Polytope of Type {224,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {224,4}*1792a
Also Known As : {224,4|2}. if this polytope has another name.
Group : SmallGroup(1792,90209)
Rank : 3
Schlafli Type : {224,4}
Number of vertices, edges, etc : 224, 448, 4
Order of s₀s₁s₂ : 224
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {112,4}*896a, {224,2}*896
   4-fold quotients : {56,4}*448a, {112,2}*448
   7-fold quotients : {32,4}*256a
   8-fold quotients : {28,4}*224, {56,2}*224
   14-fold quotients : {16,4}*128a, {32,2}*128
   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)
( 57,505)( 58,511)( 59,510)( 60,509)( 61,508)( 62,507)( 63,506)( 64,512)
( 65,518)( 66,517)( 67,516)( 68,515)( 69,514)( 70,513)( 71,526)( 72,532)
( 73,531)( 74,530)( 75,529)( 76,528)( 77,527)( 78,519)( 79,525)( 80,524)
( 81,523)( 82,522)( 83,521)( 84,520)( 85,547)( 86,553)( 87,552)( 88,551)
( 89,550)( 90,549)( 91,548)( 92,554)( 93,560)( 94,559)( 95,558)( 96,557)
( 97,556)( 98,555)( 99,533)(100,539)(101,538)(102,537)(103,536)(104,535)
(105,534)(106,540)(107,546)(108,545)(109,544)(110,543)(111,542)(112,541)
(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)
(169,645)(170,651)(171,650)(172,649)(173,648)(174,647)(175,646)(176,652)
(177,658)(178,657)(179,656)(180,655)(181,654)(182,653)(183,666)(184,672)
(185,671)(186,670)(187,669)(188,668)(189,667)(190,659)(191,665)(192,664)
(193,663)(194,662)(195,661)(196,660)(197,617)(198,623)(199,622)(200,621)
(201,620)(202,619)(203,618)(204,624)(205,630)(206,629)(207,628)(208,627)
(209,626)(210,625)(211,638)(212,644)(213,643)(214,642)(215,641)(216,640)
(217,639)(218,631)(219,637)(220,636)(221,635)(222,634)(223,633)(224,632)
(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)
(281,729)(282,735)(283,734)(284,733)(285,732)(286,731)(287,730)(288,736)
(289,742)(290,741)(291,740)(292,739)(293,738)(294,737)(295,750)(296,756)
(297,755)(298,754)(299,753)(300,752)(301,751)(302,743)(303,749)(304,748)
(305,747)(306,746)(307,745)(308,744)(309,771)(310,777)(311,776)(312,775)
(313,774)(314,773)(315,772)(316,778)(317,784)(318,783)(319,782)(320,781)
(321,780)(322,779)(323,757)(324,763)(325,762)(326,761)(327,760)(328,759)
(329,758)(330,764)(331,770)(332,769)(333,768)(334,767)(335,766)(336,765)
(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)
(393,869)(394,875)(395,874)(396,873)(397,872)(398,871)(399,870)(400,876)
(401,882)(402,881)(403,880)(404,879)(405,878)(406,877)(407,890)(408,896)
(409,895)(410,894)(411,893)(412,892)(413,891)(414,883)(415,889)(416,888)
(417,887)(418,886)(419,885)(420,884)(421,841)(422,847)(423,846)(424,845)
(425,844)(426,843)(427,842)(428,848)(429,854)(430,853)(431,852)(432,851)
(433,850)(434,849)(435,862)(436,868)(437,867)(438,866)(439,865)(440,864)
(441,863)(442,855)(443,861)(444,860)(445,859)(446,858)(447,857)(448,856);;
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)(673,842)(674,841)
(675,847)(676,846)(677,845)(678,844)(679,843)(680,849)(681,848)(682,854)
(683,853)(684,852)(685,851)(686,850)(687,863)(688,862)(689,868)(690,867)
(691,866)(692,865)(693,864)(694,856)(695,855)(696,861)(697,860)(698,859)
(699,858)(700,857)(701,884)(702,883)(703,889)(704,888)(705,887)(706,886)
(707,885)(708,891)(709,890)(710,896)(711,895)(712,894)(713,893)(714,892)
(715,870)(716,869)(717,875)(718,874)(719,873)(720,872)(721,871)(722,877)
(723,876)(724,882)(725,881)(726,880)(727,879)(728,878)(729,786)(730,785)
(731,791)(732,790)(733,789)(734,788)(735,787)(736,793)(737,792)(738,798)
(739,797)(740,796)(741,795)(742,794)(743,807)(744,806)(745,812)(746,811)
(747,810)(748,809)(749,808)(750,800)(751,799)(752,805)(753,804)(754,803)
(755,802)(756,801)(757,828)(758,827)(759,833)(760,832)(761,831)(762,830)
(763,829)(764,835)(765,834)(766,840)(767,839)(768,838)(769,837)(770,836)
(771,814)(772,813)(773,819)(774,818)(775,817)(776,816)(777,815)(778,821)
(779,820)(780,826)(781,825)(782,824)(783,823)(784,822);;
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)
(113,337)(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);;
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, 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*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*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*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)( 57,505)( 58,511)( 59,510)( 60,509)( 61,508)( 62,507)( 63,506)
( 64,512)( 65,518)( 66,517)( 67,516)( 68,515)( 69,514)( 70,513)( 71,526)
( 72,532)( 73,531)( 74,530)( 75,529)( 76,528)( 77,527)( 78,519)( 79,525)
( 80,524)( 81,523)( 82,522)( 83,521)( 84,520)( 85,547)( 86,553)( 87,552)
( 88,551)( 89,550)( 90,549)( 91,548)( 92,554)( 93,560)( 94,559)( 95,558)
( 96,557)( 97,556)( 98,555)( 99,533)(100,539)(101,538)(102,537)(103,536)
(104,535)(105,534)(106,540)(107,546)(108,545)(109,544)(110,543)(111,542)
(112,541)(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)(169,645)(170,651)(171,650)(172,649)(173,648)(174,647)(175,646)
(176,652)(177,658)(178,657)(179,656)(180,655)(181,654)(182,653)(183,666)
(184,672)(185,671)(186,670)(187,669)(188,668)(189,667)(190,659)(191,665)
(192,664)(193,663)(194,662)(195,661)(196,660)(197,617)(198,623)(199,622)
(200,621)(201,620)(202,619)(203,618)(204,624)(205,630)(206,629)(207,628)
(208,627)(209,626)(210,625)(211,638)(212,644)(213,643)(214,642)(215,641)
(216,640)(217,639)(218,631)(219,637)(220,636)(221,635)(222,634)(223,633)
(224,632)(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)(281,729)(282,735)(283,734)(284,733)(285,732)(286,731)(287,730)
(288,736)(289,742)(290,741)(291,740)(292,739)(293,738)(294,737)(295,750)
(296,756)(297,755)(298,754)(299,753)(300,752)(301,751)(302,743)(303,749)
(304,748)(305,747)(306,746)(307,745)(308,744)(309,771)(310,777)(311,776)
(312,775)(313,774)(314,773)(315,772)(316,778)(317,784)(318,783)(319,782)
(320,781)(321,780)(322,779)(323,757)(324,763)(325,762)(326,761)(327,760)
(328,759)(329,758)(330,764)(331,770)(332,769)(333,768)(334,767)(335,766)
(336,765)(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)(393,869)(394,875)(395,874)(396,873)(397,872)(398,871)(399,870)
(400,876)(401,882)(402,881)(403,880)(404,879)(405,878)(406,877)(407,890)
(408,896)(409,895)(410,894)(411,893)(412,892)(413,891)(414,883)(415,889)
(416,888)(417,887)(418,886)(419,885)(420,884)(421,841)(422,847)(423,846)
(424,845)(425,844)(426,843)(427,842)(428,848)(429,854)(430,853)(431,852)
(432,851)(433,850)(434,849)(435,862)(436,868)(437,867)(438,866)(439,865)
(440,864)(441,863)(442,855)(443,861)(444,860)(445,859)(446,858)(447,857)
(448,856);
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)(673,842)
(674,841)(675,847)(676,846)(677,845)(678,844)(679,843)(680,849)(681,848)
(682,854)(683,853)(684,852)(685,851)(686,850)(687,863)(688,862)(689,868)
(690,867)(691,866)(692,865)(693,864)(694,856)(695,855)(696,861)(697,860)
(698,859)(699,858)(700,857)(701,884)(702,883)(703,889)(704,888)(705,887)
(706,886)(707,885)(708,891)(709,890)(710,896)(711,895)(712,894)(713,893)
(714,892)(715,870)(716,869)(717,875)(718,874)(719,873)(720,872)(721,871)
(722,877)(723,876)(724,882)(725,881)(726,880)(727,879)(728,878)(729,786)
(730,785)(731,791)(732,790)(733,789)(734,788)(735,787)(736,793)(737,792)
(738,798)(739,797)(740,796)(741,795)(742,794)(743,807)(744,806)(745,812)
(746,811)(747,810)(748,809)(749,808)(750,800)(751,799)(752,805)(753,804)
(754,803)(755,802)(756,801)(757,828)(758,827)(759,833)(760,832)(761,831)
(762,830)(763,829)(764,835)(765,834)(766,840)(767,839)(768,838)(769,837)
(770,836)(771,814)(772,813)(773,819)(774,818)(775,817)(776,816)(777,815)
(778,821)(779,820)(780,826)(781,825)(782,824)(783,823)(784,822);
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)(113,337)(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);
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, 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*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*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*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