Polytope of Type {16,56}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,56}*1792d
Also Known As : {16,56|2}. if this polytope has another name.
Group : SmallGroup(1792,82995)
Rank : 3
Schlafli Type : {16,56}
Number of vertices, edges, etc : 16, 448, 56
Order of s0s1s2 : 112
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
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 : {8,56}*896b, {16,28}*896a
4-fold quotients : {4,56}*448a, {8,28}*448a, {16,14}*448
7-fold quotients : {16,8}*256d
8-fold quotients : {4,28}*224, {2,56}*224, {8,14}*224
14-fold quotients : {8,8}*128b, {16,4}*128a
16-fold quotients : {2,28}*112, {4,14}*112
28-fold quotients : {4,8}*64a, {8,4}*64a, {16,2}*64
32-fold quotients : {2,14}*56
56-fold quotients : {4,4}*32, {2,8}*32, {8,2}*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)
( 57,729)( 58,730)( 59,731)( 60,732)( 61,733)( 62,734)( 63,735)( 64,736)
( 65,737)( 66,738)( 67,739)( 68,740)( 69,741)( 70,742)( 71,743)( 72,744)
( 73,745)( 74,746)( 75,747)( 76,748)( 77,749)( 78,750)( 79,751)( 80,752)
( 81,753)( 82,754)( 83,755)( 84,756)( 85,764)( 86,765)( 87,766)( 88,767)
( 89,768)( 90,769)( 91,770)( 92,757)( 93,758)( 94,759)( 95,760)( 96,761)
( 97,762)( 98,763)( 99,778)(100,779)(101,780)(102,781)(103,782)(104,783)
(105,784)(106,771)(107,772)(108,773)(109,774)(110,775)(111,776)(112,777)
(113,827)(114,828)(115,829)(116,830)(117,831)(118,832)(119,833)(120,834)
(121,835)(122,836)(123,837)(124,838)(125,839)(126,840)(127,813)(128,814)
(129,815)(130,816)(131,817)(132,818)(133,819)(134,820)(135,821)(136,822)
(137,823)(138,824)(139,825)(140,826)(141,799)(142,800)(143,801)(144,802)
(145,803)(146,804)(147,805)(148,806)(149,807)(150,808)(151,809)(152,810)
(153,811)(154,812)(155,785)(156,786)(157,787)(158,788)(159,789)(160,790)
(161,791)(162,792)(163,793)(164,794)(165,795)(166,796)(167,797)(168,798)
(169,883)(170,884)(171,885)(172,886)(173,887)(174,888)(175,889)(176,890)
(177,891)(178,892)(179,893)(180,894)(181,895)(182,896)(183,869)(184,870)
(185,871)(186,872)(187,873)(188,874)(189,875)(190,876)(191,877)(192,878)
(193,879)(194,880)(195,881)(196,882)(197,855)(198,856)(199,857)(200,858)
(201,859)(202,860)(203,861)(204,862)(205,863)(206,864)(207,865)(208,866)
(209,867)(210,868)(211,841)(212,842)(213,843)(214,844)(215,845)(216,846)
(217,847)(218,848)(219,849)(220,850)(221,851)(222,852)(223,853)(224,854)
(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)
(281,505)(282,506)(283,507)(284,508)(285,509)(286,510)(287,511)(288,512)
(289,513)(290,514)(291,515)(292,516)(293,517)(294,518)(295,519)(296,520)
(297,521)(298,522)(299,523)(300,524)(301,525)(302,526)(303,527)(304,528)
(305,529)(306,530)(307,531)(308,532)(309,540)(310,541)(311,542)(312,543)
(313,544)(314,545)(315,546)(316,533)(317,534)(318,535)(319,536)(320,537)
(321,538)(322,539)(323,554)(324,555)(325,556)(326,557)(327,558)(328,559)
(329,560)(330,547)(331,548)(332,549)(333,550)(334,551)(335,552)(336,553)
(337,603)(338,604)(339,605)(340,606)(341,607)(342,608)(343,609)(344,610)
(345,611)(346,612)(347,613)(348,614)(349,615)(350,616)(351,589)(352,590)
(353,591)(354,592)(355,593)(356,594)(357,595)(358,596)(359,597)(360,598)
(361,599)(362,600)(363,601)(364,602)(365,575)(366,576)(367,577)(368,578)
(369,579)(370,580)(371,581)(372,582)(373,583)(374,584)(375,585)(376,586)
(377,587)(378,588)(379,561)(380,562)(381,563)(382,564)(383,565)(384,566)
(385,567)(386,568)(387,569)(388,570)(389,571)(390,572)(391,573)(392,574)
(393,659)(394,660)(395,661)(396,662)(397,663)(398,664)(399,665)(400,666)
(401,667)(402,668)(403,669)(404,670)(405,671)(406,672)(407,645)(408,646)
(409,647)(410,648)(411,649)(412,650)(413,651)(414,652)(415,653)(416,654)
(417,655)(418,656)(419,657)(420,658)(421,631)(422,632)(423,633)(424,634)
(425,635)(426,636)(427,637)(428,638)(429,639)(430,640)(431,641)(432,642)
(433,643)(434,644)(435,617)(436,618)(437,619)(438,620)(439,621)(440,622)
(441,623)(442,624)(443,625)(444,626)(445,627)(446,628)(447,629)(448,630);;
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, 36)( 30, 42)( 31, 41)( 32, 40)
( 33, 39)( 34, 38)( 35, 37)( 43, 50)( 44, 56)( 45, 55)( 46, 54)( 47, 53)
( 48, 52)( 49, 51)( 57, 71)( 58, 77)( 59, 76)( 60, 75)( 61, 74)( 62, 73)
( 63, 72)( 64, 78)( 65, 84)( 66, 83)( 67, 82)( 68, 81)( 69, 80)( 70, 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)(113,141)(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)(127,155)(128,161)(129,160)(130,159)
(131,158)(132,157)(133,156)(134,162)(135,168)(136,167)(137,166)(138,165)
(139,164)(140,163)(169,211)(170,217)(171,216)(172,215)(173,214)(174,213)
(175,212)(176,218)(177,224)(178,223)(179,222)(180,221)(181,220)(182,219)
(183,197)(184,203)(185,202)(186,201)(187,200)(188,199)(189,198)(190,204)
(191,210)(192,209)(193,208)(194,207)(195,206)(196,205)(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)(253,316)(254,322)(255,321)(256,320)(257,319)(258,318)
(259,317)(260,309)(261,315)(262,314)(263,313)(264,312)(265,311)(266,310)
(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)(337,421)(338,427)
(339,426)(340,425)(341,424)(342,423)(343,422)(344,428)(345,434)(346,433)
(347,432)(348,431)(349,430)(350,429)(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)(365,393)(366,399)(367,398)(368,397)(369,396)(370,395)
(371,394)(372,400)(373,406)(374,405)(375,404)(376,403)(377,402)(378,401)
(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)(463,575)(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)(477,596)(478,602)(479,601)(480,600)(481,599)(482,598)
(483,597)(484,589)(485,595)(486,594)(487,593)(488,592)(489,591)(490,590)
(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)(505,631)(506,637)
(507,636)(508,635)(509,634)(510,633)(511,632)(512,638)(513,644)(514,643)
(515,642)(516,641)(517,640)(518,639)(519,617)(520,623)(521,622)(522,621)
(523,620)(524,619)(525,618)(526,624)(527,630)(528,629)(529,628)(530,627)
(531,626)(532,625)(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)(673,855)(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)(687,841)(688,847)(689,846)(690,845)
(691,844)(692,843)(693,842)(694,848)(695,854)(696,853)(697,852)(698,851)
(699,850)(700,849)(701,890)(702,896)(703,895)(704,894)(705,893)(706,892)
(707,891)(708,883)(709,889)(710,888)(711,887)(712,886)(713,885)(714,884)
(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)(743,785)(744,791)(745,790)(746,789)
(747,788)(748,787)(749,786)(750,792)(751,798)(752,797)(753,796)(754,795)
(755,794)(756,793)(757,834)(758,840)(759,839)(760,838)(761,837)(762,836)
(763,835)(764,827)(765,833)(766,832)(767,831)(768,830)(769,829)(770,828)
(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 := ( 1,226)( 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)( 15,240)( 16,239)
( 17,245)( 18,244)( 19,243)( 20,242)( 21,241)( 22,247)( 23,246)( 24,252)
( 25,251)( 26,250)( 27,249)( 28,248)( 29,254)( 30,253)( 31,259)( 32,258)
( 33,257)( 34,256)( 35,255)( 36,261)( 37,260)( 38,266)( 39,265)( 40,264)
( 41,263)( 42,262)( 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)
( 57,296)( 58,295)( 59,301)( 60,300)( 61,299)( 62,298)( 63,297)( 64,303)
( 65,302)( 66,308)( 67,307)( 68,306)( 69,305)( 70,304)( 71,282)( 72,281)
( 73,287)( 74,286)( 75,285)( 76,284)( 77,283)( 78,289)( 79,288)( 80,294)
( 81,293)( 82,292)( 83,291)( 84,290)( 85,324)( 86,323)( 87,329)( 88,328)
( 89,327)( 90,326)( 91,325)( 92,331)( 93,330)( 94,336)( 95,335)( 96,334)
( 97,333)( 98,332)( 99,310)(100,309)(101,315)(102,314)(103,313)(104,312)
(105,311)(106,317)(107,316)(108,322)(109,321)(110,320)(111,319)(112,318)
(113,352)(114,351)(115,357)(116,356)(117,355)(118,354)(119,353)(120,359)
(121,358)(122,364)(123,363)(124,362)(125,361)(126,360)(127,338)(128,337)
(129,343)(130,342)(131,341)(132,340)(133,339)(134,345)(135,344)(136,350)
(137,349)(138,348)(139,347)(140,346)(141,380)(142,379)(143,385)(144,384)
(145,383)(146,382)(147,381)(148,387)(149,386)(150,392)(151,391)(152,390)
(153,389)(154,388)(155,366)(156,365)(157,371)(158,370)(159,369)(160,368)
(161,367)(162,373)(163,372)(164,378)(165,377)(166,376)(167,375)(168,374)
(169,394)(170,393)(171,399)(172,398)(173,397)(174,396)(175,395)(176,401)
(177,400)(178,406)(179,405)(180,404)(181,403)(182,402)(183,408)(184,407)
(185,413)(186,412)(187,411)(188,410)(189,409)(190,415)(191,414)(192,420)
(193,419)(194,418)(195,417)(196,416)(197,422)(198,421)(199,427)(200,426)
(201,425)(202,424)(203,423)(204,429)(205,428)(206,434)(207,433)(208,432)
(209,431)(210,430)(211,436)(212,435)(213,441)(214,440)(215,439)(216,438)
(217,437)(218,443)(219,442)(220,448)(221,447)(222,446)(223,445)(224,444)
(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)(463,688)(464,687)
(465,693)(466,692)(467,691)(468,690)(469,689)(470,695)(471,694)(472,700)
(473,699)(474,698)(475,697)(476,696)(477,702)(478,701)(479,707)(480,706)
(481,705)(482,704)(483,703)(484,709)(485,708)(486,714)(487,713)(488,712)
(489,711)(490,710)(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)
(505,744)(506,743)(507,749)(508,748)(509,747)(510,746)(511,745)(512,751)
(513,750)(514,756)(515,755)(516,754)(517,753)(518,752)(519,730)(520,729)
(521,735)(522,734)(523,733)(524,732)(525,731)(526,737)(527,736)(528,742)
(529,741)(530,740)(531,739)(532,738)(533,772)(534,771)(535,777)(536,776)
(537,775)(538,774)(539,773)(540,779)(541,778)(542,784)(543,783)(544,782)
(545,781)(546,780)(547,758)(548,757)(549,763)(550,762)(551,761)(552,760)
(553,759)(554,765)(555,764)(556,770)(557,769)(558,768)(559,767)(560,766)
(561,800)(562,799)(563,805)(564,804)(565,803)(566,802)(567,801)(568,807)
(569,806)(570,812)(571,811)(572,810)(573,809)(574,808)(575,786)(576,785)
(577,791)(578,790)(579,789)(580,788)(581,787)(582,793)(583,792)(584,798)
(585,797)(586,796)(587,795)(588,794)(589,828)(590,827)(591,833)(592,832)
(593,831)(594,830)(595,829)(596,835)(597,834)(598,840)(599,839)(600,838)
(601,837)(602,836)(603,814)(604,813)(605,819)(606,818)(607,817)(608,816)
(609,815)(610,821)(611,820)(612,826)(613,825)(614,824)(615,823)(616,822)
(617,842)(618,841)(619,847)(620,846)(621,845)(622,844)(623,843)(624,849)
(625,848)(626,854)(627,853)(628,852)(629,851)(630,850)(631,856)(632,855)
(633,861)(634,860)(635,859)(636,858)(637,857)(638,863)(639,862)(640,868)
(641,867)(642,866)(643,865)(644,864)(645,870)(646,869)(647,875)(648,874)
(649,873)(650,872)(651,871)(652,877)(653,876)(654,882)(655,881)(656,880)
(657,879)(658,878)(659,884)(660,883)(661,889)(662,888)(663,887)(664,886)
(665,885)(666,891)(667,890)(668,896)(669,895)(670,894)(671,893)(672,892);;
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*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,
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*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*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
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)( 57,729)( 58,730)( 59,731)( 60,732)( 61,733)( 62,734)( 63,735)
( 64,736)( 65,737)( 66,738)( 67,739)( 68,740)( 69,741)( 70,742)( 71,743)
( 72,744)( 73,745)( 74,746)( 75,747)( 76,748)( 77,749)( 78,750)( 79,751)
( 80,752)( 81,753)( 82,754)( 83,755)( 84,756)( 85,764)( 86,765)( 87,766)
( 88,767)( 89,768)( 90,769)( 91,770)( 92,757)( 93,758)( 94,759)( 95,760)
( 96,761)( 97,762)( 98,763)( 99,778)(100,779)(101,780)(102,781)(103,782)
(104,783)(105,784)(106,771)(107,772)(108,773)(109,774)(110,775)(111,776)
(112,777)(113,827)(114,828)(115,829)(116,830)(117,831)(118,832)(119,833)
(120,834)(121,835)(122,836)(123,837)(124,838)(125,839)(126,840)(127,813)
(128,814)(129,815)(130,816)(131,817)(132,818)(133,819)(134,820)(135,821)
(136,822)(137,823)(138,824)(139,825)(140,826)(141,799)(142,800)(143,801)
(144,802)(145,803)(146,804)(147,805)(148,806)(149,807)(150,808)(151,809)
(152,810)(153,811)(154,812)(155,785)(156,786)(157,787)(158,788)(159,789)
(160,790)(161,791)(162,792)(163,793)(164,794)(165,795)(166,796)(167,797)
(168,798)(169,883)(170,884)(171,885)(172,886)(173,887)(174,888)(175,889)
(176,890)(177,891)(178,892)(179,893)(180,894)(181,895)(182,896)(183,869)
(184,870)(185,871)(186,872)(187,873)(188,874)(189,875)(190,876)(191,877)
(192,878)(193,879)(194,880)(195,881)(196,882)(197,855)(198,856)(199,857)
(200,858)(201,859)(202,860)(203,861)(204,862)(205,863)(206,864)(207,865)
(208,866)(209,867)(210,868)(211,841)(212,842)(213,843)(214,844)(215,845)
(216,846)(217,847)(218,848)(219,849)(220,850)(221,851)(222,852)(223,853)
(224,854)(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)(281,505)(282,506)(283,507)(284,508)(285,509)(286,510)(287,511)
(288,512)(289,513)(290,514)(291,515)(292,516)(293,517)(294,518)(295,519)
(296,520)(297,521)(298,522)(299,523)(300,524)(301,525)(302,526)(303,527)
(304,528)(305,529)(306,530)(307,531)(308,532)(309,540)(310,541)(311,542)
(312,543)(313,544)(314,545)(315,546)(316,533)(317,534)(318,535)(319,536)
(320,537)(321,538)(322,539)(323,554)(324,555)(325,556)(326,557)(327,558)
(328,559)(329,560)(330,547)(331,548)(332,549)(333,550)(334,551)(335,552)
(336,553)(337,603)(338,604)(339,605)(340,606)(341,607)(342,608)(343,609)
(344,610)(345,611)(346,612)(347,613)(348,614)(349,615)(350,616)(351,589)
(352,590)(353,591)(354,592)(355,593)(356,594)(357,595)(358,596)(359,597)
(360,598)(361,599)(362,600)(363,601)(364,602)(365,575)(366,576)(367,577)
(368,578)(369,579)(370,580)(371,581)(372,582)(373,583)(374,584)(375,585)
(376,586)(377,587)(378,588)(379,561)(380,562)(381,563)(382,564)(383,565)
(384,566)(385,567)(386,568)(387,569)(388,570)(389,571)(390,572)(391,573)
(392,574)(393,659)(394,660)(395,661)(396,662)(397,663)(398,664)(399,665)
(400,666)(401,667)(402,668)(403,669)(404,670)(405,671)(406,672)(407,645)
(408,646)(409,647)(410,648)(411,649)(412,650)(413,651)(414,652)(415,653)
(416,654)(417,655)(418,656)(419,657)(420,658)(421,631)(422,632)(423,633)
(424,634)(425,635)(426,636)(427,637)(428,638)(429,639)(430,640)(431,641)
(432,642)(433,643)(434,644)(435,617)(436,618)(437,619)(438,620)(439,621)
(440,622)(441,623)(442,624)(443,625)(444,626)(445,627)(446,628)(447,629)
(448,630);
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, 36)( 30, 42)( 31, 41)
( 32, 40)( 33, 39)( 34, 38)( 35, 37)( 43, 50)( 44, 56)( 45, 55)( 46, 54)
( 47, 53)( 48, 52)( 49, 51)( 57, 71)( 58, 77)( 59, 76)( 60, 75)( 61, 74)
( 62, 73)( 63, 72)( 64, 78)( 65, 84)( 66, 83)( 67, 82)( 68, 81)( 69, 80)
( 70, 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)(113,141)
(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)(127,155)(128,161)(129,160)
(130,159)(131,158)(132,157)(133,156)(134,162)(135,168)(136,167)(137,166)
(138,165)(139,164)(140,163)(169,211)(170,217)(171,216)(172,215)(173,214)
(174,213)(175,212)(176,218)(177,224)(178,223)(179,222)(180,221)(181,220)
(182,219)(183,197)(184,203)(185,202)(186,201)(187,200)(188,199)(189,198)
(190,204)(191,210)(192,209)(193,208)(194,207)(195,206)(196,205)(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)(253,316)(254,322)(255,321)(256,320)(257,319)
(258,318)(259,317)(260,309)(261,315)(262,314)(263,313)(264,312)(265,311)
(266,310)(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)(337,421)
(338,427)(339,426)(340,425)(341,424)(342,423)(343,422)(344,428)(345,434)
(346,433)(347,432)(348,431)(349,430)(350,429)(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)(365,393)(366,399)(367,398)(368,397)(369,396)
(370,395)(371,394)(372,400)(373,406)(374,405)(375,404)(376,403)(377,402)
(378,401)(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)(463,575)(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)(477,596)(478,602)(479,601)(480,600)(481,599)
(482,598)(483,597)(484,589)(485,595)(486,594)(487,593)(488,592)(489,591)
(490,590)(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)(505,631)
(506,637)(507,636)(508,635)(509,634)(510,633)(511,632)(512,638)(513,644)
(514,643)(515,642)(516,641)(517,640)(518,639)(519,617)(520,623)(521,622)
(522,621)(523,620)(524,619)(525,618)(526,624)(527,630)(528,629)(529,628)
(530,627)(531,626)(532,625)(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)(673,855)
(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)(687,841)(688,847)(689,846)
(690,845)(691,844)(692,843)(693,842)(694,848)(695,854)(696,853)(697,852)
(698,851)(699,850)(700,849)(701,890)(702,896)(703,895)(704,894)(705,893)
(706,892)(707,891)(708,883)(709,889)(710,888)(711,887)(712,886)(713,885)
(714,884)(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)(743,785)(744,791)(745,790)
(746,789)(747,788)(748,787)(749,786)(750,792)(751,798)(752,797)(753,796)
(754,795)(755,794)(756,793)(757,834)(758,840)(759,839)(760,838)(761,837)
(762,836)(763,835)(764,827)(765,833)(766,832)(767,831)(768,830)(769,829)
(770,828)(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)!( 1,226)( 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)( 15,240)
( 16,239)( 17,245)( 18,244)( 19,243)( 20,242)( 21,241)( 22,247)( 23,246)
( 24,252)( 25,251)( 26,250)( 27,249)( 28,248)( 29,254)( 30,253)( 31,259)
( 32,258)( 33,257)( 34,256)( 35,255)( 36,261)( 37,260)( 38,266)( 39,265)
( 40,264)( 41,263)( 42,262)( 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)( 57,296)( 58,295)( 59,301)( 60,300)( 61,299)( 62,298)( 63,297)
( 64,303)( 65,302)( 66,308)( 67,307)( 68,306)( 69,305)( 70,304)( 71,282)
( 72,281)( 73,287)( 74,286)( 75,285)( 76,284)( 77,283)( 78,289)( 79,288)
( 80,294)( 81,293)( 82,292)( 83,291)( 84,290)( 85,324)( 86,323)( 87,329)
( 88,328)( 89,327)( 90,326)( 91,325)( 92,331)( 93,330)( 94,336)( 95,335)
( 96,334)( 97,333)( 98,332)( 99,310)(100,309)(101,315)(102,314)(103,313)
(104,312)(105,311)(106,317)(107,316)(108,322)(109,321)(110,320)(111,319)
(112,318)(113,352)(114,351)(115,357)(116,356)(117,355)(118,354)(119,353)
(120,359)(121,358)(122,364)(123,363)(124,362)(125,361)(126,360)(127,338)
(128,337)(129,343)(130,342)(131,341)(132,340)(133,339)(134,345)(135,344)
(136,350)(137,349)(138,348)(139,347)(140,346)(141,380)(142,379)(143,385)
(144,384)(145,383)(146,382)(147,381)(148,387)(149,386)(150,392)(151,391)
(152,390)(153,389)(154,388)(155,366)(156,365)(157,371)(158,370)(159,369)
(160,368)(161,367)(162,373)(163,372)(164,378)(165,377)(166,376)(167,375)
(168,374)(169,394)(170,393)(171,399)(172,398)(173,397)(174,396)(175,395)
(176,401)(177,400)(178,406)(179,405)(180,404)(181,403)(182,402)(183,408)
(184,407)(185,413)(186,412)(187,411)(188,410)(189,409)(190,415)(191,414)
(192,420)(193,419)(194,418)(195,417)(196,416)(197,422)(198,421)(199,427)
(200,426)(201,425)(202,424)(203,423)(204,429)(205,428)(206,434)(207,433)
(208,432)(209,431)(210,430)(211,436)(212,435)(213,441)(214,440)(215,439)
(216,438)(217,437)(218,443)(219,442)(220,448)(221,447)(222,446)(223,445)
(224,444)(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)(463,688)
(464,687)(465,693)(466,692)(467,691)(468,690)(469,689)(470,695)(471,694)
(472,700)(473,699)(474,698)(475,697)(476,696)(477,702)(478,701)(479,707)
(480,706)(481,705)(482,704)(483,703)(484,709)(485,708)(486,714)(487,713)
(488,712)(489,711)(490,710)(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)(505,744)(506,743)(507,749)(508,748)(509,747)(510,746)(511,745)
(512,751)(513,750)(514,756)(515,755)(516,754)(517,753)(518,752)(519,730)
(520,729)(521,735)(522,734)(523,733)(524,732)(525,731)(526,737)(527,736)
(528,742)(529,741)(530,740)(531,739)(532,738)(533,772)(534,771)(535,777)
(536,776)(537,775)(538,774)(539,773)(540,779)(541,778)(542,784)(543,783)
(544,782)(545,781)(546,780)(547,758)(548,757)(549,763)(550,762)(551,761)
(552,760)(553,759)(554,765)(555,764)(556,770)(557,769)(558,768)(559,767)
(560,766)(561,800)(562,799)(563,805)(564,804)(565,803)(566,802)(567,801)
(568,807)(569,806)(570,812)(571,811)(572,810)(573,809)(574,808)(575,786)
(576,785)(577,791)(578,790)(579,789)(580,788)(581,787)(582,793)(583,792)
(584,798)(585,797)(586,796)(587,795)(588,794)(589,828)(590,827)(591,833)
(592,832)(593,831)(594,830)(595,829)(596,835)(597,834)(598,840)(599,839)
(600,838)(601,837)(602,836)(603,814)(604,813)(605,819)(606,818)(607,817)
(608,816)(609,815)(610,821)(611,820)(612,826)(613,825)(614,824)(615,823)
(616,822)(617,842)(618,841)(619,847)(620,846)(621,845)(622,844)(623,843)
(624,849)(625,848)(626,854)(627,853)(628,852)(629,851)(630,850)(631,856)
(632,855)(633,861)(634,860)(635,859)(636,858)(637,857)(638,863)(639,862)
(640,868)(641,867)(642,866)(643,865)(644,864)(645,870)(646,869)(647,875)
(648,874)(649,873)(650,872)(651,871)(652,877)(653,876)(654,882)(655,881)
(656,880)(657,879)(658,878)(659,884)(660,883)(661,889)(662,888)(663,887)
(664,886)(665,885)(666,891)(667,890)(668,896)(669,895)(670,894)(671,893)
(672,892);
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*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,
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*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*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope