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