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Polytope of Type {8,56}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,56}*1792f
if this polytope has a name.
Group : SmallGroup(1792,90303)
Rank : 3
Schlafli Type : {8,56}
Number of vertices, edges, etc : 16, 448, 112
Order of s0s1s2 : 28
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {8,28}*896b
   4-fold quotients : {4,28}*448
   7-fold quotients : {8,8}*256f
   8-fold quotients : {4,28}*224
   14-fold quotients : {8,4}*128b
   16-fold quotients : {2,28}*112, {4,14}*112
   28-fold quotients : {4,4}*64
   32-fold quotients : {2,14}*56
   56-fold quotients : {4,4}*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 := (  1,673)(  2,674)(  3,675)(  4,676)(  5,677)(  6,678)(  7,679)(  8,680)
(  9,681)( 10,682)( 11,683)( 12,684)( 13,685)( 14,686)( 15,687)( 16,688)
( 17,689)( 18,690)( 19,691)( 20,692)( 21,693)( 22,694)( 23,695)( 24,696)
( 25,697)( 26,698)( 27,699)( 28,700)( 29,708)( 30,709)( 31,710)( 32,711)
( 33,712)( 34,713)( 35,714)( 36,701)( 37,702)( 38,703)( 39,704)( 40,705)
( 41,706)( 42,707)( 43,722)( 44,723)( 45,724)( 46,725)( 47,726)( 48,727)
( 49,728)( 50,715)( 51,716)( 52,717)( 53,718)( 54,719)( 55,720)( 56,721)
( 57,778)( 58,779)( 59,780)( 60,781)( 61,782)( 62,783)( 63,784)( 64,771)
( 65,772)( 66,773)( 67,774)( 68,775)( 69,776)( 70,777)( 71,764)( 72,765)
( 73,766)( 74,767)( 75,768)( 76,769)( 77,770)( 78,757)( 79,758)( 80,759)
( 81,760)( 82,761)( 83,762)( 84,763)( 85,750)( 86,751)( 87,752)( 88,753)
( 89,754)( 90,755)( 91,756)( 92,743)( 93,744)( 94,745)( 95,746)( 96,747)
( 97,748)( 98,749)( 99,736)(100,737)(101,738)(102,739)(103,740)(104,741)
(105,742)(106,729)(107,730)(108,731)(109,732)(110,733)(111,734)(112,735)
(113,820)(114,821)(115,822)(116,823)(117,824)(118,825)(119,826)(120,813)
(121,814)(122,815)(123,816)(124,817)(125,818)(126,819)(127,834)(128,835)
(129,836)(130,837)(131,838)(132,839)(133,840)(134,827)(135,828)(136,829)
(137,830)(138,831)(139,832)(140,833)(141,792)(142,793)(143,794)(144,795)
(145,796)(146,797)(147,798)(148,785)(149,786)(150,787)(151,788)(152,789)
(153,790)(154,791)(155,806)(156,807)(157,808)(158,809)(159,810)(160,811)
(161,812)(162,799)(163,800)(164,801)(165,802)(166,803)(167,804)(168,805)
(169,855)(170,856)(171,857)(172,858)(173,859)(174,860)(175,861)(176,862)
(177,863)(178,864)(179,865)(180,866)(181,867)(182,868)(183,841)(184,842)
(185,843)(186,844)(187,845)(188,846)(189,847)(190,848)(191,849)(192,850)
(193,851)(194,852)(195,853)(196,854)(197,890)(198,891)(199,892)(200,893)
(201,894)(202,895)(203,896)(204,883)(205,884)(206,885)(207,886)(208,887)
(209,888)(210,889)(211,876)(212,877)(213,878)(214,879)(215,880)(216,881)
(217,882)(218,869)(219,870)(220,871)(221,872)(222,873)(223,874)(224,875)
(225,449)(226,450)(227,451)(228,452)(229,453)(230,454)(231,455)(232,456)
(233,457)(234,458)(235,459)(236,460)(237,461)(238,462)(239,463)(240,464)
(241,465)(242,466)(243,467)(244,468)(245,469)(246,470)(247,471)(248,472)
(249,473)(250,474)(251,475)(252,476)(253,484)(254,485)(255,486)(256,487)
(257,488)(258,489)(259,490)(260,477)(261,478)(262,479)(263,480)(264,481)
(265,482)(266,483)(267,498)(268,499)(269,500)(270,501)(271,502)(272,503)
(273,504)(274,491)(275,492)(276,493)(277,494)(278,495)(279,496)(280,497)
(281,554)(282,555)(283,556)(284,557)(285,558)(286,559)(287,560)(288,547)
(289,548)(290,549)(291,550)(292,551)(293,552)(294,553)(295,540)(296,541)
(297,542)(298,543)(299,544)(300,545)(301,546)(302,533)(303,534)(304,535)
(305,536)(306,537)(307,538)(308,539)(309,526)(310,527)(311,528)(312,529)
(313,530)(314,531)(315,532)(316,519)(317,520)(318,521)(319,522)(320,523)
(321,524)(322,525)(323,512)(324,513)(325,514)(326,515)(327,516)(328,517)
(329,518)(330,505)(331,506)(332,507)(333,508)(334,509)(335,510)(336,511)
(337,596)(338,597)(339,598)(340,599)(341,600)(342,601)(343,602)(344,589)
(345,590)(346,591)(347,592)(348,593)(349,594)(350,595)(351,610)(352,611)
(353,612)(354,613)(355,614)(356,615)(357,616)(358,603)(359,604)(360,605)
(361,606)(362,607)(363,608)(364,609)(365,568)(366,569)(367,570)(368,571)
(369,572)(370,573)(371,574)(372,561)(373,562)(374,563)(375,564)(376,565)
(377,566)(378,567)(379,582)(380,583)(381,584)(382,585)(383,586)(384,587)
(385,588)(386,575)(387,576)(388,577)(389,578)(390,579)(391,580)(392,581)
(393,631)(394,632)(395,633)(396,634)(397,635)(398,636)(399,637)(400,638)
(401,639)(402,640)(403,641)(404,642)(405,643)(406,644)(407,617)(408,618)
(409,619)(410,620)(411,621)(412,622)(413,623)(414,624)(415,625)(416,626)
(417,627)(418,628)(419,629)(420,630)(421,666)(422,667)(423,668)(424,669)
(425,670)(426,671)(427,672)(428,659)(429,660)(430,661)(431,662)(432,663)
(433,664)(434,665)(435,652)(436,653)(437,654)(438,655)(439,656)(440,657)
(441,658)(442,645)(443,646)(444,647)(445,648)(446,649)(447,650)(448,651);;
s1 := (  2,  7)(  3,  6)(  4,  5)(  9, 14)( 10, 13)( 11, 12)( 16, 21)( 17, 20)
( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 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)
( 72, 77)( 73, 76)( 74, 75)( 79, 84)( 80, 83)( 81, 82)( 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)(113,120)(114,126)(115,125)(116,124)
(117,123)(118,122)(119,121)(127,134)(128,140)(129,139)(130,138)(131,137)
(132,136)(133,135)(141,162)(142,168)(143,167)(144,166)(145,165)(146,164)
(147,163)(148,155)(149,161)(150,160)(151,159)(152,158)(153,157)(154,156)
(169,176)(170,182)(171,181)(172,180)(173,179)(174,178)(175,177)(183,190)
(184,196)(185,195)(186,194)(187,193)(188,192)(189,191)(197,218)(198,224)
(199,223)(200,222)(201,221)(202,220)(203,219)(204,211)(205,217)(206,216)
(207,215)(208,214)(209,213)(210,212)(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)(239,295)(240,301)(241,300)(242,299)(243,298)(244,297)
(245,296)(246,302)(247,308)(248,307)(249,306)(250,305)(251,304)(252,303)
(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)(337,407)(338,413)(339,412)(340,411)
(341,410)(342,409)(343,408)(344,414)(345,420)(346,419)(347,418)(348,417)
(349,416)(350,415)(351,393)(352,399)(353,398)(354,397)(355,396)(356,395)
(357,394)(358,400)(359,406)(360,405)(361,404)(362,403)(363,402)(364,401)
(365,421)(366,427)(367,426)(368,425)(369,424)(370,423)(371,422)(372,428)
(373,434)(374,433)(375,432)(376,431)(377,430)(378,429)(379,435)(380,441)
(381,440)(382,439)(383,438)(384,437)(385,436)(386,442)(387,448)(388,447)
(389,446)(390,445)(391,444)(392,443)(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)(463,575)(464,581)(465,580)(466,579)(467,578)(468,577)
(469,576)(470,582)(471,588)(472,587)(473,586)(474,585)(475,584)(476,583)
(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)(519,631)(520,637)(521,636)(522,635)(523,634)(524,633)
(525,632)(526,638)(527,644)(528,643)(529,642)(530,641)(531,640)(532,639)
(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)(673,876)(674,882)(675,881)(676,880)
(677,879)(678,878)(679,877)(680,869)(681,875)(682,874)(683,873)(684,872)
(685,871)(686,870)(687,890)(688,896)(689,895)(690,894)(691,893)(692,892)
(693,891)(694,883)(695,889)(696,888)(697,887)(698,886)(699,885)(700,884)
(701,855)(702,861)(703,860)(704,859)(705,858)(706,857)(707,856)(708,862)
(709,868)(710,867)(711,866)(712,865)(713,864)(714,863)(715,841)(716,847)
(717,846)(718,845)(719,844)(720,843)(721,842)(722,848)(723,854)(724,853)
(725,852)(726,851)(727,850)(728,849)(729,813)(730,819)(731,818)(732,817)
(733,816)(734,815)(735,814)(736,820)(737,826)(738,825)(739,824)(740,823)
(741,822)(742,821)(743,827)(744,833)(745,832)(746,831)(747,830)(748,829)
(749,828)(750,834)(751,840)(752,839)(753,838)(754,837)(755,836)(756,835)
(757,806)(758,812)(759,811)(760,810)(761,809)(762,808)(763,807)(764,799)
(765,805)(766,804)(767,803)(768,802)(769,801)(770,800)(771,792)(772,798)
(773,797)(774,796)(775,795)(776,794)(777,793)(778,785)(779,791)(780,790)
(781,789)(782,788)(783,787)(784,786);;
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)( 29,478)( 30,477)( 31,483)( 32,482)
( 33,481)( 34,480)( 35,479)( 36,485)( 37,484)( 38,490)( 39,489)( 40,488)
( 41,487)( 42,486)( 43,499)( 44,498)( 45,504)( 46,503)( 47,502)( 48,501)
( 49,500)( 50,492)( 51,491)( 52,497)( 53,496)( 54,495)( 55,494)( 56,493)
( 57,555)( 58,554)( 59,560)( 60,559)( 61,558)( 62,557)( 63,556)( 64,548)
( 65,547)( 66,553)( 67,552)( 68,551)( 69,550)( 70,549)( 71,534)( 72,533)
( 73,539)( 74,538)( 75,537)( 76,536)( 77,535)( 78,541)( 79,540)( 80,546)
( 81,545)( 82,544)( 83,543)( 84,542)( 85,520)( 86,519)( 87,525)( 88,524)
( 89,523)( 90,522)( 91,521)( 92,527)( 93,526)( 94,532)( 95,531)( 96,530)
( 97,529)( 98,528)( 99,513)(100,512)(101,518)(102,517)(103,516)(104,515)
(105,514)(106,506)(107,505)(108,511)(109,510)(110,509)(111,508)(112,507)
(113,569)(114,568)(115,574)(116,573)(117,572)(118,571)(119,570)(120,562)
(121,561)(122,567)(123,566)(124,565)(125,564)(126,563)(127,576)(128,575)
(129,581)(130,580)(131,579)(132,578)(133,577)(134,583)(135,582)(136,588)
(137,587)(138,586)(139,585)(140,584)(141,597)(142,596)(143,602)(144,601)
(145,600)(146,599)(147,598)(148,590)(149,589)(150,595)(151,594)(152,593)
(153,592)(154,591)(155,604)(156,603)(157,609)(158,608)(159,607)(160,606)
(161,605)(162,611)(163,610)(164,616)(165,615)(166,614)(167,613)(168,612)
(169,660)(170,659)(171,665)(172,664)(173,663)(174,662)(175,661)(176,667)
(177,666)(178,672)(179,671)(180,670)(181,669)(182,668)(183,653)(184,652)
(185,658)(186,657)(187,656)(188,655)(189,654)(190,646)(191,645)(192,651)
(193,650)(194,649)(195,648)(196,647)(197,639)(198,638)(199,644)(200,643)
(201,642)(202,641)(203,640)(204,632)(205,631)(206,637)(207,636)(208,635)
(209,634)(210,633)(211,618)(212,617)(213,623)(214,622)(215,621)(216,620)
(217,619)(218,625)(219,624)(220,630)(221,629)(222,628)(223,627)(224,626)
(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)(253,702)(254,701)(255,707)(256,706)
(257,705)(258,704)(259,703)(260,709)(261,708)(262,714)(263,713)(264,712)
(265,711)(266,710)(267,723)(268,722)(269,728)(270,727)(271,726)(272,725)
(273,724)(274,716)(275,715)(276,721)(277,720)(278,719)(279,718)(280,717)
(281,779)(282,778)(283,784)(284,783)(285,782)(286,781)(287,780)(288,772)
(289,771)(290,777)(291,776)(292,775)(293,774)(294,773)(295,758)(296,757)
(297,763)(298,762)(299,761)(300,760)(301,759)(302,765)(303,764)(304,770)
(305,769)(306,768)(307,767)(308,766)(309,744)(310,743)(311,749)(312,748)
(313,747)(314,746)(315,745)(316,751)(317,750)(318,756)(319,755)(320,754)
(321,753)(322,752)(323,737)(324,736)(325,742)(326,741)(327,740)(328,739)
(329,738)(330,730)(331,729)(332,735)(333,734)(334,733)(335,732)(336,731)
(337,793)(338,792)(339,798)(340,797)(341,796)(342,795)(343,794)(344,786)
(345,785)(346,791)(347,790)(348,789)(349,788)(350,787)(351,800)(352,799)
(353,805)(354,804)(355,803)(356,802)(357,801)(358,807)(359,806)(360,812)
(361,811)(362,810)(363,809)(364,808)(365,821)(366,820)(367,826)(368,825)
(369,824)(370,823)(371,822)(372,814)(373,813)(374,819)(375,818)(376,817)
(377,816)(378,815)(379,828)(380,827)(381,833)(382,832)(383,831)(384,830)
(385,829)(386,835)(387,834)(388,840)(389,839)(390,838)(391,837)(392,836)
(393,884)(394,883)(395,889)(396,888)(397,887)(398,886)(399,885)(400,891)
(401,890)(402,896)(403,895)(404,894)(405,893)(406,892)(407,877)(408,876)
(409,882)(410,881)(411,880)(412,879)(413,878)(414,870)(415,869)(416,875)
(417,874)(418,873)(419,872)(420,871)(421,863)(422,862)(423,868)(424,867)
(425,866)(426,865)(427,864)(428,856)(429,855)(430,861)(431,860)(432,859)
(433,858)(434,857)(435,842)(436,841)(437,847)(438,846)(439,845)(440,844)
(441,843)(442,849)(443,848)(444,854)(445,853)(446,852)(447,851)(448,850);;
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*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s2*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(896)!(  1,673)(  2,674)(  3,675)(  4,676)(  5,677)(  6,678)(  7,679)
(  8,680)(  9,681)( 10,682)( 11,683)( 12,684)( 13,685)( 14,686)( 15,687)
( 16,688)( 17,689)( 18,690)( 19,691)( 20,692)( 21,693)( 22,694)( 23,695)
( 24,696)( 25,697)( 26,698)( 27,699)( 28,700)( 29,708)( 30,709)( 31,710)
( 32,711)( 33,712)( 34,713)( 35,714)( 36,701)( 37,702)( 38,703)( 39,704)
( 40,705)( 41,706)( 42,707)( 43,722)( 44,723)( 45,724)( 46,725)( 47,726)
( 48,727)( 49,728)( 50,715)( 51,716)( 52,717)( 53,718)( 54,719)( 55,720)
( 56,721)( 57,778)( 58,779)( 59,780)( 60,781)( 61,782)( 62,783)( 63,784)
( 64,771)( 65,772)( 66,773)( 67,774)( 68,775)( 69,776)( 70,777)( 71,764)
( 72,765)( 73,766)( 74,767)( 75,768)( 76,769)( 77,770)( 78,757)( 79,758)
( 80,759)( 81,760)( 82,761)( 83,762)( 84,763)( 85,750)( 86,751)( 87,752)
( 88,753)( 89,754)( 90,755)( 91,756)( 92,743)( 93,744)( 94,745)( 95,746)
( 96,747)( 97,748)( 98,749)( 99,736)(100,737)(101,738)(102,739)(103,740)
(104,741)(105,742)(106,729)(107,730)(108,731)(109,732)(110,733)(111,734)
(112,735)(113,820)(114,821)(115,822)(116,823)(117,824)(118,825)(119,826)
(120,813)(121,814)(122,815)(123,816)(124,817)(125,818)(126,819)(127,834)
(128,835)(129,836)(130,837)(131,838)(132,839)(133,840)(134,827)(135,828)
(136,829)(137,830)(138,831)(139,832)(140,833)(141,792)(142,793)(143,794)
(144,795)(145,796)(146,797)(147,798)(148,785)(149,786)(150,787)(151,788)
(152,789)(153,790)(154,791)(155,806)(156,807)(157,808)(158,809)(159,810)
(160,811)(161,812)(162,799)(163,800)(164,801)(165,802)(166,803)(167,804)
(168,805)(169,855)(170,856)(171,857)(172,858)(173,859)(174,860)(175,861)
(176,862)(177,863)(178,864)(179,865)(180,866)(181,867)(182,868)(183,841)
(184,842)(185,843)(186,844)(187,845)(188,846)(189,847)(190,848)(191,849)
(192,850)(193,851)(194,852)(195,853)(196,854)(197,890)(198,891)(199,892)
(200,893)(201,894)(202,895)(203,896)(204,883)(205,884)(206,885)(207,886)
(208,887)(209,888)(210,889)(211,876)(212,877)(213,878)(214,879)(215,880)
(216,881)(217,882)(218,869)(219,870)(220,871)(221,872)(222,873)(223,874)
(224,875)(225,449)(226,450)(227,451)(228,452)(229,453)(230,454)(231,455)
(232,456)(233,457)(234,458)(235,459)(236,460)(237,461)(238,462)(239,463)
(240,464)(241,465)(242,466)(243,467)(244,468)(245,469)(246,470)(247,471)
(248,472)(249,473)(250,474)(251,475)(252,476)(253,484)(254,485)(255,486)
(256,487)(257,488)(258,489)(259,490)(260,477)(261,478)(262,479)(263,480)
(264,481)(265,482)(266,483)(267,498)(268,499)(269,500)(270,501)(271,502)
(272,503)(273,504)(274,491)(275,492)(276,493)(277,494)(278,495)(279,496)
(280,497)(281,554)(282,555)(283,556)(284,557)(285,558)(286,559)(287,560)
(288,547)(289,548)(290,549)(291,550)(292,551)(293,552)(294,553)(295,540)
(296,541)(297,542)(298,543)(299,544)(300,545)(301,546)(302,533)(303,534)
(304,535)(305,536)(306,537)(307,538)(308,539)(309,526)(310,527)(311,528)
(312,529)(313,530)(314,531)(315,532)(316,519)(317,520)(318,521)(319,522)
(320,523)(321,524)(322,525)(323,512)(324,513)(325,514)(326,515)(327,516)
(328,517)(329,518)(330,505)(331,506)(332,507)(333,508)(334,509)(335,510)
(336,511)(337,596)(338,597)(339,598)(340,599)(341,600)(342,601)(343,602)
(344,589)(345,590)(346,591)(347,592)(348,593)(349,594)(350,595)(351,610)
(352,611)(353,612)(354,613)(355,614)(356,615)(357,616)(358,603)(359,604)
(360,605)(361,606)(362,607)(363,608)(364,609)(365,568)(366,569)(367,570)
(368,571)(369,572)(370,573)(371,574)(372,561)(373,562)(374,563)(375,564)
(376,565)(377,566)(378,567)(379,582)(380,583)(381,584)(382,585)(383,586)
(384,587)(385,588)(386,575)(387,576)(388,577)(389,578)(390,579)(391,580)
(392,581)(393,631)(394,632)(395,633)(396,634)(397,635)(398,636)(399,637)
(400,638)(401,639)(402,640)(403,641)(404,642)(405,643)(406,644)(407,617)
(408,618)(409,619)(410,620)(411,621)(412,622)(413,623)(414,624)(415,625)
(416,626)(417,627)(418,628)(419,629)(420,630)(421,666)(422,667)(423,668)
(424,669)(425,670)(426,671)(427,672)(428,659)(429,660)(430,661)(431,662)
(432,663)(433,664)(434,665)(435,652)(436,653)(437,654)(438,655)(439,656)
(440,657)(441,658)(442,645)(443,646)(444,647)(445,648)(446,649)(447,650)
(448,651);
s1 := Sym(896)!(  2,  7)(  3,  6)(  4,  5)(  9, 14)( 10, 13)( 11, 12)( 16, 21)
( 17, 20)( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 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)( 72, 77)( 73, 76)( 74, 75)( 79, 84)( 80, 83)( 81, 82)( 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)(113,120)(114,126)(115,125)
(116,124)(117,123)(118,122)(119,121)(127,134)(128,140)(129,139)(130,138)
(131,137)(132,136)(133,135)(141,162)(142,168)(143,167)(144,166)(145,165)
(146,164)(147,163)(148,155)(149,161)(150,160)(151,159)(152,158)(153,157)
(154,156)(169,176)(170,182)(171,181)(172,180)(173,179)(174,178)(175,177)
(183,190)(184,196)(185,195)(186,194)(187,193)(188,192)(189,191)(197,218)
(198,224)(199,223)(200,222)(201,221)(202,220)(203,219)(204,211)(205,217)
(206,216)(207,215)(208,214)(209,213)(210,212)(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)(239,295)(240,301)(241,300)(242,299)(243,298)
(244,297)(245,296)(246,302)(247,308)(248,307)(249,306)(250,305)(251,304)
(252,303)(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)(337,407)(338,413)(339,412)
(340,411)(341,410)(342,409)(343,408)(344,414)(345,420)(346,419)(347,418)
(348,417)(349,416)(350,415)(351,393)(352,399)(353,398)(354,397)(355,396)
(356,395)(357,394)(358,400)(359,406)(360,405)(361,404)(362,403)(363,402)
(364,401)(365,421)(366,427)(367,426)(368,425)(369,424)(370,423)(371,422)
(372,428)(373,434)(374,433)(375,432)(376,431)(377,430)(378,429)(379,435)
(380,441)(381,440)(382,439)(383,438)(384,437)(385,436)(386,442)(387,448)
(388,447)(389,446)(390,445)(391,444)(392,443)(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)(463,575)(464,581)(465,580)(466,579)(467,578)
(468,577)(469,576)(470,582)(471,588)(472,587)(473,586)(474,585)(475,584)
(476,583)(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)(519,631)(520,637)(521,636)(522,635)(523,634)
(524,633)(525,632)(526,638)(527,644)(528,643)(529,642)(530,641)(531,640)
(532,639)(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)(673,876)(674,882)(675,881)
(676,880)(677,879)(678,878)(679,877)(680,869)(681,875)(682,874)(683,873)
(684,872)(685,871)(686,870)(687,890)(688,896)(689,895)(690,894)(691,893)
(692,892)(693,891)(694,883)(695,889)(696,888)(697,887)(698,886)(699,885)
(700,884)(701,855)(702,861)(703,860)(704,859)(705,858)(706,857)(707,856)
(708,862)(709,868)(710,867)(711,866)(712,865)(713,864)(714,863)(715,841)
(716,847)(717,846)(718,845)(719,844)(720,843)(721,842)(722,848)(723,854)
(724,853)(725,852)(726,851)(727,850)(728,849)(729,813)(730,819)(731,818)
(732,817)(733,816)(734,815)(735,814)(736,820)(737,826)(738,825)(739,824)
(740,823)(741,822)(742,821)(743,827)(744,833)(745,832)(746,831)(747,830)
(748,829)(749,828)(750,834)(751,840)(752,839)(753,838)(754,837)(755,836)
(756,835)(757,806)(758,812)(759,811)(760,810)(761,809)(762,808)(763,807)
(764,799)(765,805)(766,804)(767,803)(768,802)(769,801)(770,800)(771,792)
(772,798)(773,797)(774,796)(775,795)(776,794)(777,793)(778,785)(779,791)
(780,790)(781,789)(782,788)(783,787)(784,786);
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)( 29,478)( 30,477)( 31,483)
( 32,482)( 33,481)( 34,480)( 35,479)( 36,485)( 37,484)( 38,490)( 39,489)
( 40,488)( 41,487)( 42,486)( 43,499)( 44,498)( 45,504)( 46,503)( 47,502)
( 48,501)( 49,500)( 50,492)( 51,491)( 52,497)( 53,496)( 54,495)( 55,494)
( 56,493)( 57,555)( 58,554)( 59,560)( 60,559)( 61,558)( 62,557)( 63,556)
( 64,548)( 65,547)( 66,553)( 67,552)( 68,551)( 69,550)( 70,549)( 71,534)
( 72,533)( 73,539)( 74,538)( 75,537)( 76,536)( 77,535)( 78,541)( 79,540)
( 80,546)( 81,545)( 82,544)( 83,543)( 84,542)( 85,520)( 86,519)( 87,525)
( 88,524)( 89,523)( 90,522)( 91,521)( 92,527)( 93,526)( 94,532)( 95,531)
( 96,530)( 97,529)( 98,528)( 99,513)(100,512)(101,518)(102,517)(103,516)
(104,515)(105,514)(106,506)(107,505)(108,511)(109,510)(110,509)(111,508)
(112,507)(113,569)(114,568)(115,574)(116,573)(117,572)(118,571)(119,570)
(120,562)(121,561)(122,567)(123,566)(124,565)(125,564)(126,563)(127,576)
(128,575)(129,581)(130,580)(131,579)(132,578)(133,577)(134,583)(135,582)
(136,588)(137,587)(138,586)(139,585)(140,584)(141,597)(142,596)(143,602)
(144,601)(145,600)(146,599)(147,598)(148,590)(149,589)(150,595)(151,594)
(152,593)(153,592)(154,591)(155,604)(156,603)(157,609)(158,608)(159,607)
(160,606)(161,605)(162,611)(163,610)(164,616)(165,615)(166,614)(167,613)
(168,612)(169,660)(170,659)(171,665)(172,664)(173,663)(174,662)(175,661)
(176,667)(177,666)(178,672)(179,671)(180,670)(181,669)(182,668)(183,653)
(184,652)(185,658)(186,657)(187,656)(188,655)(189,654)(190,646)(191,645)
(192,651)(193,650)(194,649)(195,648)(196,647)(197,639)(198,638)(199,644)
(200,643)(201,642)(202,641)(203,640)(204,632)(205,631)(206,637)(207,636)
(208,635)(209,634)(210,633)(211,618)(212,617)(213,623)(214,622)(215,621)
(216,620)(217,619)(218,625)(219,624)(220,630)(221,629)(222,628)(223,627)
(224,626)(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)(253,702)(254,701)(255,707)
(256,706)(257,705)(258,704)(259,703)(260,709)(261,708)(262,714)(263,713)
(264,712)(265,711)(266,710)(267,723)(268,722)(269,728)(270,727)(271,726)
(272,725)(273,724)(274,716)(275,715)(276,721)(277,720)(278,719)(279,718)
(280,717)(281,779)(282,778)(283,784)(284,783)(285,782)(286,781)(287,780)
(288,772)(289,771)(290,777)(291,776)(292,775)(293,774)(294,773)(295,758)
(296,757)(297,763)(298,762)(299,761)(300,760)(301,759)(302,765)(303,764)
(304,770)(305,769)(306,768)(307,767)(308,766)(309,744)(310,743)(311,749)
(312,748)(313,747)(314,746)(315,745)(316,751)(317,750)(318,756)(319,755)
(320,754)(321,753)(322,752)(323,737)(324,736)(325,742)(326,741)(327,740)
(328,739)(329,738)(330,730)(331,729)(332,735)(333,734)(334,733)(335,732)
(336,731)(337,793)(338,792)(339,798)(340,797)(341,796)(342,795)(343,794)
(344,786)(345,785)(346,791)(347,790)(348,789)(349,788)(350,787)(351,800)
(352,799)(353,805)(354,804)(355,803)(356,802)(357,801)(358,807)(359,806)
(360,812)(361,811)(362,810)(363,809)(364,808)(365,821)(366,820)(367,826)
(368,825)(369,824)(370,823)(371,822)(372,814)(373,813)(374,819)(375,818)
(376,817)(377,816)(378,815)(379,828)(380,827)(381,833)(382,832)(383,831)
(384,830)(385,829)(386,835)(387,834)(388,840)(389,839)(390,838)(391,837)
(392,836)(393,884)(394,883)(395,889)(396,888)(397,887)(398,886)(399,885)
(400,891)(401,890)(402,896)(403,895)(404,894)(405,893)(406,892)(407,877)
(408,876)(409,882)(410,881)(411,880)(412,879)(413,878)(414,870)(415,869)
(416,875)(417,874)(418,873)(419,872)(420,871)(421,863)(422,862)(423,868)
(424,867)(425,866)(426,865)(427,864)(428,856)(429,855)(430,861)(431,860)
(432,859)(433,858)(434,857)(435,842)(436,841)(437,847)(438,846)(439,845)
(440,844)(441,843)(442,849)(443,848)(444,854)(445,853)(446,852)(447,851)
(448,850);
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*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s2*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >; 
 
References : None.
to this polytope