Polytope of Type {224,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {224,4}*1792b
if this polytope has a name.
Group : SmallGroup(1792,90243)
Rank : 3
Schlafli Type : {224,4}
Number of vertices, edges, etc : 224, 448, 4
Order of s₀s₁s₂ : 224
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {112,4}*896a
   4-fold quotients : {56,4}*448a, {112,2}*448
   7-fold quotients : {32,4}*256b
   8-fold quotients : {28,4}*224, {56,2}*224
   14-fold quotients : {16,4}*128a
   16-fold quotients : {28,2}*112, {14,4}*112
   28-fold quotients : {8,4}*64a, {16,2}*64
   32-fold quotients : {14,2}*56
   56-fold quotients : {4,4}*32, {8,2}*32
   64-fold quotients : {7,2}*28
   112-fold quotients : {2,4}*16, {4,2}*16
   224-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*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*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*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*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*s2*s1*s0*s1*s0*s2*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*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*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*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*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*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*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*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*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*s2*s1*s0*s1*s0*s2*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*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*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*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*s0*s1*s0*s1 >;

References : None.
to this polytope