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Polytope of Type {4,224}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,224}*1792b
if this polytope has a name.
Group : SmallGroup(1792,90243)
Rank : 3
Schlafli Type : {4,224}
Number of vertices, edges, etc : 4, 448, 224
Order of s0s1s2 : 224
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {4,112}*896a
   4-fold quotients : {4,56}*448a, {2,112}*448
   7-fold quotients : {4,32}*256b
   8-fold quotients : {4,28}*224, {2,56}*224
   14-fold quotients : {4,16}*128a
   16-fold quotients : {2,28}*112, {4,14}*112
   28-fold quotients : {4,8}*64a, {2,16}*64
   32-fold quotients : {2,14}*56
   56-fold quotients : {4,4}*32, {2,8}*32
   64-fold quotients : {2,7}*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 := (  1,225)(  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);;
s1 := (  2,  7)(  3,  6)(  4,  5)(  9, 14)( 10, 13)( 11, 12)( 15, 22)( 16, 28)
( 17, 27)( 18, 26)( 19, 25)( 20, 24)( 21, 23)( 29, 43)( 30, 49)( 31, 48)
( 32, 47)( 33, 46)( 34, 45)( 35, 44)( 36, 50)( 37, 56)( 38, 55)( 39, 54)
( 40, 53)( 41, 52)( 42, 51)( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)
( 67, 68)( 71, 78)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)( 77, 79)
( 85, 99)( 86,105)( 87,104)( 88,103)( 89,102)( 90,101)( 91,100)( 92,106)
( 93,112)( 94,111)( 95,110)( 96,109)( 97,108)( 98,107)(113,141)(114,147)
(115,146)(116,145)(117,144)(118,143)(119,142)(120,148)(121,154)(122,153)
(123,152)(124,151)(125,150)(126,149)(127,162)(128,168)(129,167)(130,166)
(131,165)(132,164)(133,163)(134,155)(135,161)(136,160)(137,159)(138,158)
(139,157)(140,156)(169,197)(170,203)(171,202)(172,201)(173,200)(174,199)
(175,198)(176,204)(177,210)(178,209)(179,208)(180,207)(181,206)(182,205)
(183,218)(184,224)(185,223)(186,222)(187,221)(188,220)(189,219)(190,211)
(191,217)(192,216)(193,215)(194,214)(195,213)(196,212)(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)(239,302)(240,308)(241,307)(242,306)
(243,305)(244,304)(245,303)(246,295)(247,301)(248,300)(249,299)(250,298)
(251,297)(252,296)(253,323)(254,329)(255,328)(256,327)(257,326)(258,325)
(259,324)(260,330)(261,336)(262,335)(263,334)(264,333)(265,332)(266,331)
(267,309)(268,315)(269,314)(270,313)(271,312)(272,311)(273,310)(274,316)
(275,322)(276,321)(277,320)(278,319)(279,318)(280,317)(337,421)(338,427)
(339,426)(340,425)(341,424)(342,423)(343,422)(344,428)(345,434)(346,433)
(347,432)(348,431)(349,430)(350,429)(351,442)(352,448)(353,447)(354,446)
(355,445)(356,444)(357,443)(358,435)(359,441)(360,440)(361,439)(362,438)
(363,437)(364,436)(365,393)(366,399)(367,398)(368,397)(369,396)(370,395)
(371,394)(372,400)(373,406)(374,405)(375,404)(376,403)(377,402)(378,401)
(379,414)(380,420)(381,419)(382,418)(383,417)(384,416)(385,415)(386,407)
(387,413)(388,412)(389,411)(390,410)(391,409)(392,408)(449,561)(450,567)
(451,566)(452,565)(453,564)(454,563)(455,562)(456,568)(457,574)(458,573)
(459,572)(460,571)(461,570)(462,569)(463,582)(464,588)(465,587)(466,586)
(467,585)(468,584)(469,583)(470,575)(471,581)(472,580)(473,579)(474,578)
(475,577)(476,576)(477,603)(478,609)(479,608)(480,607)(481,606)(482,605)
(483,604)(484,610)(485,616)(486,615)(487,614)(488,613)(489,612)(490,611)
(491,589)(492,595)(493,594)(494,593)(495,592)(496,591)(497,590)(498,596)
(499,602)(500,601)(501,600)(502,599)(503,598)(504,597)(505,617)(506,623)
(507,622)(508,621)(509,620)(510,619)(511,618)(512,624)(513,630)(514,629)
(515,628)(516,627)(517,626)(518,625)(519,638)(520,644)(521,643)(522,642)
(523,641)(524,640)(525,639)(526,631)(527,637)(528,636)(529,635)(530,634)
(531,633)(532,632)(533,659)(534,665)(535,664)(536,663)(537,662)(538,661)
(539,660)(540,666)(541,672)(542,671)(543,670)(544,669)(545,668)(546,667)
(547,645)(548,651)(549,650)(550,649)(551,648)(552,647)(553,646)(554,652)
(555,658)(556,657)(557,656)(558,655)(559,654)(560,653)(673,848)(674,854)
(675,853)(676,852)(677,851)(678,850)(679,849)(680,841)(681,847)(682,846)
(683,845)(684,844)(685,843)(686,842)(687,855)(688,861)(689,860)(690,859)
(691,858)(692,857)(693,856)(694,862)(695,868)(696,867)(697,866)(698,865)
(699,864)(700,863)(701,890)(702,896)(703,895)(704,894)(705,893)(706,892)
(707,891)(708,883)(709,889)(710,888)(711,887)(712,886)(713,885)(714,884)
(715,876)(716,882)(717,881)(718,880)(719,879)(720,878)(721,877)(722,869)
(723,875)(724,874)(725,873)(726,872)(727,871)(728,870)(729,792)(730,798)
(731,797)(732,796)(733,795)(734,794)(735,793)(736,785)(737,791)(738,790)
(739,789)(740,788)(741,787)(742,786)(743,799)(744,805)(745,804)(746,803)
(747,802)(748,801)(749,800)(750,806)(751,812)(752,811)(753,810)(754,809)
(755,808)(756,807)(757,834)(758,840)(759,839)(760,838)(761,837)(762,836)
(763,835)(764,827)(765,833)(766,832)(767,831)(768,830)(769,829)(770,828)
(771,820)(772,826)(773,825)(774,824)(775,823)(776,822)(777,821)(778,813)
(779,819)(780,818)(781,817)(782,816)(783,815)(784,814);;
s2 := (  1,450)(  2,449)(  3,455)(  4,454)(  5,453)(  6,452)(  7,451)(  8,457)
(  9,456)( 10,462)( 11,461)( 12,460)( 13,459)( 14,458)( 15,471)( 16,470)
( 17,476)( 18,475)( 19,474)( 20,473)( 21,472)( 22,464)( 23,463)( 24,469)
( 25,468)( 26,467)( 27,466)( 28,465)( 29,492)( 30,491)( 31,497)( 32,496)
( 33,495)( 34,494)( 35,493)( 36,499)( 37,498)( 38,504)( 39,503)( 40,502)
( 41,501)( 42,500)( 43,478)( 44,477)( 45,483)( 46,482)( 47,481)( 48,480)
( 49,479)( 50,485)( 51,484)( 52,490)( 53,489)( 54,488)( 55,487)( 56,486)
( 57,513)( 58,512)( 59,518)( 60,517)( 61,516)( 62,515)( 63,514)( 64,506)
( 65,505)( 66,511)( 67,510)( 68,509)( 69,508)( 70,507)( 71,520)( 72,519)
( 73,525)( 74,524)( 75,523)( 76,522)( 77,521)( 78,527)( 79,526)( 80,532)
( 81,531)( 82,530)( 83,529)( 84,528)( 85,555)( 86,554)( 87,560)( 88,559)
( 89,558)( 90,557)( 91,556)( 92,548)( 93,547)( 94,553)( 95,552)( 96,551)
( 97,550)( 98,549)( 99,541)(100,540)(101,546)(102,545)(103,544)(104,543)
(105,542)(106,534)(107,533)(108,539)(109,538)(110,537)(111,536)(112,535)
(113,590)(114,589)(115,595)(116,594)(117,593)(118,592)(119,591)(120,597)
(121,596)(122,602)(123,601)(124,600)(125,599)(126,598)(127,611)(128,610)
(129,616)(130,615)(131,614)(132,613)(133,612)(134,604)(135,603)(136,609)
(137,608)(138,607)(139,606)(140,605)(141,562)(142,561)(143,567)(144,566)
(145,565)(146,564)(147,563)(148,569)(149,568)(150,574)(151,573)(152,572)
(153,571)(154,570)(155,583)(156,582)(157,588)(158,587)(159,586)(160,585)
(161,584)(162,576)(163,575)(164,581)(165,580)(166,579)(167,578)(168,577)
(169,653)(170,652)(171,658)(172,657)(173,656)(174,655)(175,654)(176,646)
(177,645)(178,651)(179,650)(180,649)(181,648)(182,647)(183,660)(184,659)
(185,665)(186,664)(187,663)(188,662)(189,661)(190,667)(191,666)(192,672)
(193,671)(194,670)(195,669)(196,668)(197,625)(198,624)(199,630)(200,629)
(201,628)(202,627)(203,626)(204,618)(205,617)(206,623)(207,622)(208,621)
(209,620)(210,619)(211,632)(212,631)(213,637)(214,636)(215,635)(216,634)
(217,633)(218,639)(219,638)(220,644)(221,643)(222,642)(223,641)(224,640)
(225,674)(226,673)(227,679)(228,678)(229,677)(230,676)(231,675)(232,681)
(233,680)(234,686)(235,685)(236,684)(237,683)(238,682)(239,695)(240,694)
(241,700)(242,699)(243,698)(244,697)(245,696)(246,688)(247,687)(248,693)
(249,692)(250,691)(251,690)(252,689)(253,716)(254,715)(255,721)(256,720)
(257,719)(258,718)(259,717)(260,723)(261,722)(262,728)(263,727)(264,726)
(265,725)(266,724)(267,702)(268,701)(269,707)(270,706)(271,705)(272,704)
(273,703)(274,709)(275,708)(276,714)(277,713)(278,712)(279,711)(280,710)
(281,737)(282,736)(283,742)(284,741)(285,740)(286,739)(287,738)(288,730)
(289,729)(290,735)(291,734)(292,733)(293,732)(294,731)(295,744)(296,743)
(297,749)(298,748)(299,747)(300,746)(301,745)(302,751)(303,750)(304,756)
(305,755)(306,754)(307,753)(308,752)(309,779)(310,778)(311,784)(312,783)
(313,782)(314,781)(315,780)(316,772)(317,771)(318,777)(319,776)(320,775)
(321,774)(322,773)(323,765)(324,764)(325,770)(326,769)(327,768)(328,767)
(329,766)(330,758)(331,757)(332,763)(333,762)(334,761)(335,760)(336,759)
(337,814)(338,813)(339,819)(340,818)(341,817)(342,816)(343,815)(344,821)
(345,820)(346,826)(347,825)(348,824)(349,823)(350,822)(351,835)(352,834)
(353,840)(354,839)(355,838)(356,837)(357,836)(358,828)(359,827)(360,833)
(361,832)(362,831)(363,830)(364,829)(365,786)(366,785)(367,791)(368,790)
(369,789)(370,788)(371,787)(372,793)(373,792)(374,798)(375,797)(376,796)
(377,795)(378,794)(379,807)(380,806)(381,812)(382,811)(383,810)(384,809)
(385,808)(386,800)(387,799)(388,805)(389,804)(390,803)(391,802)(392,801)
(393,877)(394,876)(395,882)(396,881)(397,880)(398,879)(399,878)(400,870)
(401,869)(402,875)(403,874)(404,873)(405,872)(406,871)(407,884)(408,883)
(409,889)(410,888)(411,887)(412,886)(413,885)(414,891)(415,890)(416,896)
(417,895)(418,894)(419,893)(420,892)(421,849)(422,848)(423,854)(424,853)
(425,852)(426,851)(427,850)(428,842)(429,841)(430,847)(431,846)(432,845)
(433,844)(434,843)(435,856)(436,855)(437,861)(438,860)(439,859)(440,858)
(441,857)(442,863)(443,862)(444,868)(445,867)(446,866)(447,865)(448,864);;
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1, 
s0*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*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*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*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*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*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*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*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*s0*s1*s2*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := 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);
s1 := Sym(896)!(  2,  7)(  3,  6)(  4,  5)(  9, 14)( 10, 13)( 11, 12)( 15, 22)
( 16, 28)( 17, 27)( 18, 26)( 19, 25)( 20, 24)( 21, 23)( 29, 43)( 30, 49)
( 31, 48)( 32, 47)( 33, 46)( 34, 45)( 35, 44)( 36, 50)( 37, 56)( 38, 55)
( 39, 54)( 40, 53)( 41, 52)( 42, 51)( 58, 63)( 59, 62)( 60, 61)( 65, 70)
( 66, 69)( 67, 68)( 71, 78)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)
( 77, 79)( 85, 99)( 86,105)( 87,104)( 88,103)( 89,102)( 90,101)( 91,100)
( 92,106)( 93,112)( 94,111)( 95,110)( 96,109)( 97,108)( 98,107)(113,141)
(114,147)(115,146)(116,145)(117,144)(118,143)(119,142)(120,148)(121,154)
(122,153)(123,152)(124,151)(125,150)(126,149)(127,162)(128,168)(129,167)
(130,166)(131,165)(132,164)(133,163)(134,155)(135,161)(136,160)(137,159)
(138,158)(139,157)(140,156)(169,197)(170,203)(171,202)(172,201)(173,200)
(174,199)(175,198)(176,204)(177,210)(178,209)(179,208)(180,207)(181,206)
(182,205)(183,218)(184,224)(185,223)(186,222)(187,221)(188,220)(189,219)
(190,211)(191,217)(192,216)(193,215)(194,214)(195,213)(196,212)(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)(239,302)(240,308)(241,307)
(242,306)(243,305)(244,304)(245,303)(246,295)(247,301)(248,300)(249,299)
(250,298)(251,297)(252,296)(253,323)(254,329)(255,328)(256,327)(257,326)
(258,325)(259,324)(260,330)(261,336)(262,335)(263,334)(264,333)(265,332)
(266,331)(267,309)(268,315)(269,314)(270,313)(271,312)(272,311)(273,310)
(274,316)(275,322)(276,321)(277,320)(278,319)(279,318)(280,317)(337,421)
(338,427)(339,426)(340,425)(341,424)(342,423)(343,422)(344,428)(345,434)
(346,433)(347,432)(348,431)(349,430)(350,429)(351,442)(352,448)(353,447)
(354,446)(355,445)(356,444)(357,443)(358,435)(359,441)(360,440)(361,439)
(362,438)(363,437)(364,436)(365,393)(366,399)(367,398)(368,397)(369,396)
(370,395)(371,394)(372,400)(373,406)(374,405)(375,404)(376,403)(377,402)
(378,401)(379,414)(380,420)(381,419)(382,418)(383,417)(384,416)(385,415)
(386,407)(387,413)(388,412)(389,411)(390,410)(391,409)(392,408)(449,561)
(450,567)(451,566)(452,565)(453,564)(454,563)(455,562)(456,568)(457,574)
(458,573)(459,572)(460,571)(461,570)(462,569)(463,582)(464,588)(465,587)
(466,586)(467,585)(468,584)(469,583)(470,575)(471,581)(472,580)(473,579)
(474,578)(475,577)(476,576)(477,603)(478,609)(479,608)(480,607)(481,606)
(482,605)(483,604)(484,610)(485,616)(486,615)(487,614)(488,613)(489,612)
(490,611)(491,589)(492,595)(493,594)(494,593)(495,592)(496,591)(497,590)
(498,596)(499,602)(500,601)(501,600)(502,599)(503,598)(504,597)(505,617)
(506,623)(507,622)(508,621)(509,620)(510,619)(511,618)(512,624)(513,630)
(514,629)(515,628)(516,627)(517,626)(518,625)(519,638)(520,644)(521,643)
(522,642)(523,641)(524,640)(525,639)(526,631)(527,637)(528,636)(529,635)
(530,634)(531,633)(532,632)(533,659)(534,665)(535,664)(536,663)(537,662)
(538,661)(539,660)(540,666)(541,672)(542,671)(543,670)(544,669)(545,668)
(546,667)(547,645)(548,651)(549,650)(550,649)(551,648)(552,647)(553,646)
(554,652)(555,658)(556,657)(557,656)(558,655)(559,654)(560,653)(673,848)
(674,854)(675,853)(676,852)(677,851)(678,850)(679,849)(680,841)(681,847)
(682,846)(683,845)(684,844)(685,843)(686,842)(687,855)(688,861)(689,860)
(690,859)(691,858)(692,857)(693,856)(694,862)(695,868)(696,867)(697,866)
(698,865)(699,864)(700,863)(701,890)(702,896)(703,895)(704,894)(705,893)
(706,892)(707,891)(708,883)(709,889)(710,888)(711,887)(712,886)(713,885)
(714,884)(715,876)(716,882)(717,881)(718,880)(719,879)(720,878)(721,877)
(722,869)(723,875)(724,874)(725,873)(726,872)(727,871)(728,870)(729,792)
(730,798)(731,797)(732,796)(733,795)(734,794)(735,793)(736,785)(737,791)
(738,790)(739,789)(740,788)(741,787)(742,786)(743,799)(744,805)(745,804)
(746,803)(747,802)(748,801)(749,800)(750,806)(751,812)(752,811)(753,810)
(754,809)(755,808)(756,807)(757,834)(758,840)(759,839)(760,838)(761,837)
(762,836)(763,835)(764,827)(765,833)(766,832)(767,831)(768,830)(769,829)
(770,828)(771,820)(772,826)(773,825)(774,824)(775,823)(776,822)(777,821)
(778,813)(779,819)(780,818)(781,817)(782,816)(783,815)(784,814);
s2 := Sym(896)!(  1,450)(  2,449)(  3,455)(  4,454)(  5,453)(  6,452)(  7,451)
(  8,457)(  9,456)( 10,462)( 11,461)( 12,460)( 13,459)( 14,458)( 15,471)
( 16,470)( 17,476)( 18,475)( 19,474)( 20,473)( 21,472)( 22,464)( 23,463)
( 24,469)( 25,468)( 26,467)( 27,466)( 28,465)( 29,492)( 30,491)( 31,497)
( 32,496)( 33,495)( 34,494)( 35,493)( 36,499)( 37,498)( 38,504)( 39,503)
( 40,502)( 41,501)( 42,500)( 43,478)( 44,477)( 45,483)( 46,482)( 47,481)
( 48,480)( 49,479)( 50,485)( 51,484)( 52,490)( 53,489)( 54,488)( 55,487)
( 56,486)( 57,513)( 58,512)( 59,518)( 60,517)( 61,516)( 62,515)( 63,514)
( 64,506)( 65,505)( 66,511)( 67,510)( 68,509)( 69,508)( 70,507)( 71,520)
( 72,519)( 73,525)( 74,524)( 75,523)( 76,522)( 77,521)( 78,527)( 79,526)
( 80,532)( 81,531)( 82,530)( 83,529)( 84,528)( 85,555)( 86,554)( 87,560)
( 88,559)( 89,558)( 90,557)( 91,556)( 92,548)( 93,547)( 94,553)( 95,552)
( 96,551)( 97,550)( 98,549)( 99,541)(100,540)(101,546)(102,545)(103,544)
(104,543)(105,542)(106,534)(107,533)(108,539)(109,538)(110,537)(111,536)
(112,535)(113,590)(114,589)(115,595)(116,594)(117,593)(118,592)(119,591)
(120,597)(121,596)(122,602)(123,601)(124,600)(125,599)(126,598)(127,611)
(128,610)(129,616)(130,615)(131,614)(132,613)(133,612)(134,604)(135,603)
(136,609)(137,608)(138,607)(139,606)(140,605)(141,562)(142,561)(143,567)
(144,566)(145,565)(146,564)(147,563)(148,569)(149,568)(150,574)(151,573)
(152,572)(153,571)(154,570)(155,583)(156,582)(157,588)(158,587)(159,586)
(160,585)(161,584)(162,576)(163,575)(164,581)(165,580)(166,579)(167,578)
(168,577)(169,653)(170,652)(171,658)(172,657)(173,656)(174,655)(175,654)
(176,646)(177,645)(178,651)(179,650)(180,649)(181,648)(182,647)(183,660)
(184,659)(185,665)(186,664)(187,663)(188,662)(189,661)(190,667)(191,666)
(192,672)(193,671)(194,670)(195,669)(196,668)(197,625)(198,624)(199,630)
(200,629)(201,628)(202,627)(203,626)(204,618)(205,617)(206,623)(207,622)
(208,621)(209,620)(210,619)(211,632)(212,631)(213,637)(214,636)(215,635)
(216,634)(217,633)(218,639)(219,638)(220,644)(221,643)(222,642)(223,641)
(224,640)(225,674)(226,673)(227,679)(228,678)(229,677)(230,676)(231,675)
(232,681)(233,680)(234,686)(235,685)(236,684)(237,683)(238,682)(239,695)
(240,694)(241,700)(242,699)(243,698)(244,697)(245,696)(246,688)(247,687)
(248,693)(249,692)(250,691)(251,690)(252,689)(253,716)(254,715)(255,721)
(256,720)(257,719)(258,718)(259,717)(260,723)(261,722)(262,728)(263,727)
(264,726)(265,725)(266,724)(267,702)(268,701)(269,707)(270,706)(271,705)
(272,704)(273,703)(274,709)(275,708)(276,714)(277,713)(278,712)(279,711)
(280,710)(281,737)(282,736)(283,742)(284,741)(285,740)(286,739)(287,738)
(288,730)(289,729)(290,735)(291,734)(292,733)(293,732)(294,731)(295,744)
(296,743)(297,749)(298,748)(299,747)(300,746)(301,745)(302,751)(303,750)
(304,756)(305,755)(306,754)(307,753)(308,752)(309,779)(310,778)(311,784)
(312,783)(313,782)(314,781)(315,780)(316,772)(317,771)(318,777)(319,776)
(320,775)(321,774)(322,773)(323,765)(324,764)(325,770)(326,769)(327,768)
(328,767)(329,766)(330,758)(331,757)(332,763)(333,762)(334,761)(335,760)
(336,759)(337,814)(338,813)(339,819)(340,818)(341,817)(342,816)(343,815)
(344,821)(345,820)(346,826)(347,825)(348,824)(349,823)(350,822)(351,835)
(352,834)(353,840)(354,839)(355,838)(356,837)(357,836)(358,828)(359,827)
(360,833)(361,832)(362,831)(363,830)(364,829)(365,786)(366,785)(367,791)
(368,790)(369,789)(370,788)(371,787)(372,793)(373,792)(374,798)(375,797)
(376,796)(377,795)(378,794)(379,807)(380,806)(381,812)(382,811)(383,810)
(384,809)(385,808)(386,800)(387,799)(388,805)(389,804)(390,803)(391,802)
(392,801)(393,877)(394,876)(395,882)(396,881)(397,880)(398,879)(399,878)
(400,870)(401,869)(402,875)(403,874)(404,873)(405,872)(406,871)(407,884)
(408,883)(409,889)(410,888)(411,887)(412,886)(413,885)(414,891)(415,890)
(416,896)(417,895)(418,894)(419,893)(420,892)(421,849)(422,848)(423,854)
(424,853)(425,852)(426,851)(427,850)(428,842)(429,841)(430,847)(431,846)
(432,845)(433,844)(434,843)(435,856)(436,855)(437,861)(438,860)(439,859)
(440,858)(441,857)(442,863)(443,862)(444,868)(445,867)(446,866)(447,865)
(448,864);
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1, 
s0*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*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*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*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*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*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*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*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*s0*s1*s2*s1 >; 
 
References : None.
to this polytope