Polytope of Type {4,4,14,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,14,4}*1792
Also Known As : {{4,4|2},{4,14|2},{14,4|2}}. if this polytope has another name.
Group : SmallGroup(1792,364857)
Rank : 5
Schlafli Type : {4,4,14,4}
Number of vertices, edges, etc : 4, 8, 28, 28, 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 : {4,4,14,2}*896, {2,4,14,4}*896, {4,2,14,4}*896
4-fold quotients : {2,2,14,4}*448, {2,4,14,2}*448, {4,2,14,2}*448
7-fold quotients : {4,4,2,4}*256
8-fold quotients : {4,2,7,2}*224, {2,2,14,2}*224
14-fold quotients : {4,4,2,2}*128, {2,4,2,4}*128, {4,2,2,4}*128
16-fold quotients : {2,2,7,2}*112
28-fold quotients : {2,2,2,4}*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 := ( 1,561)( 2,562)( 3,563)( 4,564)( 5,565)( 6,566)( 7,567)( 8,568)
( 9,569)( 10,570)( 11,571)( 12,572)( 13,573)( 14,574)( 15,575)( 16,576)
( 17,577)( 18,578)( 19,579)( 20,580)( 21,581)( 22,582)( 23,583)( 24,584)
( 25,585)( 26,586)( 27,587)( 28,588)( 29,589)( 30,590)( 31,591)( 32,592)
( 33,593)( 34,594)( 35,595)( 36,596)( 37,597)( 38,598)( 39,599)( 40,600)
( 41,601)( 42,602)( 43,603)( 44,604)( 45,605)( 46,606)( 47,607)( 48,608)
( 49,609)( 50,610)( 51,611)( 52,612)( 53,613)( 54,614)( 55,615)( 56,616)
( 57,617)( 58,618)( 59,619)( 60,620)( 61,621)( 62,622)( 63,623)( 64,624)
( 65,625)( 66,626)( 67,627)( 68,628)( 69,629)( 70,630)( 71,631)( 72,632)
( 73,633)( 74,634)( 75,635)( 76,636)( 77,637)( 78,638)( 79,639)( 80,640)
( 81,641)( 82,642)( 83,643)( 84,644)( 85,645)( 86,646)( 87,647)( 88,648)
( 89,649)( 90,650)( 91,651)( 92,652)( 93,653)( 94,654)( 95,655)( 96,656)
( 97,657)( 98,658)( 99,659)(100,660)(101,661)(102,662)(103,663)(104,664)
(105,665)(106,666)(107,667)(108,668)(109,669)(110,670)(111,671)(112,672)
(113,449)(114,450)(115,451)(116,452)(117,453)(118,454)(119,455)(120,456)
(121,457)(122,458)(123,459)(124,460)(125,461)(126,462)(127,463)(128,464)
(129,465)(130,466)(131,467)(132,468)(133,469)(134,470)(135,471)(136,472)
(137,473)(138,474)(139,475)(140,476)(141,477)(142,478)(143,479)(144,480)
(145,481)(146,482)(147,483)(148,484)(149,485)(150,486)(151,487)(152,488)
(153,489)(154,490)(155,491)(156,492)(157,493)(158,494)(159,495)(160,496)
(161,497)(162,498)(163,499)(164,500)(165,501)(166,502)(167,503)(168,504)
(169,505)(170,506)(171,507)(172,508)(173,509)(174,510)(175,511)(176,512)
(177,513)(178,514)(179,515)(180,516)(181,517)(182,518)(183,519)(184,520)
(185,521)(186,522)(187,523)(188,524)(189,525)(190,526)(191,527)(192,528)
(193,529)(194,530)(195,531)(196,532)(197,533)(198,534)(199,535)(200,536)
(201,537)(202,538)(203,539)(204,540)(205,541)(206,542)(207,543)(208,544)
(209,545)(210,546)(211,547)(212,548)(213,549)(214,550)(215,551)(216,552)
(217,553)(218,554)(219,555)(220,556)(221,557)(222,558)(223,559)(224,560)
(225,792)(226,793)(227,794)(228,795)(229,796)(230,797)(231,798)(232,785)
(233,786)(234,787)(235,788)(236,789)(237,790)(238,791)(239,806)(240,807)
(241,808)(242,809)(243,810)(244,811)(245,812)(246,799)(247,800)(248,801)
(249,802)(250,803)(251,804)(252,805)(253,820)(254,821)(255,822)(256,823)
(257,824)(258,825)(259,826)(260,813)(261,814)(262,815)(263,816)(264,817)
(265,818)(266,819)(267,834)(268,835)(269,836)(270,837)(271,838)(272,839)
(273,840)(274,827)(275,828)(276,829)(277,830)(278,831)(279,832)(280,833)
(281,848)(282,849)(283,850)(284,851)(285,852)(286,853)(287,854)(288,841)
(289,842)(290,843)(291,844)(292,845)(293,846)(294,847)(295,862)(296,863)
(297,864)(298,865)(299,866)(300,867)(301,868)(302,855)(303,856)(304,857)
(305,858)(306,859)(307,860)(308,861)(309,876)(310,877)(311,878)(312,879)
(313,880)(314,881)(315,882)(316,869)(317,870)(318,871)(319,872)(320,873)
(321,874)(322,875)(323,890)(324,891)(325,892)(326,893)(327,894)(328,895)
(329,896)(330,883)(331,884)(332,885)(333,886)(334,887)(335,888)(336,889)
(337,680)(338,681)(339,682)(340,683)(341,684)(342,685)(343,686)(344,673)
(345,674)(346,675)(347,676)(348,677)(349,678)(350,679)(351,694)(352,695)
(353,696)(354,697)(355,698)(356,699)(357,700)(358,687)(359,688)(360,689)
(361,690)(362,691)(363,692)(364,693)(365,708)(366,709)(367,710)(368,711)
(369,712)(370,713)(371,714)(372,701)(373,702)(374,703)(375,704)(376,705)
(377,706)(378,707)(379,722)(380,723)(381,724)(382,725)(383,726)(384,727)
(385,728)(386,715)(387,716)(388,717)(389,718)(390,719)(391,720)(392,721)
(393,736)(394,737)(395,738)(396,739)(397,740)(398,741)(399,742)(400,729)
(401,730)(402,731)(403,732)(404,733)(405,734)(406,735)(407,750)(408,751)
(409,752)(410,753)(411,754)(412,755)(413,756)(414,743)(415,744)(416,745)
(417,746)(418,747)(419,748)(420,749)(421,764)(422,765)(423,766)(424,767)
(425,768)(426,769)(427,770)(428,757)(429,758)(430,759)(431,760)(432,761)
(433,762)(434,763)(435,778)(436,779)(437,780)(438,781)(439,782)(440,783)
(441,784)(442,771)(443,772)(444,773)(445,774)(446,775)(447,776)(448,777);;
s1 := (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);;
s2 := ( 1,281)( 2,287)( 3,286)( 4,285)( 5,284)( 6,283)( 7,282)( 8,288)
( 9,294)( 10,293)( 11,292)( 12,291)( 13,290)( 14,289)( 15,295)( 16,301)
( 17,300)( 18,299)( 19,298)( 20,297)( 21,296)( 22,302)( 23,308)( 24,307)
( 25,306)( 26,305)( 27,304)( 28,303)( 29,309)( 30,315)( 31,314)( 32,313)
( 33,312)( 34,311)( 35,310)( 36,316)( 37,322)( 38,321)( 39,320)( 40,319)
( 41,318)( 42,317)( 43,323)( 44,329)( 45,328)( 46,327)( 47,326)( 48,325)
( 49,324)( 50,330)( 51,336)( 52,335)( 53,334)( 54,333)( 55,332)( 56,331)
( 57,225)( 58,231)( 59,230)( 60,229)( 61,228)( 62,227)( 63,226)( 64,232)
( 65,238)( 66,237)( 67,236)( 68,235)( 69,234)( 70,233)( 71,239)( 72,245)
( 73,244)( 74,243)( 75,242)( 76,241)( 77,240)( 78,246)( 79,252)( 80,251)
( 81,250)( 82,249)( 83,248)( 84,247)( 85,253)( 86,259)( 87,258)( 88,257)
( 89,256)( 90,255)( 91,254)( 92,260)( 93,266)( 94,265)( 95,264)( 96,263)
( 97,262)( 98,261)( 99,267)(100,273)(101,272)(102,271)(103,270)(104,269)
(105,268)(106,274)(107,280)(108,279)(109,278)(110,277)(111,276)(112,275)
(113,400)(114,406)(115,405)(116,404)(117,403)(118,402)(119,401)(120,393)
(121,399)(122,398)(123,397)(124,396)(125,395)(126,394)(127,414)(128,420)
(129,419)(130,418)(131,417)(132,416)(133,415)(134,407)(135,413)(136,412)
(137,411)(138,410)(139,409)(140,408)(141,428)(142,434)(143,433)(144,432)
(145,431)(146,430)(147,429)(148,421)(149,427)(150,426)(151,425)(152,424)
(153,423)(154,422)(155,442)(156,448)(157,447)(158,446)(159,445)(160,444)
(161,443)(162,435)(163,441)(164,440)(165,439)(166,438)(167,437)(168,436)
(169,344)(170,350)(171,349)(172,348)(173,347)(174,346)(175,345)(176,337)
(177,343)(178,342)(179,341)(180,340)(181,339)(182,338)(183,358)(184,364)
(185,363)(186,362)(187,361)(188,360)(189,359)(190,351)(191,357)(192,356)
(193,355)(194,354)(195,353)(196,352)(197,372)(198,378)(199,377)(200,376)
(201,375)(202,374)(203,373)(204,365)(205,371)(206,370)(207,369)(208,368)
(209,367)(210,366)(211,386)(212,392)(213,391)(214,390)(215,389)(216,388)
(217,387)(218,379)(219,385)(220,384)(221,383)(222,382)(223,381)(224,380)
(449,729)(450,735)(451,734)(452,733)(453,732)(454,731)(455,730)(456,736)
(457,742)(458,741)(459,740)(460,739)(461,738)(462,737)(463,743)(464,749)
(465,748)(466,747)(467,746)(468,745)(469,744)(470,750)(471,756)(472,755)
(473,754)(474,753)(475,752)(476,751)(477,757)(478,763)(479,762)(480,761)
(481,760)(482,759)(483,758)(484,764)(485,770)(486,769)(487,768)(488,767)
(489,766)(490,765)(491,771)(492,777)(493,776)(494,775)(495,774)(496,773)
(497,772)(498,778)(499,784)(500,783)(501,782)(502,781)(503,780)(504,779)
(505,673)(506,679)(507,678)(508,677)(509,676)(510,675)(511,674)(512,680)
(513,686)(514,685)(515,684)(516,683)(517,682)(518,681)(519,687)(520,693)
(521,692)(522,691)(523,690)(524,689)(525,688)(526,694)(527,700)(528,699)
(529,698)(530,697)(531,696)(532,695)(533,701)(534,707)(535,706)(536,705)
(537,704)(538,703)(539,702)(540,708)(541,714)(542,713)(543,712)(544,711)
(545,710)(546,709)(547,715)(548,721)(549,720)(550,719)(551,718)(552,717)
(553,716)(554,722)(555,728)(556,727)(557,726)(558,725)(559,724)(560,723)
(561,848)(562,854)(563,853)(564,852)(565,851)(566,850)(567,849)(568,841)
(569,847)(570,846)(571,845)(572,844)(573,843)(574,842)(575,862)(576,868)
(577,867)(578,866)(579,865)(580,864)(581,863)(582,855)(583,861)(584,860)
(585,859)(586,858)(587,857)(588,856)(589,876)(590,882)(591,881)(592,880)
(593,879)(594,878)(595,877)(596,869)(597,875)(598,874)(599,873)(600,872)
(601,871)(602,870)(603,890)(604,896)(605,895)(606,894)(607,893)(608,892)
(609,891)(610,883)(611,889)(612,888)(613,887)(614,886)(615,885)(616,884)
(617,792)(618,798)(619,797)(620,796)(621,795)(622,794)(623,793)(624,785)
(625,791)(626,790)(627,789)(628,788)(629,787)(630,786)(631,806)(632,812)
(633,811)(634,810)(635,809)(636,808)(637,807)(638,799)(639,805)(640,804)
(641,803)(642,802)(643,801)(644,800)(645,820)(646,826)(647,825)(648,824)
(649,823)(650,822)(651,821)(652,813)(653,819)(654,818)(655,817)(656,816)
(657,815)(658,814)(659,834)(660,840)(661,839)(662,838)(663,837)(664,836)
(665,835)(666,827)(667,833)(668,832)(669,831)(670,830)(671,829)(672,828);;
s3 := ( 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);;
s4 := ( 1,113)( 2,114)( 3,115)( 4,116)( 5,117)( 6,118)( 7,119)( 8,120)
( 9,121)( 10,122)( 11,123)( 12,124)( 13,125)( 14,126)( 15,127)( 16,128)
( 17,129)( 18,130)( 19,131)( 20,132)( 21,133)( 22,134)( 23,135)( 24,136)
( 25,137)( 26,138)( 27,139)( 28,140)( 29,141)( 30,142)( 31,143)( 32,144)
( 33,145)( 34,146)( 35,147)( 36,148)( 37,149)( 38,150)( 39,151)( 40,152)
( 41,153)( 42,154)( 43,155)( 44,156)( 45,157)( 46,158)( 47,159)( 48,160)
( 49,161)( 50,162)( 51,163)( 52,164)( 53,165)( 54,166)( 55,167)( 56,168)
( 57,176)( 58,177)( 59,178)( 60,179)( 61,180)( 62,181)( 63,182)( 64,169)
( 65,170)( 66,171)( 67,172)( 68,173)( 69,174)( 70,175)( 71,190)( 72,191)
( 73,192)( 74,193)( 75,194)( 76,195)( 77,196)( 78,183)( 79,184)( 80,185)
( 81,186)( 82,187)( 83,188)( 84,189)( 85,204)( 86,205)( 87,206)( 88,207)
( 89,208)( 90,209)( 91,210)( 92,197)( 93,198)( 94,199)( 95,200)( 96,201)
( 97,202)( 98,203)( 99,218)(100,219)(101,220)(102,221)(103,222)(104,223)
(105,224)(106,211)(107,212)(108,213)(109,214)(110,215)(111,216)(112,217)
(225,337)(226,338)(227,339)(228,340)(229,341)(230,342)(231,343)(232,344)
(233,345)(234,346)(235,347)(236,348)(237,349)(238,350)(239,351)(240,352)
(241,353)(242,354)(243,355)(244,356)(245,357)(246,358)(247,359)(248,360)
(249,361)(250,362)(251,363)(252,364)(253,365)(254,366)(255,367)(256,368)
(257,369)(258,370)(259,371)(260,372)(261,373)(262,374)(263,375)(264,376)
(265,377)(266,378)(267,379)(268,380)(269,381)(270,382)(271,383)(272,384)
(273,385)(274,386)(275,387)(276,388)(277,389)(278,390)(279,391)(280,392)
(281,400)(282,401)(283,402)(284,403)(285,404)(286,405)(287,406)(288,393)
(289,394)(290,395)(291,396)(292,397)(293,398)(294,399)(295,414)(296,415)
(297,416)(298,417)(299,418)(300,419)(301,420)(302,407)(303,408)(304,409)
(305,410)(306,411)(307,412)(308,413)(309,428)(310,429)(311,430)(312,431)
(313,432)(314,433)(315,434)(316,421)(317,422)(318,423)(319,424)(320,425)
(321,426)(322,427)(323,442)(324,443)(325,444)(326,445)(327,446)(328,447)
(329,448)(330,435)(331,436)(332,437)(333,438)(334,439)(335,440)(336,441)
(449,561)(450,562)(451,563)(452,564)(453,565)(454,566)(455,567)(456,568)
(457,569)(458,570)(459,571)(460,572)(461,573)(462,574)(463,575)(464,576)
(465,577)(466,578)(467,579)(468,580)(469,581)(470,582)(471,583)(472,584)
(473,585)(474,586)(475,587)(476,588)(477,589)(478,590)(479,591)(480,592)
(481,593)(482,594)(483,595)(484,596)(485,597)(486,598)(487,599)(488,600)
(489,601)(490,602)(491,603)(492,604)(493,605)(494,606)(495,607)(496,608)
(497,609)(498,610)(499,611)(500,612)(501,613)(502,614)(503,615)(504,616)
(505,624)(506,625)(507,626)(508,627)(509,628)(510,629)(511,630)(512,617)
(513,618)(514,619)(515,620)(516,621)(517,622)(518,623)(519,638)(520,639)
(521,640)(522,641)(523,642)(524,643)(525,644)(526,631)(527,632)(528,633)
(529,634)(530,635)(531,636)(532,637)(533,652)(534,653)(535,654)(536,655)
(537,656)(538,657)(539,658)(540,645)(541,646)(542,647)(543,648)(544,649)
(545,650)(546,651)(547,666)(548,667)(549,668)(550,669)(551,670)(552,671)
(553,672)(554,659)(555,660)(556,661)(557,662)(558,663)(559,664)(560,665)
(673,785)(674,786)(675,787)(676,788)(677,789)(678,790)(679,791)(680,792)
(681,793)(682,794)(683,795)(684,796)(685,797)(686,798)(687,799)(688,800)
(689,801)(690,802)(691,803)(692,804)(693,805)(694,806)(695,807)(696,808)
(697,809)(698,810)(699,811)(700,812)(701,813)(702,814)(703,815)(704,816)
(705,817)(706,818)(707,819)(708,820)(709,821)(710,822)(711,823)(712,824)
(713,825)(714,826)(715,827)(716,828)(717,829)(718,830)(719,831)(720,832)
(721,833)(722,834)(723,835)(724,836)(725,837)(726,838)(727,839)(728,840)
(729,848)(730,849)(731,850)(732,851)(733,852)(734,853)(735,854)(736,841)
(737,842)(738,843)(739,844)(740,845)(741,846)(742,847)(743,862)(744,863)
(745,864)(746,865)(747,866)(748,867)(749,868)(750,855)(751,856)(752,857)
(753,858)(754,859)(755,860)(756,861)(757,876)(758,877)(759,878)(760,879)
(761,880)(762,881)(763,882)(764,869)(765,870)(766,871)(767,872)(768,873)
(769,874)(770,875)(771,890)(772,891)(773,892)(774,893)(775,894)(776,895)
(777,896)(778,883)(779,884)(780,885)(781,886)(782,887)(783,888)(784,889);;
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*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(896)!( 1,561)( 2,562)( 3,563)( 4,564)( 5,565)( 6,566)( 7,567)
( 8,568)( 9,569)( 10,570)( 11,571)( 12,572)( 13,573)( 14,574)( 15,575)
( 16,576)( 17,577)( 18,578)( 19,579)( 20,580)( 21,581)( 22,582)( 23,583)
( 24,584)( 25,585)( 26,586)( 27,587)( 28,588)( 29,589)( 30,590)( 31,591)
( 32,592)( 33,593)( 34,594)( 35,595)( 36,596)( 37,597)( 38,598)( 39,599)
( 40,600)( 41,601)( 42,602)( 43,603)( 44,604)( 45,605)( 46,606)( 47,607)
( 48,608)( 49,609)( 50,610)( 51,611)( 52,612)( 53,613)( 54,614)( 55,615)
( 56,616)( 57,617)( 58,618)( 59,619)( 60,620)( 61,621)( 62,622)( 63,623)
( 64,624)( 65,625)( 66,626)( 67,627)( 68,628)( 69,629)( 70,630)( 71,631)
( 72,632)( 73,633)( 74,634)( 75,635)( 76,636)( 77,637)( 78,638)( 79,639)
( 80,640)( 81,641)( 82,642)( 83,643)( 84,644)( 85,645)( 86,646)( 87,647)
( 88,648)( 89,649)( 90,650)( 91,651)( 92,652)( 93,653)( 94,654)( 95,655)
( 96,656)( 97,657)( 98,658)( 99,659)(100,660)(101,661)(102,662)(103,663)
(104,664)(105,665)(106,666)(107,667)(108,668)(109,669)(110,670)(111,671)
(112,672)(113,449)(114,450)(115,451)(116,452)(117,453)(118,454)(119,455)
(120,456)(121,457)(122,458)(123,459)(124,460)(125,461)(126,462)(127,463)
(128,464)(129,465)(130,466)(131,467)(132,468)(133,469)(134,470)(135,471)
(136,472)(137,473)(138,474)(139,475)(140,476)(141,477)(142,478)(143,479)
(144,480)(145,481)(146,482)(147,483)(148,484)(149,485)(150,486)(151,487)
(152,488)(153,489)(154,490)(155,491)(156,492)(157,493)(158,494)(159,495)
(160,496)(161,497)(162,498)(163,499)(164,500)(165,501)(166,502)(167,503)
(168,504)(169,505)(170,506)(171,507)(172,508)(173,509)(174,510)(175,511)
(176,512)(177,513)(178,514)(179,515)(180,516)(181,517)(182,518)(183,519)
(184,520)(185,521)(186,522)(187,523)(188,524)(189,525)(190,526)(191,527)
(192,528)(193,529)(194,530)(195,531)(196,532)(197,533)(198,534)(199,535)
(200,536)(201,537)(202,538)(203,539)(204,540)(205,541)(206,542)(207,543)
(208,544)(209,545)(210,546)(211,547)(212,548)(213,549)(214,550)(215,551)
(216,552)(217,553)(218,554)(219,555)(220,556)(221,557)(222,558)(223,559)
(224,560)(225,792)(226,793)(227,794)(228,795)(229,796)(230,797)(231,798)
(232,785)(233,786)(234,787)(235,788)(236,789)(237,790)(238,791)(239,806)
(240,807)(241,808)(242,809)(243,810)(244,811)(245,812)(246,799)(247,800)
(248,801)(249,802)(250,803)(251,804)(252,805)(253,820)(254,821)(255,822)
(256,823)(257,824)(258,825)(259,826)(260,813)(261,814)(262,815)(263,816)
(264,817)(265,818)(266,819)(267,834)(268,835)(269,836)(270,837)(271,838)
(272,839)(273,840)(274,827)(275,828)(276,829)(277,830)(278,831)(279,832)
(280,833)(281,848)(282,849)(283,850)(284,851)(285,852)(286,853)(287,854)
(288,841)(289,842)(290,843)(291,844)(292,845)(293,846)(294,847)(295,862)
(296,863)(297,864)(298,865)(299,866)(300,867)(301,868)(302,855)(303,856)
(304,857)(305,858)(306,859)(307,860)(308,861)(309,876)(310,877)(311,878)
(312,879)(313,880)(314,881)(315,882)(316,869)(317,870)(318,871)(319,872)
(320,873)(321,874)(322,875)(323,890)(324,891)(325,892)(326,893)(327,894)
(328,895)(329,896)(330,883)(331,884)(332,885)(333,886)(334,887)(335,888)
(336,889)(337,680)(338,681)(339,682)(340,683)(341,684)(342,685)(343,686)
(344,673)(345,674)(346,675)(347,676)(348,677)(349,678)(350,679)(351,694)
(352,695)(353,696)(354,697)(355,698)(356,699)(357,700)(358,687)(359,688)
(360,689)(361,690)(362,691)(363,692)(364,693)(365,708)(366,709)(367,710)
(368,711)(369,712)(370,713)(371,714)(372,701)(373,702)(374,703)(375,704)
(376,705)(377,706)(378,707)(379,722)(380,723)(381,724)(382,725)(383,726)
(384,727)(385,728)(386,715)(387,716)(388,717)(389,718)(390,719)(391,720)
(392,721)(393,736)(394,737)(395,738)(396,739)(397,740)(398,741)(399,742)
(400,729)(401,730)(402,731)(403,732)(404,733)(405,734)(406,735)(407,750)
(408,751)(409,752)(410,753)(411,754)(412,755)(413,756)(414,743)(415,744)
(416,745)(417,746)(418,747)(419,748)(420,749)(421,764)(422,765)(423,766)
(424,767)(425,768)(426,769)(427,770)(428,757)(429,758)(430,759)(431,760)
(432,761)(433,762)(434,763)(435,778)(436,779)(437,780)(438,781)(439,782)
(440,783)(441,784)(442,771)(443,772)(444,773)(445,774)(446,775)(447,776)
(448,777);
s1 := 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);
s2 := Sym(896)!( 1,281)( 2,287)( 3,286)( 4,285)( 5,284)( 6,283)( 7,282)
( 8,288)( 9,294)( 10,293)( 11,292)( 12,291)( 13,290)( 14,289)( 15,295)
( 16,301)( 17,300)( 18,299)( 19,298)( 20,297)( 21,296)( 22,302)( 23,308)
( 24,307)( 25,306)( 26,305)( 27,304)( 28,303)( 29,309)( 30,315)( 31,314)
( 32,313)( 33,312)( 34,311)( 35,310)( 36,316)( 37,322)( 38,321)( 39,320)
( 40,319)( 41,318)( 42,317)( 43,323)( 44,329)( 45,328)( 46,327)( 47,326)
( 48,325)( 49,324)( 50,330)( 51,336)( 52,335)( 53,334)( 54,333)( 55,332)
( 56,331)( 57,225)( 58,231)( 59,230)( 60,229)( 61,228)( 62,227)( 63,226)
( 64,232)( 65,238)( 66,237)( 67,236)( 68,235)( 69,234)( 70,233)( 71,239)
( 72,245)( 73,244)( 74,243)( 75,242)( 76,241)( 77,240)( 78,246)( 79,252)
( 80,251)( 81,250)( 82,249)( 83,248)( 84,247)( 85,253)( 86,259)( 87,258)
( 88,257)( 89,256)( 90,255)( 91,254)( 92,260)( 93,266)( 94,265)( 95,264)
( 96,263)( 97,262)( 98,261)( 99,267)(100,273)(101,272)(102,271)(103,270)
(104,269)(105,268)(106,274)(107,280)(108,279)(109,278)(110,277)(111,276)
(112,275)(113,400)(114,406)(115,405)(116,404)(117,403)(118,402)(119,401)
(120,393)(121,399)(122,398)(123,397)(124,396)(125,395)(126,394)(127,414)
(128,420)(129,419)(130,418)(131,417)(132,416)(133,415)(134,407)(135,413)
(136,412)(137,411)(138,410)(139,409)(140,408)(141,428)(142,434)(143,433)
(144,432)(145,431)(146,430)(147,429)(148,421)(149,427)(150,426)(151,425)
(152,424)(153,423)(154,422)(155,442)(156,448)(157,447)(158,446)(159,445)
(160,444)(161,443)(162,435)(163,441)(164,440)(165,439)(166,438)(167,437)
(168,436)(169,344)(170,350)(171,349)(172,348)(173,347)(174,346)(175,345)
(176,337)(177,343)(178,342)(179,341)(180,340)(181,339)(182,338)(183,358)
(184,364)(185,363)(186,362)(187,361)(188,360)(189,359)(190,351)(191,357)
(192,356)(193,355)(194,354)(195,353)(196,352)(197,372)(198,378)(199,377)
(200,376)(201,375)(202,374)(203,373)(204,365)(205,371)(206,370)(207,369)
(208,368)(209,367)(210,366)(211,386)(212,392)(213,391)(214,390)(215,389)
(216,388)(217,387)(218,379)(219,385)(220,384)(221,383)(222,382)(223,381)
(224,380)(449,729)(450,735)(451,734)(452,733)(453,732)(454,731)(455,730)
(456,736)(457,742)(458,741)(459,740)(460,739)(461,738)(462,737)(463,743)
(464,749)(465,748)(466,747)(467,746)(468,745)(469,744)(470,750)(471,756)
(472,755)(473,754)(474,753)(475,752)(476,751)(477,757)(478,763)(479,762)
(480,761)(481,760)(482,759)(483,758)(484,764)(485,770)(486,769)(487,768)
(488,767)(489,766)(490,765)(491,771)(492,777)(493,776)(494,775)(495,774)
(496,773)(497,772)(498,778)(499,784)(500,783)(501,782)(502,781)(503,780)
(504,779)(505,673)(506,679)(507,678)(508,677)(509,676)(510,675)(511,674)
(512,680)(513,686)(514,685)(515,684)(516,683)(517,682)(518,681)(519,687)
(520,693)(521,692)(522,691)(523,690)(524,689)(525,688)(526,694)(527,700)
(528,699)(529,698)(530,697)(531,696)(532,695)(533,701)(534,707)(535,706)
(536,705)(537,704)(538,703)(539,702)(540,708)(541,714)(542,713)(543,712)
(544,711)(545,710)(546,709)(547,715)(548,721)(549,720)(550,719)(551,718)
(552,717)(553,716)(554,722)(555,728)(556,727)(557,726)(558,725)(559,724)
(560,723)(561,848)(562,854)(563,853)(564,852)(565,851)(566,850)(567,849)
(568,841)(569,847)(570,846)(571,845)(572,844)(573,843)(574,842)(575,862)
(576,868)(577,867)(578,866)(579,865)(580,864)(581,863)(582,855)(583,861)
(584,860)(585,859)(586,858)(587,857)(588,856)(589,876)(590,882)(591,881)
(592,880)(593,879)(594,878)(595,877)(596,869)(597,875)(598,874)(599,873)
(600,872)(601,871)(602,870)(603,890)(604,896)(605,895)(606,894)(607,893)
(608,892)(609,891)(610,883)(611,889)(612,888)(613,887)(614,886)(615,885)
(616,884)(617,792)(618,798)(619,797)(620,796)(621,795)(622,794)(623,793)
(624,785)(625,791)(626,790)(627,789)(628,788)(629,787)(630,786)(631,806)
(632,812)(633,811)(634,810)(635,809)(636,808)(637,807)(638,799)(639,805)
(640,804)(641,803)(642,802)(643,801)(644,800)(645,820)(646,826)(647,825)
(648,824)(649,823)(650,822)(651,821)(652,813)(653,819)(654,818)(655,817)
(656,816)(657,815)(658,814)(659,834)(660,840)(661,839)(662,838)(663,837)
(664,836)(665,835)(666,827)(667,833)(668,832)(669,831)(670,830)(671,829)
(672,828);
s3 := 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);
s4 := Sym(896)!( 1,113)( 2,114)( 3,115)( 4,116)( 5,117)( 6,118)( 7,119)
( 8,120)( 9,121)( 10,122)( 11,123)( 12,124)( 13,125)( 14,126)( 15,127)
( 16,128)( 17,129)( 18,130)( 19,131)( 20,132)( 21,133)( 22,134)( 23,135)
( 24,136)( 25,137)( 26,138)( 27,139)( 28,140)( 29,141)( 30,142)( 31,143)
( 32,144)( 33,145)( 34,146)( 35,147)( 36,148)( 37,149)( 38,150)( 39,151)
( 40,152)( 41,153)( 42,154)( 43,155)( 44,156)( 45,157)( 46,158)( 47,159)
( 48,160)( 49,161)( 50,162)( 51,163)( 52,164)( 53,165)( 54,166)( 55,167)
( 56,168)( 57,176)( 58,177)( 59,178)( 60,179)( 61,180)( 62,181)( 63,182)
( 64,169)( 65,170)( 66,171)( 67,172)( 68,173)( 69,174)( 70,175)( 71,190)
( 72,191)( 73,192)( 74,193)( 75,194)( 76,195)( 77,196)( 78,183)( 79,184)
( 80,185)( 81,186)( 82,187)( 83,188)( 84,189)( 85,204)( 86,205)( 87,206)
( 88,207)( 89,208)( 90,209)( 91,210)( 92,197)( 93,198)( 94,199)( 95,200)
( 96,201)( 97,202)( 98,203)( 99,218)(100,219)(101,220)(102,221)(103,222)
(104,223)(105,224)(106,211)(107,212)(108,213)(109,214)(110,215)(111,216)
(112,217)(225,337)(226,338)(227,339)(228,340)(229,341)(230,342)(231,343)
(232,344)(233,345)(234,346)(235,347)(236,348)(237,349)(238,350)(239,351)
(240,352)(241,353)(242,354)(243,355)(244,356)(245,357)(246,358)(247,359)
(248,360)(249,361)(250,362)(251,363)(252,364)(253,365)(254,366)(255,367)
(256,368)(257,369)(258,370)(259,371)(260,372)(261,373)(262,374)(263,375)
(264,376)(265,377)(266,378)(267,379)(268,380)(269,381)(270,382)(271,383)
(272,384)(273,385)(274,386)(275,387)(276,388)(277,389)(278,390)(279,391)
(280,392)(281,400)(282,401)(283,402)(284,403)(285,404)(286,405)(287,406)
(288,393)(289,394)(290,395)(291,396)(292,397)(293,398)(294,399)(295,414)
(296,415)(297,416)(298,417)(299,418)(300,419)(301,420)(302,407)(303,408)
(304,409)(305,410)(306,411)(307,412)(308,413)(309,428)(310,429)(311,430)
(312,431)(313,432)(314,433)(315,434)(316,421)(317,422)(318,423)(319,424)
(320,425)(321,426)(322,427)(323,442)(324,443)(325,444)(326,445)(327,446)
(328,447)(329,448)(330,435)(331,436)(332,437)(333,438)(334,439)(335,440)
(336,441)(449,561)(450,562)(451,563)(452,564)(453,565)(454,566)(455,567)
(456,568)(457,569)(458,570)(459,571)(460,572)(461,573)(462,574)(463,575)
(464,576)(465,577)(466,578)(467,579)(468,580)(469,581)(470,582)(471,583)
(472,584)(473,585)(474,586)(475,587)(476,588)(477,589)(478,590)(479,591)
(480,592)(481,593)(482,594)(483,595)(484,596)(485,597)(486,598)(487,599)
(488,600)(489,601)(490,602)(491,603)(492,604)(493,605)(494,606)(495,607)
(496,608)(497,609)(498,610)(499,611)(500,612)(501,613)(502,614)(503,615)
(504,616)(505,624)(506,625)(507,626)(508,627)(509,628)(510,629)(511,630)
(512,617)(513,618)(514,619)(515,620)(516,621)(517,622)(518,623)(519,638)
(520,639)(521,640)(522,641)(523,642)(524,643)(525,644)(526,631)(527,632)
(528,633)(529,634)(530,635)(531,636)(532,637)(533,652)(534,653)(535,654)
(536,655)(537,656)(538,657)(539,658)(540,645)(541,646)(542,647)(543,648)
(544,649)(545,650)(546,651)(547,666)(548,667)(549,668)(550,669)(551,670)
(552,671)(553,672)(554,659)(555,660)(556,661)(557,662)(558,663)(559,664)
(560,665)(673,785)(674,786)(675,787)(676,788)(677,789)(678,790)(679,791)
(680,792)(681,793)(682,794)(683,795)(684,796)(685,797)(686,798)(687,799)
(688,800)(689,801)(690,802)(691,803)(692,804)(693,805)(694,806)(695,807)
(696,808)(697,809)(698,810)(699,811)(700,812)(701,813)(702,814)(703,815)
(704,816)(705,817)(706,818)(707,819)(708,820)(709,821)(710,822)(711,823)
(712,824)(713,825)(714,826)(715,827)(716,828)(717,829)(718,830)(719,831)
(720,832)(721,833)(722,834)(723,835)(724,836)(725,837)(726,838)(727,839)
(728,840)(729,848)(730,849)(731,850)(732,851)(733,852)(734,853)(735,854)
(736,841)(737,842)(738,843)(739,844)(740,845)(741,846)(742,847)(743,862)
(744,863)(745,864)(746,865)(747,866)(748,867)(749,868)(750,855)(751,856)
(752,857)(753,858)(754,859)(755,860)(756,861)(757,876)(758,877)(759,878)
(760,879)(761,880)(762,881)(763,882)(764,869)(765,870)(766,871)(767,872)
(768,873)(769,874)(770,875)(771,890)(772,891)(773,892)(774,893)(775,894)
(776,895)(777,896)(778,883)(779,884)(780,885)(781,886)(782,887)(783,888)
(784,889);
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*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope