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