Polytope of Type {8,56}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,56}*1792h
if this polytope has a name.
Group : SmallGroup(1792,90329)
Rank : 3
Schlafli Type : {8,56}
Number of vertices, edges, etc : 16, 448, 112
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 : {8,28}*896b
4-fold quotients : {4,28}*448
7-fold quotients : {8,8}*256h
8-fold quotients : {4,28}*224
14-fold quotients : {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 := ( 1,673)( 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)
( 57,771)( 58,772)( 59,773)( 60,774)( 61,775)( 62,776)( 63,777)( 64,778)
( 65,779)( 66,780)( 67,781)( 68,782)( 69,783)( 70,784)( 71,757)( 72,758)
( 73,759)( 74,760)( 75,761)( 76,762)( 77,763)( 78,764)( 79,765)( 80,766)
( 81,767)( 82,768)( 83,769)( 84,770)( 85,743)( 86,744)( 87,745)( 88,746)
( 89,747)( 90,748)( 91,749)( 92,750)( 93,751)( 94,752)( 95,753)( 96,754)
( 97,755)( 98,756)( 99,729)(100,730)(101,731)(102,732)(103,733)(104,734)
(105,735)(106,736)(107,737)(108,738)(109,739)(110,740)(111,741)(112,742)
(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)
(169,862)(170,863)(171,864)(172,865)(173,866)(174,867)(175,868)(176,855)
(177,856)(178,857)(179,858)(180,859)(181,860)(182,861)(183,848)(184,849)
(185,850)(186,851)(187,852)(188,853)(189,854)(190,841)(191,842)(192,843)
(193,844)(194,845)(195,846)(196,847)(197,883)(198,884)(199,885)(200,886)
(201,887)(202,888)(203,889)(204,890)(205,891)(206,892)(207,893)(208,894)
(209,895)(210,896)(211,869)(212,870)(213,871)(214,872)(215,873)(216,874)
(217,875)(218,876)(219,877)(220,878)(221,879)(222,880)(223,881)(224,882)
(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)
(281,547)(282,548)(283,549)(284,550)(285,551)(286,552)(287,553)(288,554)
(289,555)(290,556)(291,557)(292,558)(293,559)(294,560)(295,533)(296,534)
(297,535)(298,536)(299,537)(300,538)(301,539)(302,540)(303,541)(304,542)
(305,543)(306,544)(307,545)(308,546)(309,519)(310,520)(311,521)(312,522)
(313,523)(314,524)(315,525)(316,526)(317,527)(318,528)(319,529)(320,530)
(321,531)(322,532)(323,505)(324,506)(325,507)(326,508)(327,509)(328,510)
(329,511)(330,512)(331,513)(332,514)(333,515)(334,516)(335,517)(336,518)
(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)
(393,638)(394,639)(395,640)(396,641)(397,642)(398,643)(399,644)(400,631)
(401,632)(402,633)(403,634)(404,635)(405,636)(406,637)(407,624)(408,625)
(409,626)(410,627)(411,628)(412,629)(413,630)(414,617)(415,618)(416,619)
(417,620)(418,621)(419,622)(420,623)(421,659)(422,660)(423,661)(424,662)
(425,663)(426,664)(427,665)(428,666)(429,667)(430,668)(431,669)(432,670)
(433,671)(434,672)(435,645)(436,646)(437,647)(438,648)(439,649)(440,650)
(441,651)(442,652)(443,653)(444,654)(445,655)(446,656)(447,657)(448,658);;
s1 := ( 2, 7)( 3, 6)( 4, 5)( 9, 14)( 10, 13)( 11, 12)( 16, 21)( 17, 20)
( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 29, 43)( 30, 49)( 31, 48)( 32, 47)
( 33, 46)( 34, 45)( 35, 44)( 36, 50)( 37, 56)( 38, 55)( 39, 54)( 40, 53)
( 41, 52)( 42, 51)( 57, 64)( 58, 70)( 59, 69)( 60, 68)( 61, 67)( 62, 66)
( 63, 65)( 71, 78)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)( 77, 79)
( 85,106)( 86,112)( 87,111)( 88,110)( 89,109)( 90,108)( 91,107)( 92, 99)
( 93,105)( 94,104)( 95,103)( 96,102)( 97,101)( 98,100)(113,120)(114,126)
(115,125)(116,124)(117,123)(118,122)(119,121)(127,134)(128,140)(129,139)
(130,138)(131,137)(132,136)(133,135)(141,162)(142,168)(143,167)(144,166)
(145,165)(146,164)(147,163)(148,155)(149,161)(150,160)(151,159)(152,158)
(153,157)(154,156)(170,175)(171,174)(172,173)(177,182)(178,181)(179,180)
(184,189)(185,188)(186,187)(191,196)(192,195)(193,194)(197,211)(198,217)
(199,216)(200,215)(201,214)(202,213)(203,212)(204,218)(205,224)(206,223)
(207,222)(208,221)(209,220)(210,219)(225,281)(226,287)(227,286)(228,285)
(229,284)(230,283)(231,282)(232,288)(233,294)(234,293)(235,292)(236,291)
(237,290)(238,289)(239,295)(240,301)(241,300)(242,299)(243,298)(244,297)
(245,296)(246,302)(247,308)(248,307)(249,306)(250,305)(251,304)(252,303)
(253,323)(254,329)(255,328)(256,327)(257,326)(258,325)(259,324)(260,330)
(261,336)(262,335)(263,334)(264,333)(265,332)(266,331)(267,309)(268,315)
(269,314)(270,313)(271,312)(272,311)(273,310)(274,316)(275,322)(276,321)
(277,320)(278,319)(279,318)(280,317)(337,407)(338,413)(339,412)(340,411)
(341,410)(342,409)(343,408)(344,414)(345,420)(346,419)(347,418)(348,417)
(349,416)(350,415)(351,393)(352,399)(353,398)(354,397)(355,396)(356,395)
(357,394)(358,400)(359,406)(360,405)(361,404)(362,403)(363,402)(364,401)
(365,421)(366,427)(367,426)(368,425)(369,424)(370,423)(371,422)(372,428)
(373,434)(374,433)(375,432)(376,431)(377,430)(378,429)(379,435)(380,441)
(381,440)(382,439)(383,438)(384,437)(385,436)(386,442)(387,448)(388,447)
(389,446)(390,445)(391,444)(392,443)(449,561)(450,567)(451,566)(452,565)
(453,564)(454,563)(455,562)(456,568)(457,574)(458,573)(459,572)(460,571)
(461,570)(462,569)(463,575)(464,581)(465,580)(466,579)(467,578)(468,577)
(469,576)(470,582)(471,588)(472,587)(473,586)(474,585)(475,584)(476,583)
(477,603)(478,609)(479,608)(480,607)(481,606)(482,605)(483,604)(484,610)
(485,616)(486,615)(487,614)(488,613)(489,612)(490,611)(491,589)(492,595)
(493,594)(494,593)(495,592)(496,591)(497,590)(498,596)(499,602)(500,601)
(501,600)(502,599)(503,598)(504,597)(505,624)(506,630)(507,629)(508,628)
(509,627)(510,626)(511,625)(512,617)(513,623)(514,622)(515,621)(516,620)
(517,619)(518,618)(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)
(533,666)(534,672)(535,671)(536,670)(537,669)(538,668)(539,667)(540,659)
(541,665)(542,664)(543,663)(544,662)(545,661)(546,660)(547,652)(548,658)
(549,657)(550,656)(551,655)(552,654)(553,653)(554,645)(555,651)(556,650)
(557,649)(558,648)(559,647)(560,646)(673,876)(674,882)(675,881)(676,880)
(677,879)(678,878)(679,877)(680,869)(681,875)(682,874)(683,873)(684,872)
(685,871)(686,870)(687,890)(688,896)(689,895)(690,894)(691,893)(692,892)
(693,891)(694,883)(695,889)(696,888)(697,887)(698,886)(699,885)(700,884)
(701,855)(702,861)(703,860)(704,859)(705,858)(706,857)(707,856)(708,862)
(709,868)(710,867)(711,866)(712,865)(713,864)(714,863)(715,841)(716,847)
(717,846)(718,845)(719,844)(720,843)(721,842)(722,848)(723,854)(724,853)
(725,852)(726,851)(727,850)(728,849)(729,813)(730,819)(731,818)(732,817)
(733,816)(734,815)(735,814)(736,820)(737,826)(738,825)(739,824)(740,823)
(741,822)(742,821)(743,827)(744,833)(745,832)(746,831)(747,830)(748,829)
(749,828)(750,834)(751,840)(752,839)(753,838)(754,837)(755,836)(756,835)
(757,806)(758,812)(759,811)(760,810)(761,809)(762,808)(763,807)(764,799)
(765,805)(766,804)(767,803)(768,802)(769,801)(770,800)(771,792)(772,798)
(773,797)(774,796)(775,795)(776,794)(777,793)(778,785)(779,791)(780,790)
(781,789)(782,788)(783,787)(784,786);;
s2 := ( 1,226)( 2,225)( 3,231)( 4,230)( 5,229)( 6,228)( 7,227)( 8,233)
( 9,232)( 10,238)( 11,237)( 12,236)( 13,235)( 14,234)( 15,247)( 16,246)
( 17,252)( 18,251)( 19,250)( 20,249)( 21,248)( 22,240)( 23,239)( 24,245)
( 25,244)( 26,243)( 27,242)( 28,241)( 29,261)( 30,260)( 31,266)( 32,265)
( 33,264)( 34,263)( 35,262)( 36,254)( 37,253)( 38,259)( 39,258)( 40,257)
( 41,256)( 42,255)( 43,268)( 44,267)( 45,273)( 46,272)( 47,271)( 48,270)
( 49,269)( 50,275)( 51,274)( 52,280)( 53,279)( 54,278)( 55,277)( 56,276)
( 57,289)( 58,288)( 59,294)( 60,293)( 61,292)( 62,291)( 63,290)( 64,282)
( 65,281)( 66,287)( 67,286)( 68,285)( 69,284)( 70,283)( 71,296)( 72,295)
( 73,301)( 74,300)( 75,299)( 76,298)( 77,297)( 78,303)( 79,302)( 80,308)
( 81,307)( 82,306)( 83,305)( 84,304)( 85,310)( 86,309)( 87,315)( 88,314)
( 89,313)( 90,312)( 91,311)( 92,317)( 93,316)( 94,322)( 95,321)( 96,320)
( 97,319)( 98,318)( 99,331)(100,330)(101,336)(102,335)(103,334)(104,333)
(105,332)(106,324)(107,323)(108,329)(109,328)(110,327)(111,326)(112,325)
(113,366)(114,365)(115,371)(116,370)(117,369)(118,368)(119,367)(120,373)
(121,372)(122,378)(123,377)(124,376)(125,375)(126,374)(127,387)(128,386)
(129,392)(130,391)(131,390)(132,389)(133,388)(134,380)(135,379)(136,385)
(137,384)(138,383)(139,382)(140,381)(141,338)(142,337)(143,343)(144,342)
(145,341)(146,340)(147,339)(148,345)(149,344)(150,350)(151,349)(152,348)
(153,347)(154,346)(155,359)(156,358)(157,364)(158,363)(159,362)(160,361)
(161,360)(162,352)(163,351)(164,357)(165,356)(166,355)(167,354)(168,353)
(169,422)(170,421)(171,427)(172,426)(173,425)(174,424)(175,423)(176,429)
(177,428)(178,434)(179,433)(180,432)(181,431)(182,430)(183,443)(184,442)
(185,448)(186,447)(187,446)(188,445)(189,444)(190,436)(191,435)(192,441)
(193,440)(194,439)(195,438)(196,437)(197,394)(198,393)(199,399)(200,398)
(201,397)(202,396)(203,395)(204,401)(205,400)(206,406)(207,405)(208,404)
(209,403)(210,402)(211,415)(212,414)(213,420)(214,419)(215,418)(216,417)
(217,416)(218,408)(219,407)(220,413)(221,412)(222,411)(223,410)(224,409)
(449,674)(450,673)(451,679)(452,678)(453,677)(454,676)(455,675)(456,681)
(457,680)(458,686)(459,685)(460,684)(461,683)(462,682)(463,695)(464,694)
(465,700)(466,699)(467,698)(468,697)(469,696)(470,688)(471,687)(472,693)
(473,692)(474,691)(475,690)(476,689)(477,709)(478,708)(479,714)(480,713)
(481,712)(482,711)(483,710)(484,702)(485,701)(486,707)(487,706)(488,705)
(489,704)(490,703)(491,716)(492,715)(493,721)(494,720)(495,719)(496,718)
(497,717)(498,723)(499,722)(500,728)(501,727)(502,726)(503,725)(504,724)
(505,737)(506,736)(507,742)(508,741)(509,740)(510,739)(511,738)(512,730)
(513,729)(514,735)(515,734)(516,733)(517,732)(518,731)(519,744)(520,743)
(521,749)(522,748)(523,747)(524,746)(525,745)(526,751)(527,750)(528,756)
(529,755)(530,754)(531,753)(532,752)(533,758)(534,757)(535,763)(536,762)
(537,761)(538,760)(539,759)(540,765)(541,764)(542,770)(543,769)(544,768)
(545,767)(546,766)(547,779)(548,778)(549,784)(550,783)(551,782)(552,781)
(553,780)(554,772)(555,771)(556,777)(557,776)(558,775)(559,774)(560,773)
(561,814)(562,813)(563,819)(564,818)(565,817)(566,816)(567,815)(568,821)
(569,820)(570,826)(571,825)(572,824)(573,823)(574,822)(575,835)(576,834)
(577,840)(578,839)(579,838)(580,837)(581,836)(582,828)(583,827)(584,833)
(585,832)(586,831)(587,830)(588,829)(589,786)(590,785)(591,791)(592,790)
(593,789)(594,788)(595,787)(596,793)(597,792)(598,798)(599,797)(600,796)
(601,795)(602,794)(603,807)(604,806)(605,812)(606,811)(607,810)(608,809)
(609,808)(610,800)(611,799)(612,805)(613,804)(614,803)(615,802)(616,801)
(617,870)(618,869)(619,875)(620,874)(621,873)(622,872)(623,871)(624,877)
(625,876)(626,882)(627,881)(628,880)(629,879)(630,878)(631,891)(632,890)
(633,896)(634,895)(635,894)(636,893)(637,892)(638,884)(639,883)(640,889)
(641,888)(642,887)(643,886)(644,885)(645,842)(646,841)(647,847)(648,846)
(649,845)(650,844)(651,843)(652,849)(653,848)(654,854)(655,853)(656,852)
(657,851)(658,850)(659,863)(660,862)(661,868)(662,867)(663,866)(664,865)
(665,864)(666,856)(667,855)(668,861)(669,860)(670,859)(671,858)(672,857);;
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, s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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)( 57,771)( 58,772)( 59,773)( 60,774)( 61,775)( 62,776)( 63,777)
( 64,778)( 65,779)( 66,780)( 67,781)( 68,782)( 69,783)( 70,784)( 71,757)
( 72,758)( 73,759)( 74,760)( 75,761)( 76,762)( 77,763)( 78,764)( 79,765)
( 80,766)( 81,767)( 82,768)( 83,769)( 84,770)( 85,743)( 86,744)( 87,745)
( 88,746)( 89,747)( 90,748)( 91,749)( 92,750)( 93,751)( 94,752)( 95,753)
( 96,754)( 97,755)( 98,756)( 99,729)(100,730)(101,731)(102,732)(103,733)
(104,734)(105,735)(106,736)(107,737)(108,738)(109,739)(110,740)(111,741)
(112,742)(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)(169,862)(170,863)(171,864)(172,865)(173,866)(174,867)(175,868)
(176,855)(177,856)(178,857)(179,858)(180,859)(181,860)(182,861)(183,848)
(184,849)(185,850)(186,851)(187,852)(188,853)(189,854)(190,841)(191,842)
(192,843)(193,844)(194,845)(195,846)(196,847)(197,883)(198,884)(199,885)
(200,886)(201,887)(202,888)(203,889)(204,890)(205,891)(206,892)(207,893)
(208,894)(209,895)(210,896)(211,869)(212,870)(213,871)(214,872)(215,873)
(216,874)(217,875)(218,876)(219,877)(220,878)(221,879)(222,880)(223,881)
(224,882)(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)(281,547)(282,548)(283,549)(284,550)(285,551)(286,552)(287,553)
(288,554)(289,555)(290,556)(291,557)(292,558)(293,559)(294,560)(295,533)
(296,534)(297,535)(298,536)(299,537)(300,538)(301,539)(302,540)(303,541)
(304,542)(305,543)(306,544)(307,545)(308,546)(309,519)(310,520)(311,521)
(312,522)(313,523)(314,524)(315,525)(316,526)(317,527)(318,528)(319,529)
(320,530)(321,531)(322,532)(323,505)(324,506)(325,507)(326,508)(327,509)
(328,510)(329,511)(330,512)(331,513)(332,514)(333,515)(334,516)(335,517)
(336,518)(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)(393,638)(394,639)(395,640)(396,641)(397,642)(398,643)(399,644)
(400,631)(401,632)(402,633)(403,634)(404,635)(405,636)(406,637)(407,624)
(408,625)(409,626)(410,627)(411,628)(412,629)(413,630)(414,617)(415,618)
(416,619)(417,620)(418,621)(419,622)(420,623)(421,659)(422,660)(423,661)
(424,662)(425,663)(426,664)(427,665)(428,666)(429,667)(430,668)(431,669)
(432,670)(433,671)(434,672)(435,645)(436,646)(437,647)(438,648)(439,649)
(440,650)(441,651)(442,652)(443,653)(444,654)(445,655)(446,656)(447,657)
(448,658);
s1 := Sym(896)!( 2, 7)( 3, 6)( 4, 5)( 9, 14)( 10, 13)( 11, 12)( 16, 21)
( 17, 20)( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 29, 43)( 30, 49)( 31, 48)
( 32, 47)( 33, 46)( 34, 45)( 35, 44)( 36, 50)( 37, 56)( 38, 55)( 39, 54)
( 40, 53)( 41, 52)( 42, 51)( 57, 64)( 58, 70)( 59, 69)( 60, 68)( 61, 67)
( 62, 66)( 63, 65)( 71, 78)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)
( 77, 79)( 85,106)( 86,112)( 87,111)( 88,110)( 89,109)( 90,108)( 91,107)
( 92, 99)( 93,105)( 94,104)( 95,103)( 96,102)( 97,101)( 98,100)(113,120)
(114,126)(115,125)(116,124)(117,123)(118,122)(119,121)(127,134)(128,140)
(129,139)(130,138)(131,137)(132,136)(133,135)(141,162)(142,168)(143,167)
(144,166)(145,165)(146,164)(147,163)(148,155)(149,161)(150,160)(151,159)
(152,158)(153,157)(154,156)(170,175)(171,174)(172,173)(177,182)(178,181)
(179,180)(184,189)(185,188)(186,187)(191,196)(192,195)(193,194)(197,211)
(198,217)(199,216)(200,215)(201,214)(202,213)(203,212)(204,218)(205,224)
(206,223)(207,222)(208,221)(209,220)(210,219)(225,281)(226,287)(227,286)
(228,285)(229,284)(230,283)(231,282)(232,288)(233,294)(234,293)(235,292)
(236,291)(237,290)(238,289)(239,295)(240,301)(241,300)(242,299)(243,298)
(244,297)(245,296)(246,302)(247,308)(248,307)(249,306)(250,305)(251,304)
(252,303)(253,323)(254,329)(255,328)(256,327)(257,326)(258,325)(259,324)
(260,330)(261,336)(262,335)(263,334)(264,333)(265,332)(266,331)(267,309)
(268,315)(269,314)(270,313)(271,312)(272,311)(273,310)(274,316)(275,322)
(276,321)(277,320)(278,319)(279,318)(280,317)(337,407)(338,413)(339,412)
(340,411)(341,410)(342,409)(343,408)(344,414)(345,420)(346,419)(347,418)
(348,417)(349,416)(350,415)(351,393)(352,399)(353,398)(354,397)(355,396)
(356,395)(357,394)(358,400)(359,406)(360,405)(361,404)(362,403)(363,402)
(364,401)(365,421)(366,427)(367,426)(368,425)(369,424)(370,423)(371,422)
(372,428)(373,434)(374,433)(375,432)(376,431)(377,430)(378,429)(379,435)
(380,441)(381,440)(382,439)(383,438)(384,437)(385,436)(386,442)(387,448)
(388,447)(389,446)(390,445)(391,444)(392,443)(449,561)(450,567)(451,566)
(452,565)(453,564)(454,563)(455,562)(456,568)(457,574)(458,573)(459,572)
(460,571)(461,570)(462,569)(463,575)(464,581)(465,580)(466,579)(467,578)
(468,577)(469,576)(470,582)(471,588)(472,587)(473,586)(474,585)(475,584)
(476,583)(477,603)(478,609)(479,608)(480,607)(481,606)(482,605)(483,604)
(484,610)(485,616)(486,615)(487,614)(488,613)(489,612)(490,611)(491,589)
(492,595)(493,594)(494,593)(495,592)(496,591)(497,590)(498,596)(499,602)
(500,601)(501,600)(502,599)(503,598)(504,597)(505,624)(506,630)(507,629)
(508,628)(509,627)(510,626)(511,625)(512,617)(513,623)(514,622)(515,621)
(516,620)(517,619)(518,618)(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)(533,666)(534,672)(535,671)(536,670)(537,669)(538,668)(539,667)
(540,659)(541,665)(542,664)(543,663)(544,662)(545,661)(546,660)(547,652)
(548,658)(549,657)(550,656)(551,655)(552,654)(553,653)(554,645)(555,651)
(556,650)(557,649)(558,648)(559,647)(560,646)(673,876)(674,882)(675,881)
(676,880)(677,879)(678,878)(679,877)(680,869)(681,875)(682,874)(683,873)
(684,872)(685,871)(686,870)(687,890)(688,896)(689,895)(690,894)(691,893)
(692,892)(693,891)(694,883)(695,889)(696,888)(697,887)(698,886)(699,885)
(700,884)(701,855)(702,861)(703,860)(704,859)(705,858)(706,857)(707,856)
(708,862)(709,868)(710,867)(711,866)(712,865)(713,864)(714,863)(715,841)
(716,847)(717,846)(718,845)(719,844)(720,843)(721,842)(722,848)(723,854)
(724,853)(725,852)(726,851)(727,850)(728,849)(729,813)(730,819)(731,818)
(732,817)(733,816)(734,815)(735,814)(736,820)(737,826)(738,825)(739,824)
(740,823)(741,822)(742,821)(743,827)(744,833)(745,832)(746,831)(747,830)
(748,829)(749,828)(750,834)(751,840)(752,839)(753,838)(754,837)(755,836)
(756,835)(757,806)(758,812)(759,811)(760,810)(761,809)(762,808)(763,807)
(764,799)(765,805)(766,804)(767,803)(768,802)(769,801)(770,800)(771,792)
(772,798)(773,797)(774,796)(775,795)(776,794)(777,793)(778,785)(779,791)
(780,790)(781,789)(782,788)(783,787)(784,786);
s2 := Sym(896)!( 1,226)( 2,225)( 3,231)( 4,230)( 5,229)( 6,228)( 7,227)
( 8,233)( 9,232)( 10,238)( 11,237)( 12,236)( 13,235)( 14,234)( 15,247)
( 16,246)( 17,252)( 18,251)( 19,250)( 20,249)( 21,248)( 22,240)( 23,239)
( 24,245)( 25,244)( 26,243)( 27,242)( 28,241)( 29,261)( 30,260)( 31,266)
( 32,265)( 33,264)( 34,263)( 35,262)( 36,254)( 37,253)( 38,259)( 39,258)
( 40,257)( 41,256)( 42,255)( 43,268)( 44,267)( 45,273)( 46,272)( 47,271)
( 48,270)( 49,269)( 50,275)( 51,274)( 52,280)( 53,279)( 54,278)( 55,277)
( 56,276)( 57,289)( 58,288)( 59,294)( 60,293)( 61,292)( 62,291)( 63,290)
( 64,282)( 65,281)( 66,287)( 67,286)( 68,285)( 69,284)( 70,283)( 71,296)
( 72,295)( 73,301)( 74,300)( 75,299)( 76,298)( 77,297)( 78,303)( 79,302)
( 80,308)( 81,307)( 82,306)( 83,305)( 84,304)( 85,310)( 86,309)( 87,315)
( 88,314)( 89,313)( 90,312)( 91,311)( 92,317)( 93,316)( 94,322)( 95,321)
( 96,320)( 97,319)( 98,318)( 99,331)(100,330)(101,336)(102,335)(103,334)
(104,333)(105,332)(106,324)(107,323)(108,329)(109,328)(110,327)(111,326)
(112,325)(113,366)(114,365)(115,371)(116,370)(117,369)(118,368)(119,367)
(120,373)(121,372)(122,378)(123,377)(124,376)(125,375)(126,374)(127,387)
(128,386)(129,392)(130,391)(131,390)(132,389)(133,388)(134,380)(135,379)
(136,385)(137,384)(138,383)(139,382)(140,381)(141,338)(142,337)(143,343)
(144,342)(145,341)(146,340)(147,339)(148,345)(149,344)(150,350)(151,349)
(152,348)(153,347)(154,346)(155,359)(156,358)(157,364)(158,363)(159,362)
(160,361)(161,360)(162,352)(163,351)(164,357)(165,356)(166,355)(167,354)
(168,353)(169,422)(170,421)(171,427)(172,426)(173,425)(174,424)(175,423)
(176,429)(177,428)(178,434)(179,433)(180,432)(181,431)(182,430)(183,443)
(184,442)(185,448)(186,447)(187,446)(188,445)(189,444)(190,436)(191,435)
(192,441)(193,440)(194,439)(195,438)(196,437)(197,394)(198,393)(199,399)
(200,398)(201,397)(202,396)(203,395)(204,401)(205,400)(206,406)(207,405)
(208,404)(209,403)(210,402)(211,415)(212,414)(213,420)(214,419)(215,418)
(216,417)(217,416)(218,408)(219,407)(220,413)(221,412)(222,411)(223,410)
(224,409)(449,674)(450,673)(451,679)(452,678)(453,677)(454,676)(455,675)
(456,681)(457,680)(458,686)(459,685)(460,684)(461,683)(462,682)(463,695)
(464,694)(465,700)(466,699)(467,698)(468,697)(469,696)(470,688)(471,687)
(472,693)(473,692)(474,691)(475,690)(476,689)(477,709)(478,708)(479,714)
(480,713)(481,712)(482,711)(483,710)(484,702)(485,701)(486,707)(487,706)
(488,705)(489,704)(490,703)(491,716)(492,715)(493,721)(494,720)(495,719)
(496,718)(497,717)(498,723)(499,722)(500,728)(501,727)(502,726)(503,725)
(504,724)(505,737)(506,736)(507,742)(508,741)(509,740)(510,739)(511,738)
(512,730)(513,729)(514,735)(515,734)(516,733)(517,732)(518,731)(519,744)
(520,743)(521,749)(522,748)(523,747)(524,746)(525,745)(526,751)(527,750)
(528,756)(529,755)(530,754)(531,753)(532,752)(533,758)(534,757)(535,763)
(536,762)(537,761)(538,760)(539,759)(540,765)(541,764)(542,770)(543,769)
(544,768)(545,767)(546,766)(547,779)(548,778)(549,784)(550,783)(551,782)
(552,781)(553,780)(554,772)(555,771)(556,777)(557,776)(558,775)(559,774)
(560,773)(561,814)(562,813)(563,819)(564,818)(565,817)(566,816)(567,815)
(568,821)(569,820)(570,826)(571,825)(572,824)(573,823)(574,822)(575,835)
(576,834)(577,840)(578,839)(579,838)(580,837)(581,836)(582,828)(583,827)
(584,833)(585,832)(586,831)(587,830)(588,829)(589,786)(590,785)(591,791)
(592,790)(593,789)(594,788)(595,787)(596,793)(597,792)(598,798)(599,797)
(600,796)(601,795)(602,794)(603,807)(604,806)(605,812)(606,811)(607,810)
(608,809)(609,808)(610,800)(611,799)(612,805)(613,804)(614,803)(615,802)
(616,801)(617,870)(618,869)(619,875)(620,874)(621,873)(622,872)(623,871)
(624,877)(625,876)(626,882)(627,881)(628,880)(629,879)(630,878)(631,891)
(632,890)(633,896)(634,895)(635,894)(636,893)(637,892)(638,884)(639,883)
(640,889)(641,888)(642,887)(643,886)(644,885)(645,842)(646,841)(647,847)
(648,846)(649,845)(650,844)(651,843)(652,849)(653,848)(654,854)(655,853)
(656,852)(657,851)(658,850)(659,863)(660,862)(661,868)(662,867)(663,866)
(664,865)(665,864)(666,856)(667,855)(668,861)(669,860)(670,859)(671,858)
(672,857);
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, s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 >;
References : None.
to this polytope