Polytope of Type {8,56}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,56}*1792b
if this polytope has a name.
Group : SmallGroup(1792,81598)
Rank : 3
Schlafli Type : {8,56}
Number of vertices, edges, etc : 16, 448, 112
Order of s0s1s2 : 28
Order of s0s1s2s1 : 4
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, {8,28}*896b
4-fold quotients : {4,28}*448
7-fold quotients : {8,8}*256b
8-fold quotients : {4,28}*224
14-fold quotients : {4,8}*128b, {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 := ( 1,449)( 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)( 15,463)( 16,464)
( 17,465)( 18,466)( 19,467)( 20,468)( 21,469)( 22,470)( 23,471)( 24,472)
( 25,473)( 26,474)( 27,475)( 28,476)( 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)( 43,491)( 44,492)( 45,493)( 46,494)( 47,495)( 48,496)
( 49,497)( 50,498)( 51,499)( 52,500)( 53,501)( 54,502)( 55,503)( 56,504)
( 57,526)( 58,527)( 59,528)( 60,529)( 61,530)( 62,531)( 63,532)( 64,519)
( 65,520)( 66,521)( 67,522)( 68,523)( 69,524)( 70,525)( 71,512)( 72,513)
( 73,514)( 74,515)( 75,516)( 76,517)( 77,518)( 78,505)( 79,506)( 80,507)
( 81,508)( 82,509)( 83,510)( 84,511)( 85,554)( 86,555)( 87,556)( 88,557)
( 89,558)( 90,559)( 91,560)( 92,547)( 93,548)( 94,549)( 95,550)( 96,551)
( 97,552)( 98,553)( 99,540)(100,541)(101,542)(102,543)(103,544)(104,545)
(105,546)(106,533)(107,534)(108,535)(109,536)(110,537)(111,538)(112,539)
(113,589)(114,590)(115,591)(116,592)(117,593)(118,594)(119,595)(120,596)
(121,597)(122,598)(123,599)(124,600)(125,601)(126,602)(127,603)(128,604)
(129,605)(130,606)(131,607)(132,608)(133,609)(134,610)(135,611)(136,612)
(137,613)(138,614)(139,615)(140,616)(141,561)(142,562)(143,563)(144,564)
(145,565)(146,566)(147,567)(148,568)(149,569)(150,570)(151,571)(152,572)
(153,573)(154,574)(155,575)(156,576)(157,577)(158,578)(159,579)(160,580)
(161,581)(162,582)(163,583)(164,584)(165,585)(166,586)(167,587)(168,588)
(169,666)(170,667)(171,668)(172,669)(173,670)(174,671)(175,672)(176,659)
(177,660)(178,661)(179,662)(180,663)(181,664)(182,665)(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)(211,624)(212,625)(213,626)(214,627)(215,628)(216,629)
(217,630)(218,617)(219,618)(220,619)(221,620)(222,621)(223,622)(224,623)
(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)(239,687)(240,688)
(241,689)(242,690)(243,691)(244,692)(245,693)(246,694)(247,695)(248,696)
(249,697)(250,698)(251,699)(252,700)(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)(267,715)(268,716)(269,717)(270,718)(271,719)(272,720)
(273,721)(274,722)(275,723)(276,724)(277,725)(278,726)(279,727)(280,728)
(281,750)(282,751)(283,752)(284,753)(285,754)(286,755)(287,756)(288,743)
(289,744)(290,745)(291,746)(292,747)(293,748)(294,749)(295,736)(296,737)
(297,738)(298,739)(299,740)(300,741)(301,742)(302,729)(303,730)(304,731)
(305,732)(306,733)(307,734)(308,735)(309,778)(310,779)(311,780)(312,781)
(313,782)(314,783)(315,784)(316,771)(317,772)(318,773)(319,774)(320,775)
(321,776)(322,777)(323,764)(324,765)(325,766)(326,767)(327,768)(328,769)
(329,770)(330,757)(331,758)(332,759)(333,760)(334,761)(335,762)(336,763)
(337,813)(338,814)(339,815)(340,816)(341,817)(342,818)(343,819)(344,820)
(345,821)(346,822)(347,823)(348,824)(349,825)(350,826)(351,827)(352,828)
(353,829)(354,830)(355,831)(356,832)(357,833)(358,834)(359,835)(360,836)
(361,837)(362,838)(363,839)(364,840)(365,785)(366,786)(367,787)(368,788)
(369,789)(370,790)(371,791)(372,792)(373,793)(374,794)(375,795)(376,796)
(377,797)(378,798)(379,799)(380,800)(381,801)(382,802)(383,803)(384,804)
(385,805)(386,806)(387,807)(388,808)(389,809)(390,810)(391,811)(392,812)
(393,890)(394,891)(395,892)(396,893)(397,894)(398,895)(399,896)(400,883)
(401,884)(402,885)(403,886)(404,887)(405,888)(406,889)(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)(435,848)(436,849)(437,850)(438,851)(439,852)(440,853)
(441,854)(442,841)(443,842)(444,843)(445,844)(446,845)(447,846)(448,847);;
s1 := ( 2, 7)( 3, 6)( 4, 5)( 9, 14)( 10, 13)( 11, 12)( 15, 22)( 16, 28)
( 17, 27)( 18, 26)( 19, 25)( 20, 24)( 21, 23)( 30, 35)( 31, 34)( 32, 33)
( 37, 42)( 38, 41)( 39, 40)( 43, 50)( 44, 56)( 45, 55)( 46, 54)( 47, 53)
( 48, 52)( 49, 51)( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)( 67, 68)
( 71, 78)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)( 77, 79)( 86, 91)
( 87, 90)( 88, 89)( 93, 98)( 94, 97)( 95, 96)( 99,106)(100,112)(101,111)
(102,110)(103,109)(104,108)(105,107)(113,141)(114,147)(115,146)(116,145)
(117,144)(118,143)(119,142)(120,148)(121,154)(122,153)(123,152)(124,151)
(125,150)(126,149)(127,162)(128,168)(129,167)(130,166)(131,165)(132,164)
(133,163)(134,155)(135,161)(136,160)(137,159)(138,158)(139,157)(140,156)
(169,197)(170,203)(171,202)(172,201)(173,200)(174,199)(175,198)(176,204)
(177,210)(178,209)(179,208)(180,207)(181,206)(182,205)(183,218)(184,224)
(185,223)(186,222)(187,221)(188,220)(189,219)(190,211)(191,217)(192,216)
(193,215)(194,214)(195,213)(196,212)(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)(239,302)(240,308)(241,307)(242,306)(243,305)(244,304)
(245,303)(246,295)(247,301)(248,300)(249,299)(250,298)(251,297)(252,296)
(253,309)(254,315)(255,314)(256,313)(257,312)(258,311)(259,310)(260,316)
(261,322)(262,321)(263,320)(264,319)(265,318)(266,317)(267,330)(268,336)
(269,335)(270,334)(271,333)(272,332)(273,331)(274,323)(275,329)(276,328)
(277,327)(278,326)(279,325)(280,324)(337,428)(338,434)(339,433)(340,432)
(341,431)(342,430)(343,429)(344,421)(345,427)(346,426)(347,425)(348,424)
(349,423)(350,422)(351,435)(352,441)(353,440)(354,439)(355,438)(356,437)
(357,436)(358,442)(359,448)(360,447)(361,446)(362,445)(363,444)(364,443)
(365,400)(366,406)(367,405)(368,404)(369,403)(370,402)(371,401)(372,393)
(373,399)(374,398)(375,397)(376,396)(377,395)(378,394)(379,407)(380,413)
(381,412)(382,411)(383,410)(384,409)(385,408)(386,414)(387,420)(388,419)
(389,418)(390,417)(391,416)(392,415)(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)(463,582)(464,588)(465,587)(466,586)(467,585)(468,584)
(469,583)(470,575)(471,581)(472,580)(473,579)(474,578)(475,577)(476,576)
(477,589)(478,595)(479,594)(480,593)(481,592)(482,591)(483,590)(484,596)
(485,602)(486,601)(487,600)(488,599)(489,598)(490,597)(491,610)(492,616)
(493,615)(494,614)(495,613)(496,612)(497,611)(498,603)(499,609)(500,608)
(501,607)(502,606)(503,605)(504,604)(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)(519,638)(520,644)(521,643)(522,642)(523,641)(524,640)
(525,639)(526,631)(527,637)(528,636)(529,635)(530,634)(531,633)(532,632)
(533,645)(534,651)(535,650)(536,649)(537,648)(538,647)(539,646)(540,652)
(541,658)(542,657)(543,656)(544,655)(545,654)(546,653)(547,666)(548,672)
(549,671)(550,670)(551,669)(552,668)(553,667)(554,659)(555,665)(556,664)
(557,663)(558,662)(559,661)(560,660)(673,855)(674,861)(675,860)(676,859)
(677,858)(678,857)(679,856)(680,862)(681,868)(682,867)(683,866)(684,865)
(685,864)(686,863)(687,848)(688,854)(689,853)(690,852)(691,851)(692,850)
(693,849)(694,841)(695,847)(696,846)(697,845)(698,844)(699,843)(700,842)
(701,883)(702,889)(703,888)(704,887)(705,886)(706,885)(707,884)(708,890)
(709,896)(710,895)(711,894)(712,893)(713,892)(714,891)(715,876)(716,882)
(717,881)(718,880)(719,879)(720,878)(721,877)(722,869)(723,875)(724,874)
(725,873)(726,872)(727,871)(728,870)(729,799)(730,805)(731,804)(732,803)
(733,802)(734,801)(735,800)(736,806)(737,812)(738,811)(739,810)(740,809)
(741,808)(742,807)(743,792)(744,798)(745,797)(746,796)(747,795)(748,794)
(749,793)(750,785)(751,791)(752,790)(753,789)(754,788)(755,787)(756,786)
(757,827)(758,833)(759,832)(760,831)(761,830)(762,829)(763,828)(764,834)
(765,840)(766,839)(767,838)(768,837)(769,836)(770,835)(771,820)(772,826)
(773,825)(774,824)(775,823)(776,822)(777,821)(778,813)(779,819)(780,818)
(781,817)(782,816)(783,815)(784,814);;
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)( 29,702)( 30,701)( 31,707)( 32,706)
( 33,705)( 34,704)( 35,703)( 36,709)( 37,708)( 38,714)( 39,713)( 40,712)
( 41,711)( 42,710)( 43,716)( 44,715)( 45,721)( 46,720)( 47,719)( 48,718)
( 49,717)( 50,723)( 51,722)( 52,728)( 53,727)( 54,726)( 55,725)( 56,724)
( 57,751)( 58,750)( 59,756)( 60,755)( 61,754)( 62,753)( 63,752)( 64,744)
( 65,743)( 66,749)( 67,748)( 68,747)( 69,746)( 70,745)( 71,737)( 72,736)
( 73,742)( 74,741)( 75,740)( 76,739)( 77,738)( 78,730)( 79,729)( 80,735)
( 81,734)( 82,733)( 83,732)( 84,731)( 85,779)( 86,778)( 87,784)( 88,783)
( 89,782)( 90,781)( 91,780)( 92,772)( 93,771)( 94,777)( 95,776)( 96,775)
( 97,774)( 98,773)( 99,765)(100,764)(101,770)(102,769)(103,768)(104,767)
(105,766)(106,758)(107,757)(108,763)(109,762)(110,761)(111,760)(112,759)
(113,828)(114,827)(115,833)(116,832)(117,831)(118,830)(119,829)(120,835)
(121,834)(122,840)(123,839)(124,838)(125,837)(126,836)(127,814)(128,813)
(129,819)(130,818)(131,817)(132,816)(133,815)(134,821)(135,820)(136,826)
(137,825)(138,824)(139,823)(140,822)(141,800)(142,799)(143,805)(144,804)
(145,803)(146,802)(147,801)(148,807)(149,806)(150,812)(151,811)(152,810)
(153,809)(154,808)(155,786)(156,785)(157,791)(158,790)(159,789)(160,788)
(161,787)(162,793)(163,792)(164,798)(165,797)(166,796)(167,795)(168,794)
(169,877)(170,876)(171,882)(172,881)(173,880)(174,879)(175,878)(176,870)
(177,869)(178,875)(179,874)(180,873)(181,872)(182,871)(183,891)(184,890)
(185,896)(186,895)(187,894)(188,893)(189,892)(190,884)(191,883)(192,889)
(193,888)(194,887)(195,886)(196,885)(197,849)(198,848)(199,854)(200,853)
(201,852)(202,851)(203,850)(204,842)(205,841)(206,847)(207,846)(208,845)
(209,844)(210,843)(211,863)(212,862)(213,868)(214,867)(215,866)(216,865)
(217,864)(218,856)(219,855)(220,861)(221,860)(222,859)(223,858)(224,857)
(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)(253,478)(254,477)(255,483)(256,482)
(257,481)(258,480)(259,479)(260,485)(261,484)(262,490)(263,489)(264,488)
(265,487)(266,486)(267,492)(268,491)(269,497)(270,496)(271,495)(272,494)
(273,493)(274,499)(275,498)(276,504)(277,503)(278,502)(279,501)(280,500)
(281,527)(282,526)(283,532)(284,531)(285,530)(286,529)(287,528)(288,520)
(289,519)(290,525)(291,524)(292,523)(293,522)(294,521)(295,513)(296,512)
(297,518)(298,517)(299,516)(300,515)(301,514)(302,506)(303,505)(304,511)
(305,510)(306,509)(307,508)(308,507)(309,555)(310,554)(311,560)(312,559)
(313,558)(314,557)(315,556)(316,548)(317,547)(318,553)(319,552)(320,551)
(321,550)(322,549)(323,541)(324,540)(325,546)(326,545)(327,544)(328,543)
(329,542)(330,534)(331,533)(332,539)(333,538)(334,537)(335,536)(336,535)
(337,604)(338,603)(339,609)(340,608)(341,607)(342,606)(343,605)(344,611)
(345,610)(346,616)(347,615)(348,614)(349,613)(350,612)(351,590)(352,589)
(353,595)(354,594)(355,593)(356,592)(357,591)(358,597)(359,596)(360,602)
(361,601)(362,600)(363,599)(364,598)(365,576)(366,575)(367,581)(368,580)
(369,579)(370,578)(371,577)(372,583)(373,582)(374,588)(375,587)(376,586)
(377,585)(378,584)(379,562)(380,561)(381,567)(382,566)(383,565)(384,564)
(385,563)(386,569)(387,568)(388,574)(389,573)(390,572)(391,571)(392,570)
(393,653)(394,652)(395,658)(396,657)(397,656)(398,655)(399,654)(400,646)
(401,645)(402,651)(403,650)(404,649)(405,648)(406,647)(407,667)(408,666)
(409,672)(410,671)(411,670)(412,669)(413,668)(414,660)(415,659)(416,665)
(417,664)(418,663)(419,662)(420,661)(421,625)(422,624)(423,630)(424,629)
(425,628)(426,627)(427,626)(428,618)(429,617)(430,623)(431,622)(432,621)
(433,620)(434,619)(435,639)(436,638)(437,644)(438,643)(439,642)(440,641)
(441,640)(442,632)(443,631)(444,637)(445,636)(446,635)(447,634)(448,633);;
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,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s2*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*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)!( 1,449)( 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)( 15,463)
( 16,464)( 17,465)( 18,466)( 19,467)( 20,468)( 21,469)( 22,470)( 23,471)
( 24,472)( 25,473)( 26,474)( 27,475)( 28,476)( 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)( 43,491)( 44,492)( 45,493)( 46,494)( 47,495)
( 48,496)( 49,497)( 50,498)( 51,499)( 52,500)( 53,501)( 54,502)( 55,503)
( 56,504)( 57,526)( 58,527)( 59,528)( 60,529)( 61,530)( 62,531)( 63,532)
( 64,519)( 65,520)( 66,521)( 67,522)( 68,523)( 69,524)( 70,525)( 71,512)
( 72,513)( 73,514)( 74,515)( 75,516)( 76,517)( 77,518)( 78,505)( 79,506)
( 80,507)( 81,508)( 82,509)( 83,510)( 84,511)( 85,554)( 86,555)( 87,556)
( 88,557)( 89,558)( 90,559)( 91,560)( 92,547)( 93,548)( 94,549)( 95,550)
( 96,551)( 97,552)( 98,553)( 99,540)(100,541)(101,542)(102,543)(103,544)
(104,545)(105,546)(106,533)(107,534)(108,535)(109,536)(110,537)(111,538)
(112,539)(113,589)(114,590)(115,591)(116,592)(117,593)(118,594)(119,595)
(120,596)(121,597)(122,598)(123,599)(124,600)(125,601)(126,602)(127,603)
(128,604)(129,605)(130,606)(131,607)(132,608)(133,609)(134,610)(135,611)
(136,612)(137,613)(138,614)(139,615)(140,616)(141,561)(142,562)(143,563)
(144,564)(145,565)(146,566)(147,567)(148,568)(149,569)(150,570)(151,571)
(152,572)(153,573)(154,574)(155,575)(156,576)(157,577)(158,578)(159,579)
(160,580)(161,581)(162,582)(163,583)(164,584)(165,585)(166,586)(167,587)
(168,588)(169,666)(170,667)(171,668)(172,669)(173,670)(174,671)(175,672)
(176,659)(177,660)(178,661)(179,662)(180,663)(181,664)(182,665)(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)(211,624)(212,625)(213,626)(214,627)(215,628)
(216,629)(217,630)(218,617)(219,618)(220,619)(221,620)(222,621)(223,622)
(224,623)(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)(239,687)
(240,688)(241,689)(242,690)(243,691)(244,692)(245,693)(246,694)(247,695)
(248,696)(249,697)(250,698)(251,699)(252,700)(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)(267,715)(268,716)(269,717)(270,718)(271,719)
(272,720)(273,721)(274,722)(275,723)(276,724)(277,725)(278,726)(279,727)
(280,728)(281,750)(282,751)(283,752)(284,753)(285,754)(286,755)(287,756)
(288,743)(289,744)(290,745)(291,746)(292,747)(293,748)(294,749)(295,736)
(296,737)(297,738)(298,739)(299,740)(300,741)(301,742)(302,729)(303,730)
(304,731)(305,732)(306,733)(307,734)(308,735)(309,778)(310,779)(311,780)
(312,781)(313,782)(314,783)(315,784)(316,771)(317,772)(318,773)(319,774)
(320,775)(321,776)(322,777)(323,764)(324,765)(325,766)(326,767)(327,768)
(328,769)(329,770)(330,757)(331,758)(332,759)(333,760)(334,761)(335,762)
(336,763)(337,813)(338,814)(339,815)(340,816)(341,817)(342,818)(343,819)
(344,820)(345,821)(346,822)(347,823)(348,824)(349,825)(350,826)(351,827)
(352,828)(353,829)(354,830)(355,831)(356,832)(357,833)(358,834)(359,835)
(360,836)(361,837)(362,838)(363,839)(364,840)(365,785)(366,786)(367,787)
(368,788)(369,789)(370,790)(371,791)(372,792)(373,793)(374,794)(375,795)
(376,796)(377,797)(378,798)(379,799)(380,800)(381,801)(382,802)(383,803)
(384,804)(385,805)(386,806)(387,807)(388,808)(389,809)(390,810)(391,811)
(392,812)(393,890)(394,891)(395,892)(396,893)(397,894)(398,895)(399,896)
(400,883)(401,884)(402,885)(403,886)(404,887)(405,888)(406,889)(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)(435,848)(436,849)(437,850)(438,851)(439,852)
(440,853)(441,854)(442,841)(443,842)(444,843)(445,844)(446,845)(447,846)
(448,847);
s1 := Sym(896)!( 2, 7)( 3, 6)( 4, 5)( 9, 14)( 10, 13)( 11, 12)( 15, 22)
( 16, 28)( 17, 27)( 18, 26)( 19, 25)( 20, 24)( 21, 23)( 30, 35)( 31, 34)
( 32, 33)( 37, 42)( 38, 41)( 39, 40)( 43, 50)( 44, 56)( 45, 55)( 46, 54)
( 47, 53)( 48, 52)( 49, 51)( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)
( 67, 68)( 71, 78)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)( 77, 79)
( 86, 91)( 87, 90)( 88, 89)( 93, 98)( 94, 97)( 95, 96)( 99,106)(100,112)
(101,111)(102,110)(103,109)(104,108)(105,107)(113,141)(114,147)(115,146)
(116,145)(117,144)(118,143)(119,142)(120,148)(121,154)(122,153)(123,152)
(124,151)(125,150)(126,149)(127,162)(128,168)(129,167)(130,166)(131,165)
(132,164)(133,163)(134,155)(135,161)(136,160)(137,159)(138,158)(139,157)
(140,156)(169,197)(170,203)(171,202)(172,201)(173,200)(174,199)(175,198)
(176,204)(177,210)(178,209)(179,208)(180,207)(181,206)(182,205)(183,218)
(184,224)(185,223)(186,222)(187,221)(188,220)(189,219)(190,211)(191,217)
(192,216)(193,215)(194,214)(195,213)(196,212)(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)(239,302)(240,308)(241,307)(242,306)(243,305)
(244,304)(245,303)(246,295)(247,301)(248,300)(249,299)(250,298)(251,297)
(252,296)(253,309)(254,315)(255,314)(256,313)(257,312)(258,311)(259,310)
(260,316)(261,322)(262,321)(263,320)(264,319)(265,318)(266,317)(267,330)
(268,336)(269,335)(270,334)(271,333)(272,332)(273,331)(274,323)(275,329)
(276,328)(277,327)(278,326)(279,325)(280,324)(337,428)(338,434)(339,433)
(340,432)(341,431)(342,430)(343,429)(344,421)(345,427)(346,426)(347,425)
(348,424)(349,423)(350,422)(351,435)(352,441)(353,440)(354,439)(355,438)
(356,437)(357,436)(358,442)(359,448)(360,447)(361,446)(362,445)(363,444)
(364,443)(365,400)(366,406)(367,405)(368,404)(369,403)(370,402)(371,401)
(372,393)(373,399)(374,398)(375,397)(376,396)(377,395)(378,394)(379,407)
(380,413)(381,412)(382,411)(383,410)(384,409)(385,408)(386,414)(387,420)
(388,419)(389,418)(390,417)(391,416)(392,415)(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)(463,582)(464,588)(465,587)(466,586)(467,585)
(468,584)(469,583)(470,575)(471,581)(472,580)(473,579)(474,578)(475,577)
(476,576)(477,589)(478,595)(479,594)(480,593)(481,592)(482,591)(483,590)
(484,596)(485,602)(486,601)(487,600)(488,599)(489,598)(490,597)(491,610)
(492,616)(493,615)(494,614)(495,613)(496,612)(497,611)(498,603)(499,609)
(500,608)(501,607)(502,606)(503,605)(504,604)(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)(519,638)(520,644)(521,643)(522,642)(523,641)
(524,640)(525,639)(526,631)(527,637)(528,636)(529,635)(530,634)(531,633)
(532,632)(533,645)(534,651)(535,650)(536,649)(537,648)(538,647)(539,646)
(540,652)(541,658)(542,657)(543,656)(544,655)(545,654)(546,653)(547,666)
(548,672)(549,671)(550,670)(551,669)(552,668)(553,667)(554,659)(555,665)
(556,664)(557,663)(558,662)(559,661)(560,660)(673,855)(674,861)(675,860)
(676,859)(677,858)(678,857)(679,856)(680,862)(681,868)(682,867)(683,866)
(684,865)(685,864)(686,863)(687,848)(688,854)(689,853)(690,852)(691,851)
(692,850)(693,849)(694,841)(695,847)(696,846)(697,845)(698,844)(699,843)
(700,842)(701,883)(702,889)(703,888)(704,887)(705,886)(706,885)(707,884)
(708,890)(709,896)(710,895)(711,894)(712,893)(713,892)(714,891)(715,876)
(716,882)(717,881)(718,880)(719,879)(720,878)(721,877)(722,869)(723,875)
(724,874)(725,873)(726,872)(727,871)(728,870)(729,799)(730,805)(731,804)
(732,803)(733,802)(734,801)(735,800)(736,806)(737,812)(738,811)(739,810)
(740,809)(741,808)(742,807)(743,792)(744,798)(745,797)(746,796)(747,795)
(748,794)(749,793)(750,785)(751,791)(752,790)(753,789)(754,788)(755,787)
(756,786)(757,827)(758,833)(759,832)(760,831)(761,830)(762,829)(763,828)
(764,834)(765,840)(766,839)(767,838)(768,837)(769,836)(770,835)(771,820)
(772,826)(773,825)(774,824)(775,823)(776,822)(777,821)(778,813)(779,819)
(780,818)(781,817)(782,816)(783,815)(784,814);
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)( 29,702)( 30,701)( 31,707)
( 32,706)( 33,705)( 34,704)( 35,703)( 36,709)( 37,708)( 38,714)( 39,713)
( 40,712)( 41,711)( 42,710)( 43,716)( 44,715)( 45,721)( 46,720)( 47,719)
( 48,718)( 49,717)( 50,723)( 51,722)( 52,728)( 53,727)( 54,726)( 55,725)
( 56,724)( 57,751)( 58,750)( 59,756)( 60,755)( 61,754)( 62,753)( 63,752)
( 64,744)( 65,743)( 66,749)( 67,748)( 68,747)( 69,746)( 70,745)( 71,737)
( 72,736)( 73,742)( 74,741)( 75,740)( 76,739)( 77,738)( 78,730)( 79,729)
( 80,735)( 81,734)( 82,733)( 83,732)( 84,731)( 85,779)( 86,778)( 87,784)
( 88,783)( 89,782)( 90,781)( 91,780)( 92,772)( 93,771)( 94,777)( 95,776)
( 96,775)( 97,774)( 98,773)( 99,765)(100,764)(101,770)(102,769)(103,768)
(104,767)(105,766)(106,758)(107,757)(108,763)(109,762)(110,761)(111,760)
(112,759)(113,828)(114,827)(115,833)(116,832)(117,831)(118,830)(119,829)
(120,835)(121,834)(122,840)(123,839)(124,838)(125,837)(126,836)(127,814)
(128,813)(129,819)(130,818)(131,817)(132,816)(133,815)(134,821)(135,820)
(136,826)(137,825)(138,824)(139,823)(140,822)(141,800)(142,799)(143,805)
(144,804)(145,803)(146,802)(147,801)(148,807)(149,806)(150,812)(151,811)
(152,810)(153,809)(154,808)(155,786)(156,785)(157,791)(158,790)(159,789)
(160,788)(161,787)(162,793)(163,792)(164,798)(165,797)(166,796)(167,795)
(168,794)(169,877)(170,876)(171,882)(172,881)(173,880)(174,879)(175,878)
(176,870)(177,869)(178,875)(179,874)(180,873)(181,872)(182,871)(183,891)
(184,890)(185,896)(186,895)(187,894)(188,893)(189,892)(190,884)(191,883)
(192,889)(193,888)(194,887)(195,886)(196,885)(197,849)(198,848)(199,854)
(200,853)(201,852)(202,851)(203,850)(204,842)(205,841)(206,847)(207,846)
(208,845)(209,844)(210,843)(211,863)(212,862)(213,868)(214,867)(215,866)
(216,865)(217,864)(218,856)(219,855)(220,861)(221,860)(222,859)(223,858)
(224,857)(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)(253,478)(254,477)(255,483)
(256,482)(257,481)(258,480)(259,479)(260,485)(261,484)(262,490)(263,489)
(264,488)(265,487)(266,486)(267,492)(268,491)(269,497)(270,496)(271,495)
(272,494)(273,493)(274,499)(275,498)(276,504)(277,503)(278,502)(279,501)
(280,500)(281,527)(282,526)(283,532)(284,531)(285,530)(286,529)(287,528)
(288,520)(289,519)(290,525)(291,524)(292,523)(293,522)(294,521)(295,513)
(296,512)(297,518)(298,517)(299,516)(300,515)(301,514)(302,506)(303,505)
(304,511)(305,510)(306,509)(307,508)(308,507)(309,555)(310,554)(311,560)
(312,559)(313,558)(314,557)(315,556)(316,548)(317,547)(318,553)(319,552)
(320,551)(321,550)(322,549)(323,541)(324,540)(325,546)(326,545)(327,544)
(328,543)(329,542)(330,534)(331,533)(332,539)(333,538)(334,537)(335,536)
(336,535)(337,604)(338,603)(339,609)(340,608)(341,607)(342,606)(343,605)
(344,611)(345,610)(346,616)(347,615)(348,614)(349,613)(350,612)(351,590)
(352,589)(353,595)(354,594)(355,593)(356,592)(357,591)(358,597)(359,596)
(360,602)(361,601)(362,600)(363,599)(364,598)(365,576)(366,575)(367,581)
(368,580)(369,579)(370,578)(371,577)(372,583)(373,582)(374,588)(375,587)
(376,586)(377,585)(378,584)(379,562)(380,561)(381,567)(382,566)(383,565)
(384,564)(385,563)(386,569)(387,568)(388,574)(389,573)(390,572)(391,571)
(392,570)(393,653)(394,652)(395,658)(396,657)(397,656)(398,655)(399,654)
(400,646)(401,645)(402,651)(403,650)(404,649)(405,648)(406,647)(407,667)
(408,666)(409,672)(410,671)(411,670)(412,669)(413,668)(414,660)(415,659)
(416,665)(417,664)(418,663)(419,662)(420,661)(421,625)(422,624)(423,630)
(424,629)(425,628)(426,627)(427,626)(428,618)(429,617)(430,623)(431,622)
(432,621)(433,620)(434,619)(435,639)(436,638)(437,644)(438,643)(439,642)
(440,641)(441,640)(442,632)(443,631)(444,637)(445,636)(446,635)(447,634)
(448,633);
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,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s2*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*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