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Polytope of Type {56,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {56,4}*1792d
if this polytope has a name.
Group : SmallGroup(1792,90302)
Rank : 3
Schlafli Type : {56,4}
Number of vertices, edges, etc : 224, 448, 16
Order of s0s1s2 : 56
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {56,4}*896b
   4-fold quotients : {28,4}*448
   7-fold quotients : {8,4}*256d
   8-fold quotients : {28,4}*224
   14-fold quotients : {8,4}*128b
   16-fold quotients : {28,2}*112, {14,4}*112
   28-fold quotients : {4,4}*64
   32-fold quotients : {14,2}*56
   56-fold quotients : {4,4}*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 := (  1,673)(  2,679)(  3,678)(  4,677)(  5,676)(  6,675)(  7,674)(  8,680)
(  9,686)( 10,685)( 11,684)( 12,683)( 13,682)( 14,681)( 15,687)( 16,693)
( 17,692)( 18,691)( 19,690)( 20,689)( 21,688)( 22,694)( 23,700)( 24,699)
( 25,698)( 26,697)( 27,696)( 28,695)( 29,708)( 30,714)( 31,713)( 32,712)
( 33,711)( 34,710)( 35,709)( 36,701)( 37,707)( 38,706)( 39,705)( 40,704)
( 41,703)( 42,702)( 43,722)( 44,728)( 45,727)( 46,726)( 47,725)( 48,724)
( 49,723)( 50,715)( 51,721)( 52,720)( 53,719)( 54,718)( 55,717)( 56,716)
( 57,778)( 58,784)( 59,783)( 60,782)( 61,781)( 62,780)( 63,779)( 64,771)
( 65,777)( 66,776)( 67,775)( 68,774)( 69,773)( 70,772)( 71,764)( 72,770)
( 73,769)( 74,768)( 75,767)( 76,766)( 77,765)( 78,757)( 79,763)( 80,762)
( 81,761)( 82,760)( 83,759)( 84,758)( 85,750)( 86,756)( 87,755)( 88,754)
( 89,753)( 90,752)( 91,751)( 92,743)( 93,749)( 94,748)( 95,747)( 96,746)
( 97,745)( 98,744)( 99,736)(100,742)(101,741)(102,740)(103,739)(104,738)
(105,737)(106,729)(107,735)(108,734)(109,733)(110,732)(111,731)(112,730)
(113,820)(114,826)(115,825)(116,824)(117,823)(118,822)(119,821)(120,813)
(121,819)(122,818)(123,817)(124,816)(125,815)(126,814)(127,834)(128,840)
(129,839)(130,838)(131,837)(132,836)(133,835)(134,827)(135,833)(136,832)
(137,831)(138,830)(139,829)(140,828)(141,792)(142,798)(143,797)(144,796)
(145,795)(146,794)(147,793)(148,785)(149,791)(150,790)(151,789)(152,788)
(153,787)(154,786)(155,806)(156,812)(157,811)(158,810)(159,809)(160,808)
(161,807)(162,799)(163,805)(164,804)(165,803)(166,802)(167,801)(168,800)
(169,855)(170,861)(171,860)(172,859)(173,858)(174,857)(175,856)(176,862)
(177,868)(178,867)(179,866)(180,865)(181,864)(182,863)(183,841)(184,847)
(185,846)(186,845)(187,844)(188,843)(189,842)(190,848)(191,854)(192,853)
(193,852)(194,851)(195,850)(196,849)(197,890)(198,896)(199,895)(200,894)
(201,893)(202,892)(203,891)(204,883)(205,889)(206,888)(207,887)(208,886)
(209,885)(210,884)(211,876)(212,882)(213,881)(214,880)(215,879)(216,878)
(217,877)(218,869)(219,875)(220,874)(221,873)(222,872)(223,871)(224,870)
(225,449)(226,455)(227,454)(228,453)(229,452)(230,451)(231,450)(232,456)
(233,462)(234,461)(235,460)(236,459)(237,458)(238,457)(239,463)(240,469)
(241,468)(242,467)(243,466)(244,465)(245,464)(246,470)(247,476)(248,475)
(249,474)(250,473)(251,472)(252,471)(253,484)(254,490)(255,489)(256,488)
(257,487)(258,486)(259,485)(260,477)(261,483)(262,482)(263,481)(264,480)
(265,479)(266,478)(267,498)(268,504)(269,503)(270,502)(271,501)(272,500)
(273,499)(274,491)(275,497)(276,496)(277,495)(278,494)(279,493)(280,492)
(281,554)(282,560)(283,559)(284,558)(285,557)(286,556)(287,555)(288,547)
(289,553)(290,552)(291,551)(292,550)(293,549)(294,548)(295,540)(296,546)
(297,545)(298,544)(299,543)(300,542)(301,541)(302,533)(303,539)(304,538)
(305,537)(306,536)(307,535)(308,534)(309,526)(310,532)(311,531)(312,530)
(313,529)(314,528)(315,527)(316,519)(317,525)(318,524)(319,523)(320,522)
(321,521)(322,520)(323,512)(324,518)(325,517)(326,516)(327,515)(328,514)
(329,513)(330,505)(331,511)(332,510)(333,509)(334,508)(335,507)(336,506)
(337,596)(338,602)(339,601)(340,600)(341,599)(342,598)(343,597)(344,589)
(345,595)(346,594)(347,593)(348,592)(349,591)(350,590)(351,610)(352,616)
(353,615)(354,614)(355,613)(356,612)(357,611)(358,603)(359,609)(360,608)
(361,607)(362,606)(363,605)(364,604)(365,568)(366,574)(367,573)(368,572)
(369,571)(370,570)(371,569)(372,561)(373,567)(374,566)(375,565)(376,564)
(377,563)(378,562)(379,582)(380,588)(381,587)(382,586)(383,585)(384,584)
(385,583)(386,575)(387,581)(388,580)(389,579)(390,578)(391,577)(392,576)
(393,631)(394,637)(395,636)(396,635)(397,634)(398,633)(399,632)(400,638)
(401,644)(402,643)(403,642)(404,641)(405,640)(406,639)(407,617)(408,623)
(409,622)(410,621)(411,620)(412,619)(413,618)(414,624)(415,630)(416,629)
(417,628)(418,627)(419,626)(420,625)(421,666)(422,672)(423,671)(424,670)
(425,669)(426,668)(427,667)(428,659)(429,665)(430,664)(431,663)(432,662)
(433,661)(434,660)(435,652)(436,658)(437,657)(438,656)(439,655)(440,654)
(441,653)(442,645)(443,651)(444,650)(445,649)(446,648)(447,647)(448,646);;
s1 := (  1,  2)(  3,  7)(  4,  6)(  8,  9)( 10, 14)( 11, 13)( 15, 16)( 17, 21)
( 18, 20)( 22, 23)( 24, 28)( 25, 27)( 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, 72)( 73, 77)( 74, 76)( 78, 79)( 80, 84)( 81, 83)( 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)(113,121)(114,120)(115,126)(116,125)
(117,124)(118,123)(119,122)(127,135)(128,134)(129,140)(130,139)(131,138)
(132,137)(133,136)(141,163)(142,162)(143,168)(144,167)(145,166)(146,165)
(147,164)(148,156)(149,155)(150,161)(151,160)(152,159)(153,158)(154,157)
(169,177)(170,176)(171,182)(172,181)(173,180)(174,179)(175,178)(183,191)
(184,190)(185,196)(186,195)(187,194)(188,193)(189,192)(197,219)(198,218)
(199,224)(200,223)(201,222)(202,221)(203,220)(204,212)(205,211)(206,217)
(207,216)(208,215)(209,214)(210,213)(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)(239,296)(240,295)(241,301)(242,300)(243,299)(244,298)
(245,297)(246,303)(247,302)(248,308)(249,307)(250,306)(251,305)(252,304)
(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)(337,408)(338,407)(339,413)(340,412)
(341,411)(342,410)(343,409)(344,415)(345,414)(346,420)(347,419)(348,418)
(349,417)(350,416)(351,394)(352,393)(353,399)(354,398)(355,397)(356,396)
(357,395)(358,401)(359,400)(360,406)(361,405)(362,404)(363,403)(364,402)
(365,422)(366,421)(367,427)(368,426)(369,425)(370,424)(371,423)(372,429)
(373,428)(374,434)(375,433)(376,432)(377,431)(378,430)(379,436)(380,435)
(381,441)(382,440)(383,439)(384,438)(385,437)(386,443)(387,442)(388,448)
(389,447)(390,446)(391,445)(392,444)(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)(463,576)(464,575)(465,581)(466,580)(467,579)(468,578)
(469,577)(470,583)(471,582)(472,588)(473,587)(474,586)(475,585)(476,584)
(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)(519,632)(520,631)(521,637)(522,636)(523,635)(524,634)
(525,633)(526,639)(527,638)(528,644)(529,643)(530,642)(531,641)(532,640)
(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)(673,877)(674,876)(675,882)(676,881)
(677,880)(678,879)(679,878)(680,870)(681,869)(682,875)(683,874)(684,873)
(685,872)(686,871)(687,891)(688,890)(689,896)(690,895)(691,894)(692,893)
(693,892)(694,884)(695,883)(696,889)(697,888)(698,887)(699,886)(700,885)
(701,856)(702,855)(703,861)(704,860)(705,859)(706,858)(707,857)(708,863)
(709,862)(710,868)(711,867)(712,866)(713,865)(714,864)(715,842)(716,841)
(717,847)(718,846)(719,845)(720,844)(721,843)(722,849)(723,848)(724,854)
(725,853)(726,852)(727,851)(728,850)(729,814)(730,813)(731,819)(732,818)
(733,817)(734,816)(735,815)(736,821)(737,820)(738,826)(739,825)(740,824)
(741,823)(742,822)(743,828)(744,827)(745,833)(746,832)(747,831)(748,830)
(749,829)(750,835)(751,834)(752,840)(753,839)(754,838)(755,837)(756,836)
(757,807)(758,806)(759,812)(760,811)(761,810)(762,809)(763,808)(764,800)
(765,799)(766,805)(767,804)(768,803)(769,802)(770,801)(771,793)(772,792)
(773,798)(774,797)(775,796)(776,795)(777,794)(778,786)(779,785)(780,791)
(781,790)(782,789)(783,788)(784,787);;
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)( 15,246)( 16,247)
( 17,248)( 18,249)( 19,250)( 20,251)( 21,252)( 22,239)( 23,240)( 24,241)
( 25,242)( 26,243)( 27,244)( 28,245)( 29,260)( 30,261)( 31,262)( 32,263)
( 33,264)( 34,265)( 35,266)( 36,253)( 37,254)( 38,255)( 39,256)( 40,257)
( 41,258)( 42,259)( 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)( 71,302)( 72,303)
( 73,304)( 74,305)( 75,306)( 76,307)( 77,308)( 78,295)( 79,296)( 80,297)
( 81,298)( 82,299)( 83,300)( 84,301)( 85,316)( 86,317)( 87,318)( 88,319)
( 89,320)( 90,321)( 91,322)( 92,309)( 93,310)( 94,311)( 95,312)( 96,313)
( 97,314)( 98,315)( 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)
(113,365)(114,366)(115,367)(116,368)(117,369)(118,370)(119,371)(120,372)
(121,373)(122,374)(123,375)(124,376)(125,377)(126,378)(127,386)(128,387)
(129,388)(130,389)(131,390)(132,391)(133,392)(134,379)(135,380)(136,381)
(137,382)(138,383)(139,384)(140,385)(141,337)(142,338)(143,339)(144,340)
(145,341)(146,342)(147,343)(148,344)(149,345)(150,346)(151,347)(152,348)
(153,349)(154,350)(155,358)(156,359)(157,360)(158,361)(159,362)(160,363)
(161,364)(162,351)(163,352)(164,353)(165,354)(166,355)(167,356)(168,357)
(169,428)(170,429)(171,430)(172,431)(173,432)(174,433)(175,434)(176,421)
(177,422)(178,423)(179,424)(180,425)(181,426)(182,427)(183,435)(184,436)
(185,437)(186,438)(187,439)(188,440)(189,441)(190,442)(191,443)(192,444)
(193,445)(194,446)(195,447)(196,448)(197,400)(198,401)(199,402)(200,403)
(201,404)(202,405)(203,406)(204,393)(205,394)(206,395)(207,396)(208,397)
(209,398)(210,399)(211,407)(212,408)(213,409)(214,410)(215,411)(216,412)
(217,413)(218,414)(219,415)(220,416)(221,417)(222,418)(223,419)(224,420)
(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)(463,694)(464,695)
(465,696)(466,697)(467,698)(468,699)(469,700)(470,687)(471,688)(472,689)
(473,690)(474,691)(475,692)(476,693)(477,708)(478,709)(479,710)(480,711)
(481,712)(482,713)(483,714)(484,701)(485,702)(486,703)(487,704)(488,705)
(489,706)(490,707)(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)(519,750)(520,751)
(521,752)(522,753)(523,754)(524,755)(525,756)(526,743)(527,744)(528,745)
(529,746)(530,747)(531,748)(532,749)(533,764)(534,765)(535,766)(536,767)
(537,768)(538,769)(539,770)(540,757)(541,758)(542,759)(543,760)(544,761)
(545,762)(546,763)(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)
(561,813)(562,814)(563,815)(564,816)(565,817)(566,818)(567,819)(568,820)
(569,821)(570,822)(571,823)(572,824)(573,825)(574,826)(575,834)(576,835)
(577,836)(578,837)(579,838)(580,839)(581,840)(582,827)(583,828)(584,829)
(585,830)(586,831)(587,832)(588,833)(589,785)(590,786)(591,787)(592,788)
(593,789)(594,790)(595,791)(596,792)(597,793)(598,794)(599,795)(600,796)
(601,797)(602,798)(603,806)(604,807)(605,808)(606,809)(607,810)(608,811)
(609,812)(610,799)(611,800)(612,801)(613,802)(614,803)(615,804)(616,805)
(617,876)(618,877)(619,878)(620,879)(621,880)(622,881)(623,882)(624,869)
(625,870)(626,871)(627,872)(628,873)(629,874)(630,875)(631,883)(632,884)
(633,885)(634,886)(635,887)(636,888)(637,889)(638,890)(639,891)(640,892)
(641,893)(642,894)(643,895)(644,896)(645,848)(646,849)(647,850)(648,851)
(649,852)(650,853)(651,854)(652,841)(653,842)(654,843)(655,844)(656,845)
(657,846)(658,847)(659,855)(660,856)(661,857)(662,858)(663,859)(664,860)
(665,861)(666,862)(667,863)(668,864)(669,865)(670,866)(671,867)(672,868);;
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, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s2*s1*s2*s1*s0*s1*s0*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*s2*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(896)!(  1,673)(  2,679)(  3,678)(  4,677)(  5,676)(  6,675)(  7,674)
(  8,680)(  9,686)( 10,685)( 11,684)( 12,683)( 13,682)( 14,681)( 15,687)
( 16,693)( 17,692)( 18,691)( 19,690)( 20,689)( 21,688)( 22,694)( 23,700)
( 24,699)( 25,698)( 26,697)( 27,696)( 28,695)( 29,708)( 30,714)( 31,713)
( 32,712)( 33,711)( 34,710)( 35,709)( 36,701)( 37,707)( 38,706)( 39,705)
( 40,704)( 41,703)( 42,702)( 43,722)( 44,728)( 45,727)( 46,726)( 47,725)
( 48,724)( 49,723)( 50,715)( 51,721)( 52,720)( 53,719)( 54,718)( 55,717)
( 56,716)( 57,778)( 58,784)( 59,783)( 60,782)( 61,781)( 62,780)( 63,779)
( 64,771)( 65,777)( 66,776)( 67,775)( 68,774)( 69,773)( 70,772)( 71,764)
( 72,770)( 73,769)( 74,768)( 75,767)( 76,766)( 77,765)( 78,757)( 79,763)
( 80,762)( 81,761)( 82,760)( 83,759)( 84,758)( 85,750)( 86,756)( 87,755)
( 88,754)( 89,753)( 90,752)( 91,751)( 92,743)( 93,749)( 94,748)( 95,747)
( 96,746)( 97,745)( 98,744)( 99,736)(100,742)(101,741)(102,740)(103,739)
(104,738)(105,737)(106,729)(107,735)(108,734)(109,733)(110,732)(111,731)
(112,730)(113,820)(114,826)(115,825)(116,824)(117,823)(118,822)(119,821)
(120,813)(121,819)(122,818)(123,817)(124,816)(125,815)(126,814)(127,834)
(128,840)(129,839)(130,838)(131,837)(132,836)(133,835)(134,827)(135,833)
(136,832)(137,831)(138,830)(139,829)(140,828)(141,792)(142,798)(143,797)
(144,796)(145,795)(146,794)(147,793)(148,785)(149,791)(150,790)(151,789)
(152,788)(153,787)(154,786)(155,806)(156,812)(157,811)(158,810)(159,809)
(160,808)(161,807)(162,799)(163,805)(164,804)(165,803)(166,802)(167,801)
(168,800)(169,855)(170,861)(171,860)(172,859)(173,858)(174,857)(175,856)
(176,862)(177,868)(178,867)(179,866)(180,865)(181,864)(182,863)(183,841)
(184,847)(185,846)(186,845)(187,844)(188,843)(189,842)(190,848)(191,854)
(192,853)(193,852)(194,851)(195,850)(196,849)(197,890)(198,896)(199,895)
(200,894)(201,893)(202,892)(203,891)(204,883)(205,889)(206,888)(207,887)
(208,886)(209,885)(210,884)(211,876)(212,882)(213,881)(214,880)(215,879)
(216,878)(217,877)(218,869)(219,875)(220,874)(221,873)(222,872)(223,871)
(224,870)(225,449)(226,455)(227,454)(228,453)(229,452)(230,451)(231,450)
(232,456)(233,462)(234,461)(235,460)(236,459)(237,458)(238,457)(239,463)
(240,469)(241,468)(242,467)(243,466)(244,465)(245,464)(246,470)(247,476)
(248,475)(249,474)(250,473)(251,472)(252,471)(253,484)(254,490)(255,489)
(256,488)(257,487)(258,486)(259,485)(260,477)(261,483)(262,482)(263,481)
(264,480)(265,479)(266,478)(267,498)(268,504)(269,503)(270,502)(271,501)
(272,500)(273,499)(274,491)(275,497)(276,496)(277,495)(278,494)(279,493)
(280,492)(281,554)(282,560)(283,559)(284,558)(285,557)(286,556)(287,555)
(288,547)(289,553)(290,552)(291,551)(292,550)(293,549)(294,548)(295,540)
(296,546)(297,545)(298,544)(299,543)(300,542)(301,541)(302,533)(303,539)
(304,538)(305,537)(306,536)(307,535)(308,534)(309,526)(310,532)(311,531)
(312,530)(313,529)(314,528)(315,527)(316,519)(317,525)(318,524)(319,523)
(320,522)(321,521)(322,520)(323,512)(324,518)(325,517)(326,516)(327,515)
(328,514)(329,513)(330,505)(331,511)(332,510)(333,509)(334,508)(335,507)
(336,506)(337,596)(338,602)(339,601)(340,600)(341,599)(342,598)(343,597)
(344,589)(345,595)(346,594)(347,593)(348,592)(349,591)(350,590)(351,610)
(352,616)(353,615)(354,614)(355,613)(356,612)(357,611)(358,603)(359,609)
(360,608)(361,607)(362,606)(363,605)(364,604)(365,568)(366,574)(367,573)
(368,572)(369,571)(370,570)(371,569)(372,561)(373,567)(374,566)(375,565)
(376,564)(377,563)(378,562)(379,582)(380,588)(381,587)(382,586)(383,585)
(384,584)(385,583)(386,575)(387,581)(388,580)(389,579)(390,578)(391,577)
(392,576)(393,631)(394,637)(395,636)(396,635)(397,634)(398,633)(399,632)
(400,638)(401,644)(402,643)(403,642)(404,641)(405,640)(406,639)(407,617)
(408,623)(409,622)(410,621)(411,620)(412,619)(413,618)(414,624)(415,630)
(416,629)(417,628)(418,627)(419,626)(420,625)(421,666)(422,672)(423,671)
(424,670)(425,669)(426,668)(427,667)(428,659)(429,665)(430,664)(431,663)
(432,662)(433,661)(434,660)(435,652)(436,658)(437,657)(438,656)(439,655)
(440,654)(441,653)(442,645)(443,651)(444,650)(445,649)(446,648)(447,647)
(448,646);
s1 := Sym(896)!(  1,  2)(  3,  7)(  4,  6)(  8,  9)( 10, 14)( 11, 13)( 15, 16)
( 17, 21)( 18, 20)( 22, 23)( 24, 28)( 25, 27)( 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, 72)( 73, 77)( 74, 76)( 78, 79)( 80, 84)( 81, 83)( 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)(113,121)(114,120)(115,126)
(116,125)(117,124)(118,123)(119,122)(127,135)(128,134)(129,140)(130,139)
(131,138)(132,137)(133,136)(141,163)(142,162)(143,168)(144,167)(145,166)
(146,165)(147,164)(148,156)(149,155)(150,161)(151,160)(152,159)(153,158)
(154,157)(169,177)(170,176)(171,182)(172,181)(173,180)(174,179)(175,178)
(183,191)(184,190)(185,196)(186,195)(187,194)(188,193)(189,192)(197,219)
(198,218)(199,224)(200,223)(201,222)(202,221)(203,220)(204,212)(205,211)
(206,217)(207,216)(208,215)(209,214)(210,213)(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)(239,296)(240,295)(241,301)(242,300)(243,299)
(244,298)(245,297)(246,303)(247,302)(248,308)(249,307)(250,306)(251,305)
(252,304)(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)(337,408)(338,407)(339,413)
(340,412)(341,411)(342,410)(343,409)(344,415)(345,414)(346,420)(347,419)
(348,418)(349,417)(350,416)(351,394)(352,393)(353,399)(354,398)(355,397)
(356,396)(357,395)(358,401)(359,400)(360,406)(361,405)(362,404)(363,403)
(364,402)(365,422)(366,421)(367,427)(368,426)(369,425)(370,424)(371,423)
(372,429)(373,428)(374,434)(375,433)(376,432)(377,431)(378,430)(379,436)
(380,435)(381,441)(382,440)(383,439)(384,438)(385,437)(386,443)(387,442)
(388,448)(389,447)(390,446)(391,445)(392,444)(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)(463,576)(464,575)(465,581)(466,580)(467,579)
(468,578)(469,577)(470,583)(471,582)(472,588)(473,587)(474,586)(475,585)
(476,584)(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)(519,632)(520,631)(521,637)(522,636)(523,635)
(524,634)(525,633)(526,639)(527,638)(528,644)(529,643)(530,642)(531,641)
(532,640)(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)(673,877)(674,876)(675,882)
(676,881)(677,880)(678,879)(679,878)(680,870)(681,869)(682,875)(683,874)
(684,873)(685,872)(686,871)(687,891)(688,890)(689,896)(690,895)(691,894)
(692,893)(693,892)(694,884)(695,883)(696,889)(697,888)(698,887)(699,886)
(700,885)(701,856)(702,855)(703,861)(704,860)(705,859)(706,858)(707,857)
(708,863)(709,862)(710,868)(711,867)(712,866)(713,865)(714,864)(715,842)
(716,841)(717,847)(718,846)(719,845)(720,844)(721,843)(722,849)(723,848)
(724,854)(725,853)(726,852)(727,851)(728,850)(729,814)(730,813)(731,819)
(732,818)(733,817)(734,816)(735,815)(736,821)(737,820)(738,826)(739,825)
(740,824)(741,823)(742,822)(743,828)(744,827)(745,833)(746,832)(747,831)
(748,830)(749,829)(750,835)(751,834)(752,840)(753,839)(754,838)(755,837)
(756,836)(757,807)(758,806)(759,812)(760,811)(761,810)(762,809)(763,808)
(764,800)(765,799)(766,805)(767,804)(768,803)(769,802)(770,801)(771,793)
(772,792)(773,798)(774,797)(775,796)(776,795)(777,794)(778,786)(779,785)
(780,791)(781,790)(782,789)(783,788)(784,787);
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)( 15,246)
( 16,247)( 17,248)( 18,249)( 19,250)( 20,251)( 21,252)( 22,239)( 23,240)
( 24,241)( 25,242)( 26,243)( 27,244)( 28,245)( 29,260)( 30,261)( 31,262)
( 32,263)( 33,264)( 34,265)( 35,266)( 36,253)( 37,254)( 38,255)( 39,256)
( 40,257)( 41,258)( 42,259)( 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)( 71,302)
( 72,303)( 73,304)( 74,305)( 75,306)( 76,307)( 77,308)( 78,295)( 79,296)
( 80,297)( 81,298)( 82,299)( 83,300)( 84,301)( 85,316)( 86,317)( 87,318)
( 88,319)( 89,320)( 90,321)( 91,322)( 92,309)( 93,310)( 94,311)( 95,312)
( 96,313)( 97,314)( 98,315)( 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)(113,365)(114,366)(115,367)(116,368)(117,369)(118,370)(119,371)
(120,372)(121,373)(122,374)(123,375)(124,376)(125,377)(126,378)(127,386)
(128,387)(129,388)(130,389)(131,390)(132,391)(133,392)(134,379)(135,380)
(136,381)(137,382)(138,383)(139,384)(140,385)(141,337)(142,338)(143,339)
(144,340)(145,341)(146,342)(147,343)(148,344)(149,345)(150,346)(151,347)
(152,348)(153,349)(154,350)(155,358)(156,359)(157,360)(158,361)(159,362)
(160,363)(161,364)(162,351)(163,352)(164,353)(165,354)(166,355)(167,356)
(168,357)(169,428)(170,429)(171,430)(172,431)(173,432)(174,433)(175,434)
(176,421)(177,422)(178,423)(179,424)(180,425)(181,426)(182,427)(183,435)
(184,436)(185,437)(186,438)(187,439)(188,440)(189,441)(190,442)(191,443)
(192,444)(193,445)(194,446)(195,447)(196,448)(197,400)(198,401)(199,402)
(200,403)(201,404)(202,405)(203,406)(204,393)(205,394)(206,395)(207,396)
(208,397)(209,398)(210,399)(211,407)(212,408)(213,409)(214,410)(215,411)
(216,412)(217,413)(218,414)(219,415)(220,416)(221,417)(222,418)(223,419)
(224,420)(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)(463,694)
(464,695)(465,696)(466,697)(467,698)(468,699)(469,700)(470,687)(471,688)
(472,689)(473,690)(474,691)(475,692)(476,693)(477,708)(478,709)(479,710)
(480,711)(481,712)(482,713)(483,714)(484,701)(485,702)(486,703)(487,704)
(488,705)(489,706)(490,707)(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)(519,750)
(520,751)(521,752)(522,753)(523,754)(524,755)(525,756)(526,743)(527,744)
(528,745)(529,746)(530,747)(531,748)(532,749)(533,764)(534,765)(535,766)
(536,767)(537,768)(538,769)(539,770)(540,757)(541,758)(542,759)(543,760)
(544,761)(545,762)(546,763)(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)(561,813)(562,814)(563,815)(564,816)(565,817)(566,818)(567,819)
(568,820)(569,821)(570,822)(571,823)(572,824)(573,825)(574,826)(575,834)
(576,835)(577,836)(578,837)(579,838)(580,839)(581,840)(582,827)(583,828)
(584,829)(585,830)(586,831)(587,832)(588,833)(589,785)(590,786)(591,787)
(592,788)(593,789)(594,790)(595,791)(596,792)(597,793)(598,794)(599,795)
(600,796)(601,797)(602,798)(603,806)(604,807)(605,808)(606,809)(607,810)
(608,811)(609,812)(610,799)(611,800)(612,801)(613,802)(614,803)(615,804)
(616,805)(617,876)(618,877)(619,878)(620,879)(621,880)(622,881)(623,882)
(624,869)(625,870)(626,871)(627,872)(628,873)(629,874)(630,875)(631,883)
(632,884)(633,885)(634,886)(635,887)(636,888)(637,889)(638,890)(639,891)
(640,892)(641,893)(642,894)(643,895)(644,896)(645,848)(646,849)(647,850)
(648,851)(649,852)(650,853)(651,854)(652,841)(653,842)(654,843)(655,844)
(656,845)(657,846)(658,847)(659,855)(660,856)(661,857)(662,858)(663,859)
(664,860)(665,861)(666,862)(667,863)(668,864)(669,865)(670,866)(671,867)
(672,868);
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, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s2*s1*s2*s1*s0*s1*s0*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*s2*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*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 >; 
 
References : None.
to this polytope