Polytope of Type {56,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {56,8}*1792f
if this polytope has a name.
Group : SmallGroup(1792,90303)
Rank : 3
Schlafli Type : {56,8}
Number of vertices, edges, etc : 112, 448, 16
Order of s₀s₁s₂ : 28
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 : {28,8}*896b
   4-fold quotients : {28,4}*448
   7-fold quotients : {8,8}*256e
   8-fold quotients : {28,4}*224
   14-fold quotients : {4,8}*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 := (  1,449)(  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)( 29,477)( 30,483)( 31,482)( 32,481)
( 33,480)( 34,479)( 35,478)( 36,484)( 37,490)( 38,489)( 39,488)( 40,487)
( 41,486)( 42,485)( 43,498)( 44,504)( 45,503)( 46,502)( 47,501)( 48,500)
( 49,499)( 50,491)( 51,497)( 52,496)( 53,495)( 54,494)( 55,493)( 56,492)
( 57,554)( 58,560)( 59,559)( 60,558)( 61,557)( 62,556)( 63,555)( 64,547)
( 65,553)( 66,552)( 67,551)( 68,550)( 69,549)( 70,548)( 71,533)( 72,539)
( 73,538)( 74,537)( 75,536)( 76,535)( 77,534)( 78,540)( 79,546)( 80,545)
( 81,544)( 82,543)( 83,542)( 84,541)( 85,519)( 86,525)( 87,524)( 88,523)
( 89,522)( 90,521)( 91,520)( 92,526)( 93,532)( 94,531)( 95,530)( 96,529)
( 97,528)( 98,527)( 99,512)(100,518)(101,517)(102,516)(103,515)(104,514)
(105,513)(106,505)(107,511)(108,510)(109,509)(110,508)(111,507)(112,506)
(113,568)(114,574)(115,573)(116,572)(117,571)(118,570)(119,569)(120,561)
(121,567)(122,566)(123,565)(124,564)(125,563)(126,562)(127,575)(128,581)
(129,580)(130,579)(131,578)(132,577)(133,576)(134,582)(135,588)(136,587)
(137,586)(138,585)(139,584)(140,583)(141,596)(142,602)(143,601)(144,600)
(145,599)(146,598)(147,597)(148,589)(149,595)(150,594)(151,593)(152,592)
(153,591)(154,590)(155,603)(156,609)(157,608)(158,607)(159,606)(160,605)
(161,604)(162,610)(163,616)(164,615)(165,614)(166,613)(167,612)(168,611)
(169,659)(170,665)(171,664)(172,663)(173,662)(174,661)(175,660)(176,666)
(177,672)(178,671)(179,670)(180,669)(181,668)(182,667)(183,652)(184,658)
(185,657)(186,656)(187,655)(188,654)(189,653)(190,645)(191,651)(192,650)
(193,649)(194,648)(195,647)(196,646)(197,638)(198,644)(199,643)(200,642)
(201,641)(202,640)(203,639)(204,631)(205,637)(206,636)(207,635)(208,634)
(209,633)(210,632)(211,617)(212,623)(213,622)(214,621)(215,620)(216,619)
(217,618)(218,624)(219,630)(220,629)(221,628)(222,627)(223,626)(224,625)
(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)(253,701)(254,707)(255,706)(256,705)
(257,704)(258,703)(259,702)(260,708)(261,714)(262,713)(263,712)(264,711)
(265,710)(266,709)(267,722)(268,728)(269,727)(270,726)(271,725)(272,724)
(273,723)(274,715)(275,721)(276,720)(277,719)(278,718)(279,717)(280,716)
(281,778)(282,784)(283,783)(284,782)(285,781)(286,780)(287,779)(288,771)
(289,777)(290,776)(291,775)(292,774)(293,773)(294,772)(295,757)(296,763)
(297,762)(298,761)(299,760)(300,759)(301,758)(302,764)(303,770)(304,769)
(305,768)(306,767)(307,766)(308,765)(309,743)(310,749)(311,748)(312,747)
(313,746)(314,745)(315,744)(316,750)(317,756)(318,755)(319,754)(320,753)
(321,752)(322,751)(323,736)(324,742)(325,741)(326,740)(327,739)(328,738)
(329,737)(330,729)(331,735)(332,734)(333,733)(334,732)(335,731)(336,730)
(337,792)(338,798)(339,797)(340,796)(341,795)(342,794)(343,793)(344,785)
(345,791)(346,790)(347,789)(348,788)(349,787)(350,786)(351,799)(352,805)
(353,804)(354,803)(355,802)(356,801)(357,800)(358,806)(359,812)(360,811)
(361,810)(362,809)(363,808)(364,807)(365,820)(366,826)(367,825)(368,824)
(369,823)(370,822)(371,821)(372,813)(373,819)(374,818)(375,817)(376,816)
(377,815)(378,814)(379,827)(380,833)(381,832)(382,831)(383,830)(384,829)
(385,828)(386,834)(387,840)(388,839)(389,838)(390,837)(391,836)(392,835)
(393,883)(394,889)(395,888)(396,887)(397,886)(398,885)(399,884)(400,890)
(401,896)(402,895)(403,894)(404,893)(405,892)(406,891)(407,876)(408,882)
(409,881)(410,880)(411,879)(412,878)(413,877)(414,869)(415,875)(416,874)
(417,873)(418,872)(419,871)(420,870)(421,862)(422,868)(423,867)(424,866)
(425,865)(426,864)(427,863)(428,855)(429,861)(430,860)(431,859)(432,858)
(433,857)(434,856)(435,841)(436,847)(437,846)(438,845)(439,844)(440,843)
(441,842)(442,848)(443,854)(444,853)(445,852)(446,851)(447,850)(448,849);;
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 := (  1,673)(  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);;
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*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
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*s0*s1*s0*s1*s2*s1*s0, 
s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0 ];;
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)( 29,477)( 30,483)( 31,482)
( 32,481)( 33,480)( 34,479)( 35,478)( 36,484)( 37,490)( 38,489)( 39,488)
( 40,487)( 41,486)( 42,485)( 43,498)( 44,504)( 45,503)( 46,502)( 47,501)
( 48,500)( 49,499)( 50,491)( 51,497)( 52,496)( 53,495)( 54,494)( 55,493)
( 56,492)( 57,554)( 58,560)( 59,559)( 60,558)( 61,557)( 62,556)( 63,555)
( 64,547)( 65,553)( 66,552)( 67,551)( 68,550)( 69,549)( 70,548)( 71,533)
( 72,539)( 73,538)( 74,537)( 75,536)( 76,535)( 77,534)( 78,540)( 79,546)
( 80,545)( 81,544)( 82,543)( 83,542)( 84,541)( 85,519)( 86,525)( 87,524)
( 88,523)( 89,522)( 90,521)( 91,520)( 92,526)( 93,532)( 94,531)( 95,530)
( 96,529)( 97,528)( 98,527)( 99,512)(100,518)(101,517)(102,516)(103,515)
(104,514)(105,513)(106,505)(107,511)(108,510)(109,509)(110,508)(111,507)
(112,506)(113,568)(114,574)(115,573)(116,572)(117,571)(118,570)(119,569)
(120,561)(121,567)(122,566)(123,565)(124,564)(125,563)(126,562)(127,575)
(128,581)(129,580)(130,579)(131,578)(132,577)(133,576)(134,582)(135,588)
(136,587)(137,586)(138,585)(139,584)(140,583)(141,596)(142,602)(143,601)
(144,600)(145,599)(146,598)(147,597)(148,589)(149,595)(150,594)(151,593)
(152,592)(153,591)(154,590)(155,603)(156,609)(157,608)(158,607)(159,606)
(160,605)(161,604)(162,610)(163,616)(164,615)(165,614)(166,613)(167,612)
(168,611)(169,659)(170,665)(171,664)(172,663)(173,662)(174,661)(175,660)
(176,666)(177,672)(178,671)(179,670)(180,669)(181,668)(182,667)(183,652)
(184,658)(185,657)(186,656)(187,655)(188,654)(189,653)(190,645)(191,651)
(192,650)(193,649)(194,648)(195,647)(196,646)(197,638)(198,644)(199,643)
(200,642)(201,641)(202,640)(203,639)(204,631)(205,637)(206,636)(207,635)
(208,634)(209,633)(210,632)(211,617)(212,623)(213,622)(214,621)(215,620)
(216,619)(217,618)(218,624)(219,630)(220,629)(221,628)(222,627)(223,626)
(224,625)(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)(253,701)(254,707)(255,706)
(256,705)(257,704)(258,703)(259,702)(260,708)(261,714)(262,713)(263,712)
(264,711)(265,710)(266,709)(267,722)(268,728)(269,727)(270,726)(271,725)
(272,724)(273,723)(274,715)(275,721)(276,720)(277,719)(278,718)(279,717)
(280,716)(281,778)(282,784)(283,783)(284,782)(285,781)(286,780)(287,779)
(288,771)(289,777)(290,776)(291,775)(292,774)(293,773)(294,772)(295,757)
(296,763)(297,762)(298,761)(299,760)(300,759)(301,758)(302,764)(303,770)
(304,769)(305,768)(306,767)(307,766)(308,765)(309,743)(310,749)(311,748)
(312,747)(313,746)(314,745)(315,744)(316,750)(317,756)(318,755)(319,754)
(320,753)(321,752)(322,751)(323,736)(324,742)(325,741)(326,740)(327,739)
(328,738)(329,737)(330,729)(331,735)(332,734)(333,733)(334,732)(335,731)
(336,730)(337,792)(338,798)(339,797)(340,796)(341,795)(342,794)(343,793)
(344,785)(345,791)(346,790)(347,789)(348,788)(349,787)(350,786)(351,799)
(352,805)(353,804)(354,803)(355,802)(356,801)(357,800)(358,806)(359,812)
(360,811)(361,810)(362,809)(363,808)(364,807)(365,820)(366,826)(367,825)
(368,824)(369,823)(370,822)(371,821)(372,813)(373,819)(374,818)(375,817)
(376,816)(377,815)(378,814)(379,827)(380,833)(381,832)(382,831)(383,830)
(384,829)(385,828)(386,834)(387,840)(388,839)(389,838)(390,837)(391,836)
(392,835)(393,883)(394,889)(395,888)(396,887)(397,886)(398,885)(399,884)
(400,890)(401,896)(402,895)(403,894)(404,893)(405,892)(406,891)(407,876)
(408,882)(409,881)(410,880)(411,879)(412,878)(413,877)(414,869)(415,875)
(416,874)(417,873)(418,872)(419,871)(420,870)(421,862)(422,868)(423,867)
(424,866)(425,865)(426,864)(427,863)(428,855)(429,861)(430,860)(431,859)
(432,858)(433,857)(434,856)(435,841)(436,847)(437,846)(438,845)(439,844)
(440,843)(441,842)(442,848)(443,854)(444,853)(445,852)(446,851)(447,850)
(448,849);
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)!(  1,673)(  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);
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*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
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*s0*s1*s0*s1*s2*s1*s0, 
s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0 >;

References : None.
to this polytope