Polytope of Type {4,224}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,224}*1792a
Also Known As : {4,224|2}. if this polytope has another name.
Group : SmallGroup(1792,90209)
Rank : 3
Schlafli Type : {4,224}
Number of vertices, edges, etc : 4, 448, 224
Order of s₀s₁s₂ : 224
Order of s₀s₁s₂s₁ : 2
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, {2,224}*896
   4-fold quotients : {4,56}*448a, {2,112}*448
   7-fold quotients : {4,32}*256a
   8-fold quotients : {4,28}*224, {2,56}*224
   14-fold quotients : {4,16}*128a, {2,32}*128
   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)
(113,337)(114,338)(115,339)(116,340)(117,341)(118,342)(119,343)(120,344)
(121,345)(122,346)(123,347)(124,348)(125,349)(126,350)(127,351)(128,352)
(129,353)(130,354)(131,355)(132,356)(133,357)(134,358)(135,359)(136,360)
(137,361)(138,362)(139,363)(140,364)(141,365)(142,366)(143,367)(144,368)
(145,369)(146,370)(147,371)(148,372)(149,373)(150,374)(151,375)(152,376)
(153,377)(154,378)(155,379)(156,380)(157,381)(158,382)(159,383)(160,384)
(161,385)(162,386)(163,387)(164,388)(165,389)(166,390)(167,391)(168,392)
(169,393)(170,394)(171,395)(172,396)(173,397)(174,398)(175,399)(176,400)
(177,401)(178,402)(179,403)(180,404)(181,405)(182,406)(183,407)(184,408)
(185,409)(186,410)(187,411)(188,412)(189,413)(190,414)(191,415)(192,416)
(193,417)(194,418)(195,419)(196,420)(197,421)(198,422)(199,423)(200,424)
(201,425)(202,426)(203,427)(204,428)(205,429)(206,430)(207,431)(208,432)
(209,433)(210,434)(211,435)(212,436)(213,437)(214,438)(215,439)(216,440)
(217,441)(218,442)(219,443)(220,444)(221,445)(222,446)(223,447)(224,448)
(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)
(561,785)(562,786)(563,787)(564,788)(565,789)(566,790)(567,791)(568,792)
(569,793)(570,794)(571,795)(572,796)(573,797)(574,798)(575,799)(576,800)
(577,801)(578,802)(579,803)(580,804)(581,805)(582,806)(583,807)(584,808)
(585,809)(586,810)(587,811)(588,812)(589,813)(590,814)(591,815)(592,816)
(593,817)(594,818)(595,819)(596,820)(597,821)(598,822)(599,823)(600,824)
(601,825)(602,826)(603,827)(604,828)(605,829)(606,830)(607,831)(608,832)
(609,833)(610,834)(611,835)(612,836)(613,837)(614,838)(615,839)(616,840)
(617,841)(618,842)(619,843)(620,844)(621,845)(622,846)(623,847)(624,848)
(625,849)(626,850)(627,851)(628,852)(629,853)(630,854)(631,855)(632,856)
(633,857)(634,858)(635,859)(636,860)(637,861)(638,862)(639,863)(640,864)
(641,865)(642,866)(643,867)(644,868)(645,869)(646,870)(647,871)(648,872)
(649,873)(650,874)(651,875)(652,876)(653,877)(654,878)(655,879)(656,880)
(657,881)(658,882)(659,883)(660,884)(661,885)(662,886)(663,887)(664,888)
(665,889)(666,890)(667,891)(668,892)(669,893)(670,894)(671,895)(672,896);;
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)(673,841)(674,847)
(675,846)(676,845)(677,844)(678,843)(679,842)(680,848)(681,854)(682,853)
(683,852)(684,851)(685,850)(686,849)(687,862)(688,868)(689,867)(690,866)
(691,865)(692,864)(693,863)(694,855)(695,861)(696,860)(697,859)(698,858)
(699,857)(700,856)(701,883)(702,889)(703,888)(704,887)(705,886)(706,885)
(707,884)(708,890)(709,896)(710,895)(711,894)(712,893)(713,892)(714,891)
(715,869)(716,875)(717,874)(718,873)(719,872)(720,871)(721,870)(722,876)
(723,882)(724,881)(725,880)(726,879)(727,878)(728,877)(729,785)(730,791)
(731,790)(732,789)(733,788)(734,787)(735,786)(736,792)(737,798)(738,797)
(739,796)(740,795)(741,794)(742,793)(743,806)(744,812)(745,811)(746,810)
(747,809)(748,808)(749,807)(750,799)(751,805)(752,804)(753,803)(754,802)
(755,801)(756,800)(757,827)(758,833)(759,832)(760,831)(761,830)(762,829)
(763,828)(764,834)(765,840)(766,839)(767,838)(768,837)(769,836)(770,835)
(771,813)(772,819)(773,818)(774,817)(775,816)(776,815)(777,814)(778,820)
(779,826)(780,825)(781,824)(782,823)(783,822)(784,821);;
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)
( 57,506)( 58,505)( 59,511)( 60,510)( 61,509)( 62,508)( 63,507)( 64,513)
( 65,512)( 66,518)( 67,517)( 68,516)( 69,515)( 70,514)( 71,527)( 72,526)
( 73,532)( 74,531)( 75,530)( 76,529)( 77,528)( 78,520)( 79,519)( 80,525)
( 81,524)( 82,523)( 83,522)( 84,521)( 85,548)( 86,547)( 87,553)( 88,552)
( 89,551)( 90,550)( 91,549)( 92,555)( 93,554)( 94,560)( 95,559)( 96,558)
( 97,557)( 98,556)( 99,534)(100,533)(101,539)(102,538)(103,537)(104,536)
(105,535)(106,541)(107,540)(108,546)(109,545)(110,544)(111,543)(112,542)
(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)
(169,646)(170,645)(171,651)(172,650)(173,649)(174,648)(175,647)(176,653)
(177,652)(178,658)(179,657)(180,656)(181,655)(182,654)(183,667)(184,666)
(185,672)(186,671)(187,670)(188,669)(189,668)(190,660)(191,659)(192,665)
(193,664)(194,663)(195,662)(196,661)(197,618)(198,617)(199,623)(200,622)
(201,621)(202,620)(203,619)(204,625)(205,624)(206,630)(207,629)(208,628)
(209,627)(210,626)(211,639)(212,638)(213,644)(214,643)(215,642)(216,641)
(217,640)(218,632)(219,631)(220,637)(221,636)(222,635)(223,634)(224,633)
(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)
(281,730)(282,729)(283,735)(284,734)(285,733)(286,732)(287,731)(288,737)
(289,736)(290,742)(291,741)(292,740)(293,739)(294,738)(295,751)(296,750)
(297,756)(298,755)(299,754)(300,753)(301,752)(302,744)(303,743)(304,749)
(305,748)(306,747)(307,746)(308,745)(309,772)(310,771)(311,777)(312,776)
(313,775)(314,774)(315,773)(316,779)(317,778)(318,784)(319,783)(320,782)
(321,781)(322,780)(323,758)(324,757)(325,763)(326,762)(327,761)(328,760)
(329,759)(330,765)(331,764)(332,770)(333,769)(334,768)(335,767)(336,766)
(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)
(393,870)(394,869)(395,875)(396,874)(397,873)(398,872)(399,871)(400,877)
(401,876)(402,882)(403,881)(404,880)(405,879)(406,878)(407,891)(408,890)
(409,896)(410,895)(411,894)(412,893)(413,892)(414,884)(415,883)(416,889)
(417,888)(418,887)(419,886)(420,885)(421,842)(422,841)(423,847)(424,846)
(425,845)(426,844)(427,843)(428,849)(429,848)(430,854)(431,853)(432,852)
(433,851)(434,850)(435,863)(436,862)(437,868)(438,867)(439,866)(440,865)
(441,864)(442,856)(443,855)(444,861)(445,860)(446,859)(447,858)(448,857);;
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, 
s0*s1*s2*s1*s0*s1*s2*s1, 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*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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
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)(113,337)(114,338)(115,339)(116,340)(117,341)(118,342)(119,343)
(120,344)(121,345)(122,346)(123,347)(124,348)(125,349)(126,350)(127,351)
(128,352)(129,353)(130,354)(131,355)(132,356)(133,357)(134,358)(135,359)
(136,360)(137,361)(138,362)(139,363)(140,364)(141,365)(142,366)(143,367)
(144,368)(145,369)(146,370)(147,371)(148,372)(149,373)(150,374)(151,375)
(152,376)(153,377)(154,378)(155,379)(156,380)(157,381)(158,382)(159,383)
(160,384)(161,385)(162,386)(163,387)(164,388)(165,389)(166,390)(167,391)
(168,392)(169,393)(170,394)(171,395)(172,396)(173,397)(174,398)(175,399)
(176,400)(177,401)(178,402)(179,403)(180,404)(181,405)(182,406)(183,407)
(184,408)(185,409)(186,410)(187,411)(188,412)(189,413)(190,414)(191,415)
(192,416)(193,417)(194,418)(195,419)(196,420)(197,421)(198,422)(199,423)
(200,424)(201,425)(202,426)(203,427)(204,428)(205,429)(206,430)(207,431)
(208,432)(209,433)(210,434)(211,435)(212,436)(213,437)(214,438)(215,439)
(216,440)(217,441)(218,442)(219,443)(220,444)(221,445)(222,446)(223,447)
(224,448)(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)(561,785)(562,786)(563,787)(564,788)(565,789)(566,790)(567,791)
(568,792)(569,793)(570,794)(571,795)(572,796)(573,797)(574,798)(575,799)
(576,800)(577,801)(578,802)(579,803)(580,804)(581,805)(582,806)(583,807)
(584,808)(585,809)(586,810)(587,811)(588,812)(589,813)(590,814)(591,815)
(592,816)(593,817)(594,818)(595,819)(596,820)(597,821)(598,822)(599,823)
(600,824)(601,825)(602,826)(603,827)(604,828)(605,829)(606,830)(607,831)
(608,832)(609,833)(610,834)(611,835)(612,836)(613,837)(614,838)(615,839)
(616,840)(617,841)(618,842)(619,843)(620,844)(621,845)(622,846)(623,847)
(624,848)(625,849)(626,850)(627,851)(628,852)(629,853)(630,854)(631,855)
(632,856)(633,857)(634,858)(635,859)(636,860)(637,861)(638,862)(639,863)
(640,864)(641,865)(642,866)(643,867)(644,868)(645,869)(646,870)(647,871)
(648,872)(649,873)(650,874)(651,875)(652,876)(653,877)(654,878)(655,879)
(656,880)(657,881)(658,882)(659,883)(660,884)(661,885)(662,886)(663,887)
(664,888)(665,889)(666,890)(667,891)(668,892)(669,893)(670,894)(671,895)
(672,896);
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)(673,841)
(674,847)(675,846)(676,845)(677,844)(678,843)(679,842)(680,848)(681,854)
(682,853)(683,852)(684,851)(685,850)(686,849)(687,862)(688,868)(689,867)
(690,866)(691,865)(692,864)(693,863)(694,855)(695,861)(696,860)(697,859)
(698,858)(699,857)(700,856)(701,883)(702,889)(703,888)(704,887)(705,886)
(706,885)(707,884)(708,890)(709,896)(710,895)(711,894)(712,893)(713,892)
(714,891)(715,869)(716,875)(717,874)(718,873)(719,872)(720,871)(721,870)
(722,876)(723,882)(724,881)(725,880)(726,879)(727,878)(728,877)(729,785)
(730,791)(731,790)(732,789)(733,788)(734,787)(735,786)(736,792)(737,798)
(738,797)(739,796)(740,795)(741,794)(742,793)(743,806)(744,812)(745,811)
(746,810)(747,809)(748,808)(749,807)(750,799)(751,805)(752,804)(753,803)
(754,802)(755,801)(756,800)(757,827)(758,833)(759,832)(760,831)(761,830)
(762,829)(763,828)(764,834)(765,840)(766,839)(767,838)(768,837)(769,836)
(770,835)(771,813)(772,819)(773,818)(774,817)(775,816)(776,815)(777,814)
(778,820)(779,826)(780,825)(781,824)(782,823)(783,822)(784,821);
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)( 57,506)( 58,505)( 59,511)( 60,510)( 61,509)( 62,508)( 63,507)
( 64,513)( 65,512)( 66,518)( 67,517)( 68,516)( 69,515)( 70,514)( 71,527)
( 72,526)( 73,532)( 74,531)( 75,530)( 76,529)( 77,528)( 78,520)( 79,519)
( 80,525)( 81,524)( 82,523)( 83,522)( 84,521)( 85,548)( 86,547)( 87,553)
( 88,552)( 89,551)( 90,550)( 91,549)( 92,555)( 93,554)( 94,560)( 95,559)
( 96,558)( 97,557)( 98,556)( 99,534)(100,533)(101,539)(102,538)(103,537)
(104,536)(105,535)(106,541)(107,540)(108,546)(109,545)(110,544)(111,543)
(112,542)(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)(169,646)(170,645)(171,651)(172,650)(173,649)(174,648)(175,647)
(176,653)(177,652)(178,658)(179,657)(180,656)(181,655)(182,654)(183,667)
(184,666)(185,672)(186,671)(187,670)(188,669)(189,668)(190,660)(191,659)
(192,665)(193,664)(194,663)(195,662)(196,661)(197,618)(198,617)(199,623)
(200,622)(201,621)(202,620)(203,619)(204,625)(205,624)(206,630)(207,629)
(208,628)(209,627)(210,626)(211,639)(212,638)(213,644)(214,643)(215,642)
(216,641)(217,640)(218,632)(219,631)(220,637)(221,636)(222,635)(223,634)
(224,633)(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)(281,730)(282,729)(283,735)(284,734)(285,733)(286,732)(287,731)
(288,737)(289,736)(290,742)(291,741)(292,740)(293,739)(294,738)(295,751)
(296,750)(297,756)(298,755)(299,754)(300,753)(301,752)(302,744)(303,743)
(304,749)(305,748)(306,747)(307,746)(308,745)(309,772)(310,771)(311,777)
(312,776)(313,775)(314,774)(315,773)(316,779)(317,778)(318,784)(319,783)
(320,782)(321,781)(322,780)(323,758)(324,757)(325,763)(326,762)(327,761)
(328,760)(329,759)(330,765)(331,764)(332,770)(333,769)(334,768)(335,767)
(336,766)(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)(393,870)(394,869)(395,875)(396,874)(397,873)(398,872)(399,871)
(400,877)(401,876)(402,882)(403,881)(404,880)(405,879)(406,878)(407,891)
(408,890)(409,896)(410,895)(411,894)(412,893)(413,892)(414,884)(415,883)
(416,889)(417,888)(418,887)(419,886)(420,885)(421,842)(422,841)(423,847)
(424,846)(425,845)(426,844)(427,843)(428,849)(429,848)(430,854)(431,853)
(432,852)(433,851)(434,850)(435,863)(436,862)(437,868)(438,867)(439,866)
(440,865)(441,864)(442,856)(443,855)(444,861)(445,860)(446,859)(447,858)
(448,857);
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, 
s0*s1*s2*s1*s0*s1*s2*s1, 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*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*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope