Polytope of Type {8,56}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,56}*1792e
if this polytope has a name.
Group : SmallGroup(1792,90301)
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 : {4,56}*896b
   4-fold quotients : {4,28}*448
   7-fold quotients : {8,8}*256e
   8-fold quotients : {4,28}*224
   14-fold quotients : {4,8}*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 := (  1,449)(  2,450)(  3,451)(  4,452)(  5,453)(  6,454)(  7,455)(  8,456)
(  9,457)( 10,458)( 11,459)( 12,460)( 13,461)( 14,462)( 15,470)( 16,471)
( 17,472)( 18,473)( 19,474)( 20,475)( 21,476)( 22,463)( 23,464)( 24,465)
( 25,466)( 26,467)( 27,468)( 28,469)( 29,477)( 30,478)( 31,479)( 32,480)
( 33,481)( 34,482)( 35,483)( 36,484)( 37,485)( 38,486)( 39,487)( 40,488)
( 41,489)( 42,490)( 43,498)( 44,499)( 45,500)( 46,501)( 47,502)( 48,503)
( 49,504)( 50,491)( 51,492)( 52,493)( 53,494)( 54,495)( 55,496)( 56,497)
( 57,554)( 58,555)( 59,556)( 60,557)( 61,558)( 62,559)( 63,560)( 64,547)
( 65,548)( 66,549)( 67,550)( 68,551)( 69,552)( 70,553)( 71,533)( 72,534)
( 73,535)( 74,536)( 75,537)( 76,538)( 77,539)( 78,540)( 79,541)( 80,542)
( 81,543)( 82,544)( 83,545)( 84,546)( 85,519)( 86,520)( 87,521)( 88,522)
( 89,523)( 90,524)( 91,525)( 92,526)( 93,527)( 94,528)( 95,529)( 96,530)
( 97,531)( 98,532)( 99,512)(100,513)(101,514)(102,515)(103,516)(104,517)
(105,518)(106,505)(107,506)(108,507)(109,508)(110,509)(111,510)(112,511)
(113,568)(114,569)(115,570)(116,571)(117,572)(118,573)(119,574)(120,561)
(121,562)(122,563)(123,564)(124,565)(125,566)(126,567)(127,575)(128,576)
(129,577)(130,578)(131,579)(132,580)(133,581)(134,582)(135,583)(136,584)
(137,585)(138,586)(139,587)(140,588)(141,596)(142,597)(143,598)(144,599)
(145,600)(146,601)(147,602)(148,589)(149,590)(150,591)(151,592)(152,593)
(153,594)(154,595)(155,603)(156,604)(157,605)(158,606)(159,607)(160,608)
(161,609)(162,610)(163,611)(164,612)(165,613)(166,614)(167,615)(168,616)
(169,659)(170,660)(171,661)(172,662)(173,663)(174,664)(175,665)(176,666)
(177,667)(178,668)(179,669)(180,670)(181,671)(182,672)(183,652)(184,653)
(185,654)(186,655)(187,656)(188,657)(189,658)(190,645)(191,646)(192,647)
(193,648)(194,649)(195,650)(196,651)(197,638)(198,639)(199,640)(200,641)
(201,642)(202,643)(203,644)(204,631)(205,632)(206,633)(207,634)(208,635)
(209,636)(210,637)(211,617)(212,618)(213,619)(214,620)(215,621)(216,622)
(217,623)(218,624)(219,625)(220,626)(221,627)(222,628)(223,629)(224,630)
(225,673)(226,674)(227,675)(228,676)(229,677)(230,678)(231,679)(232,680)
(233,681)(234,682)(235,683)(236,684)(237,685)(238,686)(239,694)(240,695)
(241,696)(242,697)(243,698)(244,699)(245,700)(246,687)(247,688)(248,689)
(249,690)(250,691)(251,692)(252,693)(253,701)(254,702)(255,703)(256,704)
(257,705)(258,706)(259,707)(260,708)(261,709)(262,710)(263,711)(264,712)
(265,713)(266,714)(267,722)(268,723)(269,724)(270,725)(271,726)(272,727)
(273,728)(274,715)(275,716)(276,717)(277,718)(278,719)(279,720)(280,721)
(281,778)(282,779)(283,780)(284,781)(285,782)(286,783)(287,784)(288,771)
(289,772)(290,773)(291,774)(292,775)(293,776)(294,777)(295,757)(296,758)
(297,759)(298,760)(299,761)(300,762)(301,763)(302,764)(303,765)(304,766)
(305,767)(306,768)(307,769)(308,770)(309,743)(310,744)(311,745)(312,746)
(313,747)(314,748)(315,749)(316,750)(317,751)(318,752)(319,753)(320,754)
(321,755)(322,756)(323,736)(324,737)(325,738)(326,739)(327,740)(328,741)
(329,742)(330,729)(331,730)(332,731)(333,732)(334,733)(335,734)(336,735)
(337,792)(338,793)(339,794)(340,795)(341,796)(342,797)(343,798)(344,785)
(345,786)(346,787)(347,788)(348,789)(349,790)(350,791)(351,799)(352,800)
(353,801)(354,802)(355,803)(356,804)(357,805)(358,806)(359,807)(360,808)
(361,809)(362,810)(363,811)(364,812)(365,820)(366,821)(367,822)(368,823)
(369,824)(370,825)(371,826)(372,813)(373,814)(374,815)(375,816)(376,817)
(377,818)(378,819)(379,827)(380,828)(381,829)(382,830)(383,831)(384,832)
(385,833)(386,834)(387,835)(388,836)(389,837)(390,838)(391,839)(392,840)
(393,883)(394,884)(395,885)(396,886)(397,887)(398,888)(399,889)(400,890)
(401,891)(402,892)(403,893)(404,894)(405,895)(406,896)(407,876)(408,877)
(409,878)(410,879)(411,880)(412,881)(413,882)(414,869)(415,870)(416,871)
(417,872)(418,873)(419,874)(420,875)(421,862)(422,863)(423,864)(424,865)
(425,866)(426,867)(427,868)(428,855)(429,856)(430,857)(431,858)(432,859)
(433,860)(434,861)(435,841)(436,842)(437,843)(438,844)(439,845)(440,846)
(441,847)(442,848)(443,849)(444,850)(445,851)(446,852)(447,853)(448,854);;
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 := (  1,674)(  2,673)(  3,679)(  4,678)(  5,677)(  6,676)(  7,675)(  8,681)
(  9,680)( 10,686)( 11,685)( 12,684)( 13,683)( 14,682)( 15,688)( 16,687)
( 17,693)( 18,692)( 19,691)( 20,690)( 21,689)( 22,695)( 23,694)( 24,700)
( 25,699)( 26,698)( 27,697)( 28,696)( 29,709)( 30,708)( 31,714)( 32,713)
( 33,712)( 34,711)( 35,710)( 36,702)( 37,701)( 38,707)( 39,706)( 40,705)
( 41,704)( 42,703)( 43,723)( 44,722)( 45,728)( 46,727)( 47,726)( 48,725)
( 49,724)( 50,716)( 51,715)( 52,721)( 53,720)( 54,719)( 55,718)( 56,717)
( 57,779)( 58,778)( 59,784)( 60,783)( 61,782)( 62,781)( 63,780)( 64,772)
( 65,771)( 66,777)( 67,776)( 68,775)( 69,774)( 70,773)( 71,765)( 72,764)
( 73,770)( 74,769)( 75,768)( 76,767)( 77,766)( 78,758)( 79,757)( 80,763)
( 81,762)( 82,761)( 83,760)( 84,759)( 85,751)( 86,750)( 87,756)( 88,755)
( 89,754)( 90,753)( 91,752)( 92,744)( 93,743)( 94,749)( 95,748)( 96,747)
( 97,746)( 98,745)( 99,737)(100,736)(101,742)(102,741)(103,740)(104,739)
(105,738)(106,730)(107,729)(108,735)(109,734)(110,733)(111,732)(112,731)
(113,821)(114,820)(115,826)(116,825)(117,824)(118,823)(119,822)(120,814)
(121,813)(122,819)(123,818)(124,817)(125,816)(126,815)(127,835)(128,834)
(129,840)(130,839)(131,838)(132,837)(133,836)(134,828)(135,827)(136,833)
(137,832)(138,831)(139,830)(140,829)(141,793)(142,792)(143,798)(144,797)
(145,796)(146,795)(147,794)(148,786)(149,785)(150,791)(151,790)(152,789)
(153,788)(154,787)(155,807)(156,806)(157,812)(158,811)(159,810)(160,809)
(161,808)(162,800)(163,799)(164,805)(165,804)(166,803)(167,802)(168,801)
(169,856)(170,855)(171,861)(172,860)(173,859)(174,858)(175,857)(176,863)
(177,862)(178,868)(179,867)(180,866)(181,865)(182,864)(183,842)(184,841)
(185,847)(186,846)(187,845)(188,844)(189,843)(190,849)(191,848)(192,854)
(193,853)(194,852)(195,851)(196,850)(197,891)(198,890)(199,896)(200,895)
(201,894)(202,893)(203,892)(204,884)(205,883)(206,889)(207,888)(208,887)
(209,886)(210,885)(211,877)(212,876)(213,882)(214,881)(215,880)(216,879)
(217,878)(218,870)(219,869)(220,875)(221,874)(222,873)(223,872)(224,871)
(225,450)(226,449)(227,455)(228,454)(229,453)(230,452)(231,451)(232,457)
(233,456)(234,462)(235,461)(236,460)(237,459)(238,458)(239,464)(240,463)
(241,469)(242,468)(243,467)(244,466)(245,465)(246,471)(247,470)(248,476)
(249,475)(250,474)(251,473)(252,472)(253,485)(254,484)(255,490)(256,489)
(257,488)(258,487)(259,486)(260,478)(261,477)(262,483)(263,482)(264,481)
(265,480)(266,479)(267,499)(268,498)(269,504)(270,503)(271,502)(272,501)
(273,500)(274,492)(275,491)(276,497)(277,496)(278,495)(279,494)(280,493)
(281,555)(282,554)(283,560)(284,559)(285,558)(286,557)(287,556)(288,548)
(289,547)(290,553)(291,552)(292,551)(293,550)(294,549)(295,541)(296,540)
(297,546)(298,545)(299,544)(300,543)(301,542)(302,534)(303,533)(304,539)
(305,538)(306,537)(307,536)(308,535)(309,527)(310,526)(311,532)(312,531)
(313,530)(314,529)(315,528)(316,520)(317,519)(318,525)(319,524)(320,523)
(321,522)(322,521)(323,513)(324,512)(325,518)(326,517)(327,516)(328,515)
(329,514)(330,506)(331,505)(332,511)(333,510)(334,509)(335,508)(336,507)
(337,597)(338,596)(339,602)(340,601)(341,600)(342,599)(343,598)(344,590)
(345,589)(346,595)(347,594)(348,593)(349,592)(350,591)(351,611)(352,610)
(353,616)(354,615)(355,614)(356,613)(357,612)(358,604)(359,603)(360,609)
(361,608)(362,607)(363,606)(364,605)(365,569)(366,568)(367,574)(368,573)
(369,572)(370,571)(371,570)(372,562)(373,561)(374,567)(375,566)(376,565)
(377,564)(378,563)(379,583)(380,582)(381,588)(382,587)(383,586)(384,585)
(385,584)(386,576)(387,575)(388,581)(389,580)(390,579)(391,578)(392,577)
(393,632)(394,631)(395,637)(396,636)(397,635)(398,634)(399,633)(400,639)
(401,638)(402,644)(403,643)(404,642)(405,641)(406,640)(407,618)(408,617)
(409,623)(410,622)(411,621)(412,620)(413,619)(414,625)(415,624)(416,630)
(417,629)(418,628)(419,627)(420,626)(421,667)(422,666)(423,672)(424,671)
(425,670)(426,669)(427,668)(428,660)(429,659)(430,665)(431,664)(432,663)
(433,662)(434,661)(435,653)(436,652)(437,658)(438,657)(439,656)(440,655)
(441,654)(442,646)(443,645)(444,651)(445,650)(446,649)(447,648)(448,647);;
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*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0, 
s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s0*s2*s1*s2*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*s2*s1*s2*s0*s1*s2*s1*s2*s1*s0*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(896)!(  1,449)(  2,450)(  3,451)(  4,452)(  5,453)(  6,454)(  7,455)
(  8,456)(  9,457)( 10,458)( 11,459)( 12,460)( 13,461)( 14,462)( 15,470)
( 16,471)( 17,472)( 18,473)( 19,474)( 20,475)( 21,476)( 22,463)( 23,464)
( 24,465)( 25,466)( 26,467)( 27,468)( 28,469)( 29,477)( 30,478)( 31,479)
( 32,480)( 33,481)( 34,482)( 35,483)( 36,484)( 37,485)( 38,486)( 39,487)
( 40,488)( 41,489)( 42,490)( 43,498)( 44,499)( 45,500)( 46,501)( 47,502)
( 48,503)( 49,504)( 50,491)( 51,492)( 52,493)( 53,494)( 54,495)( 55,496)
( 56,497)( 57,554)( 58,555)( 59,556)( 60,557)( 61,558)( 62,559)( 63,560)
( 64,547)( 65,548)( 66,549)( 67,550)( 68,551)( 69,552)( 70,553)( 71,533)
( 72,534)( 73,535)( 74,536)( 75,537)( 76,538)( 77,539)( 78,540)( 79,541)
( 80,542)( 81,543)( 82,544)( 83,545)( 84,546)( 85,519)( 86,520)( 87,521)
( 88,522)( 89,523)( 90,524)( 91,525)( 92,526)( 93,527)( 94,528)( 95,529)
( 96,530)( 97,531)( 98,532)( 99,512)(100,513)(101,514)(102,515)(103,516)
(104,517)(105,518)(106,505)(107,506)(108,507)(109,508)(110,509)(111,510)
(112,511)(113,568)(114,569)(115,570)(116,571)(117,572)(118,573)(119,574)
(120,561)(121,562)(122,563)(123,564)(124,565)(125,566)(126,567)(127,575)
(128,576)(129,577)(130,578)(131,579)(132,580)(133,581)(134,582)(135,583)
(136,584)(137,585)(138,586)(139,587)(140,588)(141,596)(142,597)(143,598)
(144,599)(145,600)(146,601)(147,602)(148,589)(149,590)(150,591)(151,592)
(152,593)(153,594)(154,595)(155,603)(156,604)(157,605)(158,606)(159,607)
(160,608)(161,609)(162,610)(163,611)(164,612)(165,613)(166,614)(167,615)
(168,616)(169,659)(170,660)(171,661)(172,662)(173,663)(174,664)(175,665)
(176,666)(177,667)(178,668)(179,669)(180,670)(181,671)(182,672)(183,652)
(184,653)(185,654)(186,655)(187,656)(188,657)(189,658)(190,645)(191,646)
(192,647)(193,648)(194,649)(195,650)(196,651)(197,638)(198,639)(199,640)
(200,641)(201,642)(202,643)(203,644)(204,631)(205,632)(206,633)(207,634)
(208,635)(209,636)(210,637)(211,617)(212,618)(213,619)(214,620)(215,621)
(216,622)(217,623)(218,624)(219,625)(220,626)(221,627)(222,628)(223,629)
(224,630)(225,673)(226,674)(227,675)(228,676)(229,677)(230,678)(231,679)
(232,680)(233,681)(234,682)(235,683)(236,684)(237,685)(238,686)(239,694)
(240,695)(241,696)(242,697)(243,698)(244,699)(245,700)(246,687)(247,688)
(248,689)(249,690)(250,691)(251,692)(252,693)(253,701)(254,702)(255,703)
(256,704)(257,705)(258,706)(259,707)(260,708)(261,709)(262,710)(263,711)
(264,712)(265,713)(266,714)(267,722)(268,723)(269,724)(270,725)(271,726)
(272,727)(273,728)(274,715)(275,716)(276,717)(277,718)(278,719)(279,720)
(280,721)(281,778)(282,779)(283,780)(284,781)(285,782)(286,783)(287,784)
(288,771)(289,772)(290,773)(291,774)(292,775)(293,776)(294,777)(295,757)
(296,758)(297,759)(298,760)(299,761)(300,762)(301,763)(302,764)(303,765)
(304,766)(305,767)(306,768)(307,769)(308,770)(309,743)(310,744)(311,745)
(312,746)(313,747)(314,748)(315,749)(316,750)(317,751)(318,752)(319,753)
(320,754)(321,755)(322,756)(323,736)(324,737)(325,738)(326,739)(327,740)
(328,741)(329,742)(330,729)(331,730)(332,731)(333,732)(334,733)(335,734)
(336,735)(337,792)(338,793)(339,794)(340,795)(341,796)(342,797)(343,798)
(344,785)(345,786)(346,787)(347,788)(348,789)(349,790)(350,791)(351,799)
(352,800)(353,801)(354,802)(355,803)(356,804)(357,805)(358,806)(359,807)
(360,808)(361,809)(362,810)(363,811)(364,812)(365,820)(366,821)(367,822)
(368,823)(369,824)(370,825)(371,826)(372,813)(373,814)(374,815)(375,816)
(376,817)(377,818)(378,819)(379,827)(380,828)(381,829)(382,830)(383,831)
(384,832)(385,833)(386,834)(387,835)(388,836)(389,837)(390,838)(391,839)
(392,840)(393,883)(394,884)(395,885)(396,886)(397,887)(398,888)(399,889)
(400,890)(401,891)(402,892)(403,893)(404,894)(405,895)(406,896)(407,876)
(408,877)(409,878)(410,879)(411,880)(412,881)(413,882)(414,869)(415,870)
(416,871)(417,872)(418,873)(419,874)(420,875)(421,862)(422,863)(423,864)
(424,865)(425,866)(426,867)(427,868)(428,855)(429,856)(430,857)(431,858)
(432,859)(433,860)(434,861)(435,841)(436,842)(437,843)(438,844)(439,845)
(440,846)(441,847)(442,848)(443,849)(444,850)(445,851)(446,852)(447,853)
(448,854);
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)!(  1,674)(  2,673)(  3,679)(  4,678)(  5,677)(  6,676)(  7,675)
(  8,681)(  9,680)( 10,686)( 11,685)( 12,684)( 13,683)( 14,682)( 15,688)
( 16,687)( 17,693)( 18,692)( 19,691)( 20,690)( 21,689)( 22,695)( 23,694)
( 24,700)( 25,699)( 26,698)( 27,697)( 28,696)( 29,709)( 30,708)( 31,714)
( 32,713)( 33,712)( 34,711)( 35,710)( 36,702)( 37,701)( 38,707)( 39,706)
( 40,705)( 41,704)( 42,703)( 43,723)( 44,722)( 45,728)( 46,727)( 47,726)
( 48,725)( 49,724)( 50,716)( 51,715)( 52,721)( 53,720)( 54,719)( 55,718)
( 56,717)( 57,779)( 58,778)( 59,784)( 60,783)( 61,782)( 62,781)( 63,780)
( 64,772)( 65,771)( 66,777)( 67,776)( 68,775)( 69,774)( 70,773)( 71,765)
( 72,764)( 73,770)( 74,769)( 75,768)( 76,767)( 77,766)( 78,758)( 79,757)
( 80,763)( 81,762)( 82,761)( 83,760)( 84,759)( 85,751)( 86,750)( 87,756)
( 88,755)( 89,754)( 90,753)( 91,752)( 92,744)( 93,743)( 94,749)( 95,748)
( 96,747)( 97,746)( 98,745)( 99,737)(100,736)(101,742)(102,741)(103,740)
(104,739)(105,738)(106,730)(107,729)(108,735)(109,734)(110,733)(111,732)
(112,731)(113,821)(114,820)(115,826)(116,825)(117,824)(118,823)(119,822)
(120,814)(121,813)(122,819)(123,818)(124,817)(125,816)(126,815)(127,835)
(128,834)(129,840)(130,839)(131,838)(132,837)(133,836)(134,828)(135,827)
(136,833)(137,832)(138,831)(139,830)(140,829)(141,793)(142,792)(143,798)
(144,797)(145,796)(146,795)(147,794)(148,786)(149,785)(150,791)(151,790)
(152,789)(153,788)(154,787)(155,807)(156,806)(157,812)(158,811)(159,810)
(160,809)(161,808)(162,800)(163,799)(164,805)(165,804)(166,803)(167,802)
(168,801)(169,856)(170,855)(171,861)(172,860)(173,859)(174,858)(175,857)
(176,863)(177,862)(178,868)(179,867)(180,866)(181,865)(182,864)(183,842)
(184,841)(185,847)(186,846)(187,845)(188,844)(189,843)(190,849)(191,848)
(192,854)(193,853)(194,852)(195,851)(196,850)(197,891)(198,890)(199,896)
(200,895)(201,894)(202,893)(203,892)(204,884)(205,883)(206,889)(207,888)
(208,887)(209,886)(210,885)(211,877)(212,876)(213,882)(214,881)(215,880)
(216,879)(217,878)(218,870)(219,869)(220,875)(221,874)(222,873)(223,872)
(224,871)(225,450)(226,449)(227,455)(228,454)(229,453)(230,452)(231,451)
(232,457)(233,456)(234,462)(235,461)(236,460)(237,459)(238,458)(239,464)
(240,463)(241,469)(242,468)(243,467)(244,466)(245,465)(246,471)(247,470)
(248,476)(249,475)(250,474)(251,473)(252,472)(253,485)(254,484)(255,490)
(256,489)(257,488)(258,487)(259,486)(260,478)(261,477)(262,483)(263,482)
(264,481)(265,480)(266,479)(267,499)(268,498)(269,504)(270,503)(271,502)
(272,501)(273,500)(274,492)(275,491)(276,497)(277,496)(278,495)(279,494)
(280,493)(281,555)(282,554)(283,560)(284,559)(285,558)(286,557)(287,556)
(288,548)(289,547)(290,553)(291,552)(292,551)(293,550)(294,549)(295,541)
(296,540)(297,546)(298,545)(299,544)(300,543)(301,542)(302,534)(303,533)
(304,539)(305,538)(306,537)(307,536)(308,535)(309,527)(310,526)(311,532)
(312,531)(313,530)(314,529)(315,528)(316,520)(317,519)(318,525)(319,524)
(320,523)(321,522)(322,521)(323,513)(324,512)(325,518)(326,517)(327,516)
(328,515)(329,514)(330,506)(331,505)(332,511)(333,510)(334,509)(335,508)
(336,507)(337,597)(338,596)(339,602)(340,601)(341,600)(342,599)(343,598)
(344,590)(345,589)(346,595)(347,594)(348,593)(349,592)(350,591)(351,611)
(352,610)(353,616)(354,615)(355,614)(356,613)(357,612)(358,604)(359,603)
(360,609)(361,608)(362,607)(363,606)(364,605)(365,569)(366,568)(367,574)
(368,573)(369,572)(370,571)(371,570)(372,562)(373,561)(374,567)(375,566)
(376,565)(377,564)(378,563)(379,583)(380,582)(381,588)(382,587)(383,586)
(384,585)(385,584)(386,576)(387,575)(388,581)(389,580)(390,579)(391,578)
(392,577)(393,632)(394,631)(395,637)(396,636)(397,635)(398,634)(399,633)
(400,639)(401,638)(402,644)(403,643)(404,642)(405,641)(406,640)(407,618)
(408,617)(409,623)(410,622)(411,621)(412,620)(413,619)(414,625)(415,624)
(416,630)(417,629)(418,628)(419,627)(420,626)(421,667)(422,666)(423,672)
(424,671)(425,670)(426,669)(427,668)(428,660)(429,659)(430,665)(431,664)
(432,663)(433,662)(434,661)(435,653)(436,652)(437,658)(438,657)(439,656)
(440,655)(441,654)(442,646)(443,645)(444,651)(445,650)(446,649)(447,648)
(448,647);
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*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0, 
s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s0*s2*s1*s2*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*s2*s1*s2*s0*s1*s2*s1*s2*s1*s0*s2 >;

References : None.
to this polytope