Polytope of Type {56,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {56,8}*1792g
if this polytope has a name.
Group : SmallGroup(1792,90328)
Rank : 3
Schlafli Type : {56,8}
Number of vertices, edges, etc : 112, 448, 16
Order of s0s1s2 : 56
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 : {56,4}*896b
4-fold quotients : {28,4}*448
7-fold quotients : {8,8}*256h
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)
( 57,771)( 58,777)( 59,776)( 60,775)( 61,774)( 62,773)( 63,772)( 64,778)
( 65,784)( 66,783)( 67,782)( 68,781)( 69,780)( 70,779)( 71,757)( 72,763)
( 73,762)( 74,761)( 75,760)( 76,759)( 77,758)( 78,764)( 79,770)( 80,769)
( 81,768)( 82,767)( 83,766)( 84,765)( 85,743)( 86,749)( 87,748)( 88,747)
( 89,746)( 90,745)( 91,744)( 92,750)( 93,756)( 94,755)( 95,754)( 96,753)
( 97,752)( 98,751)( 99,729)(100,735)(101,734)(102,733)(103,732)(104,731)
(105,730)(106,736)(107,742)(108,741)(109,740)(110,739)(111,738)(112,737)
(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)
(169,862)(170,868)(171,867)(172,866)(173,865)(174,864)(175,863)(176,855)
(177,861)(178,860)(179,859)(180,858)(181,857)(182,856)(183,848)(184,854)
(185,853)(186,852)(187,851)(188,850)(189,849)(190,841)(191,847)(192,846)
(193,845)(194,844)(195,843)(196,842)(197,883)(198,889)(199,888)(200,887)
(201,886)(202,885)(203,884)(204,890)(205,896)(206,895)(207,894)(208,893)
(209,892)(210,891)(211,869)(212,875)(213,874)(214,873)(215,872)(216,871)
(217,870)(218,876)(219,882)(220,881)(221,880)(222,879)(223,878)(224,877)
(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)
(281,547)(282,553)(283,552)(284,551)(285,550)(286,549)(287,548)(288,554)
(289,560)(290,559)(291,558)(292,557)(293,556)(294,555)(295,533)(296,539)
(297,538)(298,537)(299,536)(300,535)(301,534)(302,540)(303,546)(304,545)
(305,544)(306,543)(307,542)(308,541)(309,519)(310,525)(311,524)(312,523)
(313,522)(314,521)(315,520)(316,526)(317,532)(318,531)(319,530)(320,529)
(321,528)(322,527)(323,505)(324,511)(325,510)(326,509)(327,508)(328,507)
(329,506)(330,512)(331,518)(332,517)(333,516)(334,515)(335,514)(336,513)
(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)
(393,638)(394,644)(395,643)(396,642)(397,641)(398,640)(399,639)(400,631)
(401,637)(402,636)(403,635)(404,634)(405,633)(406,632)(407,624)(408,630)
(409,629)(410,628)(411,627)(412,626)(413,625)(414,617)(415,623)(416,622)
(417,621)(418,620)(419,619)(420,618)(421,659)(422,665)(423,664)(424,663)
(425,662)(426,661)(427,660)(428,666)(429,672)(430,671)(431,670)(432,669)
(433,668)(434,667)(435,645)(436,651)(437,650)(438,649)(439,648)(440,647)
(441,646)(442,652)(443,658)(444,657)(445,656)(446,655)(447,654)(448,653);;
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, 65)( 58, 64)( 59, 70)( 60, 69)( 61, 68)( 62, 67)
( 63, 66)( 71, 79)( 72, 78)( 73, 84)( 74, 83)( 75, 82)( 76, 81)( 77, 80)
( 85,107)( 86,106)( 87,112)( 88,111)( 89,110)( 90,109)( 91,108)( 92,100)
( 93, 99)( 94,105)( 95,104)( 96,103)( 97,102)( 98,101)(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)(169,170)(171,175)(172,174)(176,177)(178,182)(179,181)
(183,184)(185,189)(186,188)(190,191)(192,196)(193,195)(197,212)(198,211)
(199,217)(200,216)(201,215)(202,214)(203,213)(204,219)(205,218)(206,224)
(207,223)(208,222)(209,221)(210,220)(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)(505,625)(506,624)(507,630)(508,629)
(509,628)(510,627)(511,626)(512,618)(513,617)(514,623)(515,622)(516,621)
(517,620)(518,619)(519,639)(520,638)(521,644)(522,643)(523,642)(524,641)
(525,640)(526,632)(527,631)(528,637)(529,636)(530,635)(531,634)(532,633)
(533,667)(534,666)(535,672)(536,671)(537,670)(538,669)(539,668)(540,660)
(541,659)(542,665)(543,664)(544,663)(545,662)(546,661)(547,653)(548,652)
(549,658)(550,657)(551,656)(552,655)(553,654)(554,646)(555,645)(556,651)
(557,650)(558,649)(559,648)(560,647)(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 := ( 1,449)( 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);;
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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)( 57,771)( 58,777)( 59,776)( 60,775)( 61,774)( 62,773)( 63,772)
( 64,778)( 65,784)( 66,783)( 67,782)( 68,781)( 69,780)( 70,779)( 71,757)
( 72,763)( 73,762)( 74,761)( 75,760)( 76,759)( 77,758)( 78,764)( 79,770)
( 80,769)( 81,768)( 82,767)( 83,766)( 84,765)( 85,743)( 86,749)( 87,748)
( 88,747)( 89,746)( 90,745)( 91,744)( 92,750)( 93,756)( 94,755)( 95,754)
( 96,753)( 97,752)( 98,751)( 99,729)(100,735)(101,734)(102,733)(103,732)
(104,731)(105,730)(106,736)(107,742)(108,741)(109,740)(110,739)(111,738)
(112,737)(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)(169,862)(170,868)(171,867)(172,866)(173,865)(174,864)(175,863)
(176,855)(177,861)(178,860)(179,859)(180,858)(181,857)(182,856)(183,848)
(184,854)(185,853)(186,852)(187,851)(188,850)(189,849)(190,841)(191,847)
(192,846)(193,845)(194,844)(195,843)(196,842)(197,883)(198,889)(199,888)
(200,887)(201,886)(202,885)(203,884)(204,890)(205,896)(206,895)(207,894)
(208,893)(209,892)(210,891)(211,869)(212,875)(213,874)(214,873)(215,872)
(216,871)(217,870)(218,876)(219,882)(220,881)(221,880)(222,879)(223,878)
(224,877)(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)(281,547)(282,553)(283,552)(284,551)(285,550)(286,549)(287,548)
(288,554)(289,560)(290,559)(291,558)(292,557)(293,556)(294,555)(295,533)
(296,539)(297,538)(298,537)(299,536)(300,535)(301,534)(302,540)(303,546)
(304,545)(305,544)(306,543)(307,542)(308,541)(309,519)(310,525)(311,524)
(312,523)(313,522)(314,521)(315,520)(316,526)(317,532)(318,531)(319,530)
(320,529)(321,528)(322,527)(323,505)(324,511)(325,510)(326,509)(327,508)
(328,507)(329,506)(330,512)(331,518)(332,517)(333,516)(334,515)(335,514)
(336,513)(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)(393,638)(394,644)(395,643)(396,642)(397,641)(398,640)(399,639)
(400,631)(401,637)(402,636)(403,635)(404,634)(405,633)(406,632)(407,624)
(408,630)(409,629)(410,628)(411,627)(412,626)(413,625)(414,617)(415,623)
(416,622)(417,621)(418,620)(419,619)(420,618)(421,659)(422,665)(423,664)
(424,663)(425,662)(426,661)(427,660)(428,666)(429,672)(430,671)(431,670)
(432,669)(433,668)(434,667)(435,645)(436,651)(437,650)(438,649)(439,648)
(440,647)(441,646)(442,652)(443,658)(444,657)(445,656)(446,655)(447,654)
(448,653);
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, 65)( 58, 64)( 59, 70)( 60, 69)( 61, 68)
( 62, 67)( 63, 66)( 71, 79)( 72, 78)( 73, 84)( 74, 83)( 75, 82)( 76, 81)
( 77, 80)( 85,107)( 86,106)( 87,112)( 88,111)( 89,110)( 90,109)( 91,108)
( 92,100)( 93, 99)( 94,105)( 95,104)( 96,103)( 97,102)( 98,101)(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)(169,170)(171,175)(172,174)(176,177)(178,182)
(179,181)(183,184)(185,189)(186,188)(190,191)(192,196)(193,195)(197,212)
(198,211)(199,217)(200,216)(201,215)(202,214)(203,213)(204,219)(205,218)
(206,224)(207,223)(208,222)(209,221)(210,220)(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)(505,625)(506,624)(507,630)
(508,629)(509,628)(510,627)(511,626)(512,618)(513,617)(514,623)(515,622)
(516,621)(517,620)(518,619)(519,639)(520,638)(521,644)(522,643)(523,642)
(524,641)(525,640)(526,632)(527,631)(528,637)(529,636)(530,635)(531,634)
(532,633)(533,667)(534,666)(535,672)(536,671)(537,670)(538,669)(539,668)
(540,660)(541,659)(542,665)(543,664)(544,663)(545,662)(546,661)(547,653)
(548,652)(549,658)(550,657)(551,656)(552,655)(553,654)(554,646)(555,645)
(556,651)(557,650)(558,649)(559,648)(560,647)(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)!( 1,449)( 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);
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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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