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