(119,282)
(120,288)(121,294)(122,293)(123,292)(124,291)(125,290)(126,289)(127,295)
(128,301)(129,300)(130,299)(131,298)(132,297)(133,296)(134,302)(135,308)
(136,307)(137,306)(138,305)(139,304)(140,303)(141,309)(142,315)(143,314)
(144,313)(145,312)(146,311)(147,310)(148,316)(149,322)(150,321)(151,320)
(152,319)(153,318)(154,317)(155,323)(156,329)(157,328)(158,327)(159,326)
(160,325)(161,324)(162,330)(163,336)(164,335)(165,334)(166,333)(167,332)
(168,331)(169,225)(170,231)(171,230)(172,229)(173,228)(174,227)(175,226)
(176,232)(177,238)(178,237)(179,236)(180,235)(181,234)(182,233)(183,239)
(184,245)(185,244)(186,243)(187,242)(188,241)(189,240)(190,246)(191,252)
(192,251)(193,250)(194,249)(195,248)(196,247)(197,253)(198,259)(199,258)
(200,257)(201,256)(202,255)(203,254)(204,260)(205,266)(206,265)(207,264)
(208,263)(209,262)(210,261)(211,267)(212,273)(213,272)(214,271)(215,270)
(216,269)(217,268)(218,274)(219,280)(220,279)(221,278)(222,277)(223,276)
(224,275)(449,841)(450,847)(451,846)(452,845)(453,844)(454,843)(455,842)
(456,848)(457,854)(458,853)(459,852)(460,851)(461,850)(462,849)(463,855)
(464,861)(465,860)(466,859)(467,858)(468,857)(469,856)(470,862)(471,868)
(472,867)(473,866)(474,865)(475,864)(476,863)(477,869)(478,875)(479,874)
(480,873)(481,872)(482,871)(483,870)(484,876)(485,882)(486,881)(487,880)
(488,879)(489,878)(490,877)(491,883)(492,889)(493,888)(494,887)(495,886)
(496,885)(497,884)(498,890)(499,896)(500,895)(501,894)(502,893)(503,892)
(504,891)(505,785)(506,791)(507,790)(508,789)(509,788)(510,787)(511,786)
(512,792)(513,798)(514,797)(515,796)(516,795)(517,794)(518,793)(519,799)
(520,805)(521,804)(522,803)(523,802)(524,801)(525,800)(526,806)(527,812)
(528,811)(529,810)(530,809)(531,808)(532,807)(533,813)(534,819)(535,818)
(536,817)(537,816)(538,815)(539,814)(540,820)(541,826)(542,825)(543,824)
(544,823)(545,822)(546,821)(547,827)(548,833)(549,832)(550,831)(551,830)
(552,829)(553,828)(554,834)(555,840)(556,839)(557,838)(558,837)(559,836)
(560,835)(561,729)(562,735)(563,734)(564,733)(565,732)(566,731)(567,730)
(568,736)(569,742)(570,741)(571,740)(572,739)(573,738)(574,737)(575,743)
(576,749)(577,748)(578,747)(579,746)(580,745)(581,744)(582,750)(583,756)
(584,755)(585,754)(586,753)(587,752)(588,751)(589,757)(590,763)(591,762)
(592,761)(593,760)(594,759)(595,758)(596,764)(597,770)(598,769)(599,768)
(600,767)(601,766)(602,765)(603,771)(604,777)(605,776)(606,775)(607,774)
(608,773)(609,772)(610,778)(611,784)(612,783)(613,782)(614,781)(615,780)
(616,779)(617,673)(618,679)(619,678)(620,677)(621,676)(622,675)(623,674)
(624,680)(625,686)(626,685)(627,684)(628,683)(629,682)(630,681)(631,687)
(632,693)(633,692)(634,691)(635,690)(636,689)(637,688)(638,694)(639,700)
(640,699)(641,698)(642,697)(643,696)(644,695)(645,701)(646,707)(647,706)
(648,705)(649,704)(650,703)(651,702)(652,708)(653,714)(654,713)(655,712)
(656,711)(657,710)(658,709)(659,715)(660,721)(661,720)(662,719)(663,718)
(664,717)(665,716)(666,722)(667,728)(668,727)(669,726)(670,725)(671,724)
(672,723);
s4 := Sym(896)!(  1, 58)(  2, 57)(  3, 63)(  4, 62)(  5, 61)(  6, 60)(  7, 59)
(  8, 65)(  9, 64)( 10, 70)( 11, 69)( 12, 68)( 13, 67)( 14, 66)( 15, 72)
( 16, 71)( 17, 77)( 18, 76)( 19, 75)( 20, 74)( 21, 73)( 22, 79)( 23, 78)
( 24, 84)( 25, 83)( 26, 82)( 27, 81)( 28, 80)( 29, 86)( 30, 85)( 31, 91)
( 32, 90)( 33, 89)( 34, 88)( 35, 87)( 36, 93)( 37, 92)( 38, 98)( 39, 97)
( 40, 96)( 41, 95)( 42, 94)( 43,100)( 44, 99)( 45,105)( 46,104)( 47,103)
( 48,102)( 49,101)( 50,107)( 51,106)( 52,112)( 53,111)( 54,110)( 55,109)
( 56,108)(113,170)(114,169)(115,175)(116,174)(117,173)(118,172)(119,171)
(120,177)(121,176)(122,182)(123,181)(124,180)(125,179)(126,178)(127,184)
(128,183)(129,189)(130,188)(131,187)(132,186)(133,185)(134,191)(135,190)
(136,196)(137,195)(138,194)(139,193)(140,192)(141,198)(142,197)(143,203)
(144,202)(145,201)(146,200)(147,199)(148,205)(149,204)(150,210)(151,209)
(152,208)(153,207)(154,206)(155,212)(156,211)(157,217)(158,216)(159,215)
(160,214)(161,213)(162,219)(163,218)(164,224)(165,223)(166,222)(167,221)
(168,220)(225,282)(226,281)(227,287)(228,286)(229,285)(230,284)(231,283)
(232,289)(233,288)(234,294)(235,293)(236,292)(237,291)(238,290)(239,296)
(240,295)(241,301)(242,300)(243,299)(244,298)(245,297)(246,303)(247,302)
(248,308)(249,307)(250,306)(251,305)(252,304)(253,310)(254,309)(255,315)
(256,314)(257,313)(258,312)(259,311)(260,317)(261,316)(262,322)(263,321)
(264,320)(265,319)(266,318)(267,324)(268,323)(269,329)(270,328)(271,327)
(272,326)(273,325)(274,331)(275,330)(276,336)(277,335)(278,334)(279,333)
(280,332)(337,394)(338,393)(339,399)(340,398)(341,397)(342,396)(343,395)
(344,401)(345,400)(346,406)(347,405)(348,404)(349,403)(350,402)(351,408)
(352,407)(353,413)(354,412)(355,411)(356,410)(357,409)(358,415)(359,414)
(360,420)(361,419)(362,418)(363,417)(364,416)(365,422)(366,421)(367,427)
(368,426)(369,425)(370,424)(371,423)(372,429)(373,428)(374,434)(375,433)
(376,432)(377,431)(378,430)(379,436)(380,435)(381,441)(382,440)(383,439)
(384,438)(385,437)(386,443)(387,442)(388,448)(389,447)(390,446)(391,445)
(392,444)(449,506)(450,505)(451,511)(452,510)(453,509)(454,508)(455,507)
(456,513)(457,512)(458,518)(459,517)(460,516)(461,515)(462,514)(463,520)
(464,519)(465,525)(466,524)(467,523)(468,522)(469,521)(470,527)(471,526)
(472,532)(473,531)(474,530)(475,529)(476,528)(477,534)(478,533)(479,539)
(480,538)(481,537)(482,536)(483,535)(484,541)(485,540)(486,546)(487,545)
(488,544)(489,543)(490,542)(491,548)(492,547)(493,553)(494,552)(495,551)
(496,550)(497,549)(498,555)(499,554)(500,560)(501,559)(502,558)(503,557)
(504,556)(561,618)(562,617)(563,623)(564,622)(565,621)(566,620)(567,619)
(568,625)(569,624)(570,630)(571,629)(572,628)(573,627)(574,626)(575,632)
(576,631)(577,637)(578,636)(579,635)(580,634)(581,633)(582,639)(583,638)
(584,644)(585,643)(586,642)(587,641)(588,640)(589,646)(590,645)(591,651)
(592,650)(593,649)(594,648)(595,647)(596,653)(597,652)(598,658)(599,657)
(600,656)(601,655)(602,654)(603,660)(604,659)(605,665)(606,664)(607,663)
(608,662)(609,661)(610,667)(611,666)(612,672)(613,671)(614,670)(615,669)
(616,668)(673,730)(674,729)(675,735)(676,734)(677,733)(678,732)(679,731)
(680,737)(681,736)(682,742)(683,741)(684,740)(685,739)(686,738)(687,744)
(688,743)(689,749)(690,748)(691,747)(692,746)(693,745)(694,751)(695,750)
(696,756)(697,755)(698,754)(699,753)(700,752)(701,758)(702,757)(703,763)
(704,762)(705,761)(706,760)(707,759)(708,765)(709,764)(710,770)(711,769)
(712,768)(713,767)(714,766)(715,772)(716,771)(717,777)(718,776)(719,775)
(720,774)(721,773)(722,779)(723,778)(724,784)(725,783)(726,782)(727,781)
(728,780)(785,842)(786,841)(787,847)(788,846)(789,845)(790,844)(791,843)
(792,849)(793,848)(794,854)(795,853)(796,852)(797,851)(798,850)(799,856)
(800,855)(801,861)(802,860)(803,859)(804,858)(805,857)(806,863)(807,862)
(808,868)(809,867)(810,866)(811,865)(812,864)(813,870)(814,869)(815,875)
(816,874)(817,873)(818,872)(819,871)(820,877)(821,876)(822,882)(823,881)
(824,880)(825,879)(826,878)(827,884)(828,883)(829,889)(830,888)(831,887)
(832,886)(833,885)(834,891)(835,890)(836,896)(837,895)(838,894)(839,893)
(840,892);
poly := sub<Sym(896)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 
References : None.
to this polytope