Polytope of Type {56,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {56,4}*1792c
if this polytope has a name.
Group : SmallGroup(1792,90302)
Rank : 3
Schlafli Type : {56,4}
Number of vertices, edges, etc : 224, 448, 16
Order of s0s1s2 : 56
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {28,4}*896
4-fold quotients : {28,4}*448
7-fold quotients : {8,4}*256c
8-fold quotients : {28,4}*224
14-fold quotients : {4,4}*128
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 := ( 1,449)( 2,455)( 3,454)( 4,453)( 5,452)( 6,451)( 7,450)( 8,456)
( 9,462)( 10,461)( 11,460)( 12,459)( 13,458)( 14,457)( 15,470)( 16,476)
( 17,475)( 18,474)( 19,473)( 20,472)( 21,471)( 22,463)( 23,469)( 24,468)
( 25,467)( 26,466)( 27,465)( 28,464)( 29,477)( 30,483)( 31,482)( 32,481)
( 33,480)( 34,479)( 35,478)( 36,484)( 37,490)( 38,489)( 39,488)( 40,487)
( 41,486)( 42,485)( 43,498)( 44,504)( 45,503)( 46,502)( 47,501)( 48,500)
( 49,499)( 50,491)( 51,497)( 52,496)( 53,495)( 54,494)( 55,493)( 56,492)
( 57,554)( 58,560)( 59,559)( 60,558)( 61,557)( 62,556)( 63,555)( 64,547)
( 65,553)( 66,552)( 67,551)( 68,550)( 69,549)( 70,548)( 71,533)( 72,539)
( 73,538)( 74,537)( 75,536)( 76,535)( 77,534)( 78,540)( 79,546)( 80,545)
( 81,544)( 82,543)( 83,542)( 84,541)( 85,519)( 86,525)( 87,524)( 88,523)
( 89,522)( 90,521)( 91,520)( 92,526)( 93,532)( 94,531)( 95,530)( 96,529)
( 97,528)( 98,527)( 99,512)(100,518)(101,517)(102,516)(103,515)(104,514)
(105,513)(106,505)(107,511)(108,510)(109,509)(110,508)(111,507)(112,506)
(113,568)(114,574)(115,573)(116,572)(117,571)(118,570)(119,569)(120,561)
(121,567)(122,566)(123,565)(124,564)(125,563)(126,562)(127,575)(128,581)
(129,580)(130,579)(131,578)(132,577)(133,576)(134,582)(135,588)(136,587)
(137,586)(138,585)(139,584)(140,583)(141,596)(142,602)(143,601)(144,600)
(145,599)(146,598)(147,597)(148,589)(149,595)(150,594)(151,593)(152,592)
(153,591)(154,590)(155,603)(156,609)(157,608)(158,607)(159,606)(160,605)
(161,604)(162,610)(163,616)(164,615)(165,614)(166,613)(167,612)(168,611)
(169,659)(170,665)(171,664)(172,663)(173,662)(174,661)(175,660)(176,666)
(177,672)(178,671)(179,670)(180,669)(181,668)(182,667)(183,652)(184,658)
(185,657)(186,656)(187,655)(188,654)(189,653)(190,645)(191,651)(192,650)
(193,649)(194,648)(195,647)(196,646)(197,638)(198,644)(199,643)(200,642)
(201,641)(202,640)(203,639)(204,631)(205,637)(206,636)(207,635)(208,634)
(209,633)(210,632)(211,617)(212,623)(213,622)(214,621)(215,620)(216,619)
(217,618)(218,624)(219,630)(220,629)(221,628)(222,627)(223,626)(224,625)
(225,673)(226,679)(227,678)(228,677)(229,676)(230,675)(231,674)(232,680)
(233,686)(234,685)(235,684)(236,683)(237,682)(238,681)(239,694)(240,700)
(241,699)(242,698)(243,697)(244,696)(245,695)(246,687)(247,693)(248,692)
(249,691)(250,690)(251,689)(252,688)(253,701)(254,707)(255,706)(256,705)
(257,704)(258,703)(259,702)(260,708)(261,714)(262,713)(263,712)(264,711)
(265,710)(266,709)(267,722)(268,728)(269,727)(270,726)(271,725)(272,724)
(273,723)(274,715)(275,721)(276,720)(277,719)(278,718)(279,717)(280,716)
(281,778)(282,784)(283,783)(284,782)(285,781)(286,780)(287,779)(288,771)
(289,777)(290,776)(291,775)(292,774)(293,773)(294,772)(295,757)(296,763)
(297,762)(298,761)(299,760)(300,759)(301,758)(302,764)(303,770)(304,769)
(305,768)(306,767)(307,766)(308,765)(309,743)(310,749)(311,748)(312,747)
(313,746)(314,745)(315,744)(316,750)(317,756)(318,755)(319,754)(320,753)
(321,752)(322,751)(323,736)(324,742)(325,741)(326,740)(327,739)(328,738)
(329,737)(330,729)(331,735)(332,734)(333,733)(334,732)(335,731)(336,730)
(337,792)(338,798)(339,797)(340,796)(341,795)(342,794)(343,793)(344,785)
(345,791)(346,790)(347,789)(348,788)(349,787)(350,786)(351,799)(352,805)
(353,804)(354,803)(355,802)(356,801)(357,800)(358,806)(359,812)(360,811)
(361,810)(362,809)(363,808)(364,807)(365,820)(366,826)(367,825)(368,824)
(369,823)(370,822)(371,821)(372,813)(373,819)(374,818)(375,817)(376,816)
(377,815)(378,814)(379,827)(380,833)(381,832)(382,831)(383,830)(384,829)
(385,828)(386,834)(387,840)(388,839)(389,838)(390,837)(391,836)(392,835)
(393,883)(394,889)(395,888)(396,887)(397,886)(398,885)(399,884)(400,890)
(401,896)(402,895)(403,894)(404,893)(405,892)(406,891)(407,876)(408,882)
(409,881)(410,880)(411,879)(412,878)(413,877)(414,869)(415,875)(416,874)
(417,873)(418,872)(419,871)(420,870)(421,862)(422,868)(423,867)(424,866)
(425,865)(426,864)(427,863)(428,855)(429,861)(430,860)(431,859)(432,858)
(433,857)(434,856)(435,841)(436,847)(437,846)(438,845)(439,844)(440,843)
(441,842)(442,848)(443,854)(444,853)(445,852)(446,851)(447,850)(448,849);;
s1 := ( 1, 2)( 3, 7)( 4, 6)( 8, 9)( 10, 14)( 11, 13)( 15, 16)( 17, 21)
( 18, 20)( 22, 23)( 24, 28)( 25, 27)( 29, 44)( 30, 43)( 31, 49)( 32, 48)
( 33, 47)( 34, 46)( 35, 45)( 36, 51)( 37, 50)( 38, 56)( 39, 55)( 40, 54)
( 41, 53)( 42, 52)( 57, 58)( 59, 63)( 60, 62)( 64, 65)( 66, 70)( 67, 69)
( 71, 72)( 73, 77)( 74, 76)( 78, 79)( 80, 84)( 81, 83)( 85,100)( 86, 99)
( 87,105)( 88,104)( 89,103)( 90,102)( 91,101)( 92,107)( 93,106)( 94,112)
( 95,111)( 96,110)( 97,109)( 98,108)(113,121)(114,120)(115,126)(116,125)
(117,124)(118,123)(119,122)(127,135)(128,134)(129,140)(130,139)(131,138)
(132,137)(133,136)(141,163)(142,162)(143,168)(144,167)(145,166)(146,165)
(147,164)(148,156)(149,155)(150,161)(151,160)(152,159)(153,158)(154,157)
(169,177)(170,176)(171,182)(172,181)(173,180)(174,179)(175,178)(183,191)
(184,190)(185,196)(186,195)(187,194)(188,193)(189,192)(197,219)(198,218)
(199,224)(200,223)(201,222)(202,221)(203,220)(204,212)(205,211)(206,217)
(207,216)(208,215)(209,214)(210,213)(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)(239,296)(240,295)(241,301)(242,300)(243,299)(244,298)
(245,297)(246,303)(247,302)(248,308)(249,307)(250,306)(251,305)(252,304)
(253,324)(254,323)(255,329)(256,328)(257,327)(258,326)(259,325)(260,331)
(261,330)(262,336)(263,335)(264,334)(265,333)(266,332)(267,310)(268,309)
(269,315)(270,314)(271,313)(272,312)(273,311)(274,317)(275,316)(276,322)
(277,321)(278,320)(279,319)(280,318)(337,408)(338,407)(339,413)(340,412)
(341,411)(342,410)(343,409)(344,415)(345,414)(346,420)(347,419)(348,418)
(349,417)(350,416)(351,394)(352,393)(353,399)(354,398)(355,397)(356,396)
(357,395)(358,401)(359,400)(360,406)(361,405)(362,404)(363,403)(364,402)
(365,422)(366,421)(367,427)(368,426)(369,425)(370,424)(371,423)(372,429)
(373,428)(374,434)(375,433)(376,432)(377,431)(378,430)(379,436)(380,435)
(381,441)(382,440)(383,439)(384,438)(385,437)(386,443)(387,442)(388,448)
(389,447)(390,446)(391,445)(392,444)(449,562)(450,561)(451,567)(452,566)
(453,565)(454,564)(455,563)(456,569)(457,568)(458,574)(459,573)(460,572)
(461,571)(462,570)(463,576)(464,575)(465,581)(466,580)(467,579)(468,578)
(469,577)(470,583)(471,582)(472,588)(473,587)(474,586)(475,585)(476,584)
(477,604)(478,603)(479,609)(480,608)(481,607)(482,606)(483,605)(484,611)
(485,610)(486,616)(487,615)(488,614)(489,613)(490,612)(491,590)(492,589)
(493,595)(494,594)(495,593)(496,592)(497,591)(498,597)(499,596)(500,602)
(501,601)(502,600)(503,599)(504,598)(505,618)(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)(519,632)(520,631)(521,637)(522,636)(523,635)(524,634)
(525,633)(526,639)(527,638)(528,644)(529,643)(530,642)(531,641)(532,640)
(533,660)(534,659)(535,665)(536,664)(537,663)(538,662)(539,661)(540,667)
(541,666)(542,672)(543,671)(544,670)(545,669)(546,668)(547,646)(548,645)
(549,651)(550,650)(551,649)(552,648)(553,647)(554,653)(555,652)(556,658)
(557,657)(558,656)(559,655)(560,654)(673,877)(674,876)(675,882)(676,881)
(677,880)(678,879)(679,878)(680,870)(681,869)(682,875)(683,874)(684,873)
(685,872)(686,871)(687,891)(688,890)(689,896)(690,895)(691,894)(692,893)
(693,892)(694,884)(695,883)(696,889)(697,888)(698,887)(699,886)(700,885)
(701,856)(702,855)(703,861)(704,860)(705,859)(706,858)(707,857)(708,863)
(709,862)(710,868)(711,867)(712,866)(713,865)(714,864)(715,842)(716,841)
(717,847)(718,846)(719,845)(720,844)(721,843)(722,849)(723,848)(724,854)
(725,853)(726,852)(727,851)(728,850)(729,814)(730,813)(731,819)(732,818)
(733,817)(734,816)(735,815)(736,821)(737,820)(738,826)(739,825)(740,824)
(741,823)(742,822)(743,828)(744,827)(745,833)(746,832)(747,831)(748,830)
(749,829)(750,835)(751,834)(752,840)(753,839)(754,838)(755,837)(756,836)
(757,807)(758,806)(759,812)(760,811)(761,810)(762,809)(763,808)(764,800)
(765,799)(766,805)(767,804)(768,803)(769,802)(770,801)(771,793)(772,792)
(773,798)(774,797)(775,796)(776,795)(777,794)(778,786)(779,785)(780,791)
(781,790)(782,789)(783,788)(784,787);;
s2 := ( 1,225)( 2,226)( 3,227)( 4,228)( 5,229)( 6,230)( 7,231)( 8,232)
( 9,233)( 10,234)( 11,235)( 12,236)( 13,237)( 14,238)( 15,246)( 16,247)
( 17,248)( 18,249)( 19,250)( 20,251)( 21,252)( 22,239)( 23,240)( 24,241)
( 25,242)( 26,243)( 27,244)( 28,245)( 29,260)( 30,261)( 31,262)( 32,263)
( 33,264)( 34,265)( 35,266)( 36,253)( 37,254)( 38,255)( 39,256)( 40,257)
( 41,258)( 42,259)( 43,267)( 44,268)( 45,269)( 46,270)( 47,271)( 48,272)
( 49,273)( 50,274)( 51,275)( 52,276)( 53,277)( 54,278)( 55,279)( 56,280)
( 57,281)( 58,282)( 59,283)( 60,284)( 61,285)( 62,286)( 63,287)( 64,288)
( 65,289)( 66,290)( 67,291)( 68,292)( 69,293)( 70,294)( 71,302)( 72,303)
( 73,304)( 74,305)( 75,306)( 76,307)( 77,308)( 78,295)( 79,296)( 80,297)
( 81,298)( 82,299)( 83,300)( 84,301)( 85,316)( 86,317)( 87,318)( 88,319)
( 89,320)( 90,321)( 91,322)( 92,309)( 93,310)( 94,311)( 95,312)( 96,313)
( 97,314)( 98,315)( 99,323)(100,324)(101,325)(102,326)(103,327)(104,328)
(105,329)(106,330)(107,331)(108,332)(109,333)(110,334)(111,335)(112,336)
(113,365)(114,366)(115,367)(116,368)(117,369)(118,370)(119,371)(120,372)
(121,373)(122,374)(123,375)(124,376)(125,377)(126,378)(127,386)(128,387)
(129,388)(130,389)(131,390)(132,391)(133,392)(134,379)(135,380)(136,381)
(137,382)(138,383)(139,384)(140,385)(141,337)(142,338)(143,339)(144,340)
(145,341)(146,342)(147,343)(148,344)(149,345)(150,346)(151,347)(152,348)
(153,349)(154,350)(155,358)(156,359)(157,360)(158,361)(159,362)(160,363)
(161,364)(162,351)(163,352)(164,353)(165,354)(166,355)(167,356)(168,357)
(169,428)(170,429)(171,430)(172,431)(173,432)(174,433)(175,434)(176,421)
(177,422)(178,423)(179,424)(180,425)(181,426)(182,427)(183,435)(184,436)
(185,437)(186,438)(187,439)(188,440)(189,441)(190,442)(191,443)(192,444)
(193,445)(194,446)(195,447)(196,448)(197,400)(198,401)(199,402)(200,403)
(201,404)(202,405)(203,406)(204,393)(205,394)(206,395)(207,396)(208,397)
(209,398)(210,399)(211,407)(212,408)(213,409)(214,410)(215,411)(216,412)
(217,413)(218,414)(219,415)(220,416)(221,417)(222,418)(223,419)(224,420)
(449,673)(450,674)(451,675)(452,676)(453,677)(454,678)(455,679)(456,680)
(457,681)(458,682)(459,683)(460,684)(461,685)(462,686)(463,694)(464,695)
(465,696)(466,697)(467,698)(468,699)(469,700)(470,687)(471,688)(472,689)
(473,690)(474,691)(475,692)(476,693)(477,708)(478,709)(479,710)(480,711)
(481,712)(482,713)(483,714)(484,701)(485,702)(486,703)(487,704)(488,705)
(489,706)(490,707)(491,715)(492,716)(493,717)(494,718)(495,719)(496,720)
(497,721)(498,722)(499,723)(500,724)(501,725)(502,726)(503,727)(504,728)
(505,729)(506,730)(507,731)(508,732)(509,733)(510,734)(511,735)(512,736)
(513,737)(514,738)(515,739)(516,740)(517,741)(518,742)(519,750)(520,751)
(521,752)(522,753)(523,754)(524,755)(525,756)(526,743)(527,744)(528,745)
(529,746)(530,747)(531,748)(532,749)(533,764)(534,765)(535,766)(536,767)
(537,768)(538,769)(539,770)(540,757)(541,758)(542,759)(543,760)(544,761)
(545,762)(546,763)(547,771)(548,772)(549,773)(550,774)(551,775)(552,776)
(553,777)(554,778)(555,779)(556,780)(557,781)(558,782)(559,783)(560,784)
(561,813)(562,814)(563,815)(564,816)(565,817)(566,818)(567,819)(568,820)
(569,821)(570,822)(571,823)(572,824)(573,825)(574,826)(575,834)(576,835)
(577,836)(578,837)(579,838)(580,839)(581,840)(582,827)(583,828)(584,829)
(585,830)(586,831)(587,832)(588,833)(589,785)(590,786)(591,787)(592,788)
(593,789)(594,790)(595,791)(596,792)(597,793)(598,794)(599,795)(600,796)
(601,797)(602,798)(603,806)(604,807)(605,808)(606,809)(607,810)(608,811)
(609,812)(610,799)(611,800)(612,801)(613,802)(614,803)(615,804)(616,805)
(617,876)(618,877)(619,878)(620,879)(621,880)(622,881)(623,882)(624,869)
(625,870)(626,871)(627,872)(628,873)(629,874)(630,875)(631,883)(632,884)
(633,885)(634,886)(635,887)(636,888)(637,889)(638,890)(639,891)(640,892)
(641,893)(642,894)(643,895)(644,896)(645,848)(646,849)(647,850)(648,851)
(649,852)(650,853)(651,854)(652,841)(653,842)(654,843)(655,844)(656,845)
(657,846)(658,847)(659,855)(660,856)(661,857)(662,858)(663,859)(664,860)
(665,861)(666,862)(667,863)(668,864)(669,865)(670,866)(671,867)(672,868);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*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*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(896)!( 1,449)( 2,455)( 3,454)( 4,453)( 5,452)( 6,451)( 7,450)
( 8,456)( 9,462)( 10,461)( 11,460)( 12,459)( 13,458)( 14,457)( 15,470)
( 16,476)( 17,475)( 18,474)( 19,473)( 20,472)( 21,471)( 22,463)( 23,469)
( 24,468)( 25,467)( 26,466)( 27,465)( 28,464)( 29,477)( 30,483)( 31,482)
( 32,481)( 33,480)( 34,479)( 35,478)( 36,484)( 37,490)( 38,489)( 39,488)
( 40,487)( 41,486)( 42,485)( 43,498)( 44,504)( 45,503)( 46,502)( 47,501)
( 48,500)( 49,499)( 50,491)( 51,497)( 52,496)( 53,495)( 54,494)( 55,493)
( 56,492)( 57,554)( 58,560)( 59,559)( 60,558)( 61,557)( 62,556)( 63,555)
( 64,547)( 65,553)( 66,552)( 67,551)( 68,550)( 69,549)( 70,548)( 71,533)
( 72,539)( 73,538)( 74,537)( 75,536)( 76,535)( 77,534)( 78,540)( 79,546)
( 80,545)( 81,544)( 82,543)( 83,542)( 84,541)( 85,519)( 86,525)( 87,524)
( 88,523)( 89,522)( 90,521)( 91,520)( 92,526)( 93,532)( 94,531)( 95,530)
( 96,529)( 97,528)( 98,527)( 99,512)(100,518)(101,517)(102,516)(103,515)
(104,514)(105,513)(106,505)(107,511)(108,510)(109,509)(110,508)(111,507)
(112,506)(113,568)(114,574)(115,573)(116,572)(117,571)(118,570)(119,569)
(120,561)(121,567)(122,566)(123,565)(124,564)(125,563)(126,562)(127,575)
(128,581)(129,580)(130,579)(131,578)(132,577)(133,576)(134,582)(135,588)
(136,587)(137,586)(138,585)(139,584)(140,583)(141,596)(142,602)(143,601)
(144,600)(145,599)(146,598)(147,597)(148,589)(149,595)(150,594)(151,593)
(152,592)(153,591)(154,590)(155,603)(156,609)(157,608)(158,607)(159,606)
(160,605)(161,604)(162,610)(163,616)(164,615)(165,614)(166,613)(167,612)
(168,611)(169,659)(170,665)(171,664)(172,663)(173,662)(174,661)(175,660)
(176,666)(177,672)(178,671)(179,670)(180,669)(181,668)(182,667)(183,652)
(184,658)(185,657)(186,656)(187,655)(188,654)(189,653)(190,645)(191,651)
(192,650)(193,649)(194,648)(195,647)(196,646)(197,638)(198,644)(199,643)
(200,642)(201,641)(202,640)(203,639)(204,631)(205,637)(206,636)(207,635)
(208,634)(209,633)(210,632)(211,617)(212,623)(213,622)(214,621)(215,620)
(216,619)(217,618)(218,624)(219,630)(220,629)(221,628)(222,627)(223,626)
(224,625)(225,673)(226,679)(227,678)(228,677)(229,676)(230,675)(231,674)
(232,680)(233,686)(234,685)(235,684)(236,683)(237,682)(238,681)(239,694)
(240,700)(241,699)(242,698)(243,697)(244,696)(245,695)(246,687)(247,693)
(248,692)(249,691)(250,690)(251,689)(252,688)(253,701)(254,707)(255,706)
(256,705)(257,704)(258,703)(259,702)(260,708)(261,714)(262,713)(263,712)
(264,711)(265,710)(266,709)(267,722)(268,728)(269,727)(270,726)(271,725)
(272,724)(273,723)(274,715)(275,721)(276,720)(277,719)(278,718)(279,717)
(280,716)(281,778)(282,784)(283,783)(284,782)(285,781)(286,780)(287,779)
(288,771)(289,777)(290,776)(291,775)(292,774)(293,773)(294,772)(295,757)
(296,763)(297,762)(298,761)(299,760)(300,759)(301,758)(302,764)(303,770)
(304,769)(305,768)(306,767)(307,766)(308,765)(309,743)(310,749)(311,748)
(312,747)(313,746)(314,745)(315,744)(316,750)(317,756)(318,755)(319,754)
(320,753)(321,752)(322,751)(323,736)(324,742)(325,741)(326,740)(327,739)
(328,738)(329,737)(330,729)(331,735)(332,734)(333,733)(334,732)(335,731)
(336,730)(337,792)(338,798)(339,797)(340,796)(341,795)(342,794)(343,793)
(344,785)(345,791)(346,790)(347,789)(348,788)(349,787)(350,786)(351,799)
(352,805)(353,804)(354,803)(355,802)(356,801)(357,800)(358,806)(359,812)
(360,811)(361,810)(362,809)(363,808)(364,807)(365,820)(366,826)(367,825)
(368,824)(369,823)(370,822)(371,821)(372,813)(373,819)(374,818)(375,817)
(376,816)(377,815)(378,814)(379,827)(380,833)(381,832)(382,831)(383,830)
(384,829)(385,828)(386,834)(387,840)(388,839)(389,838)(390,837)(391,836)
(392,835)(393,883)(394,889)(395,888)(396,887)(397,886)(398,885)(399,884)
(400,890)(401,896)(402,895)(403,894)(404,893)(405,892)(406,891)(407,876)
(408,882)(409,881)(410,880)(411,879)(412,878)(413,877)(414,869)(415,875)
(416,874)(417,873)(418,872)(419,871)(420,870)(421,862)(422,868)(423,867)
(424,866)(425,865)(426,864)(427,863)(428,855)(429,861)(430,860)(431,859)
(432,858)(433,857)(434,856)(435,841)(436,847)(437,846)(438,845)(439,844)
(440,843)(441,842)(442,848)(443,854)(444,853)(445,852)(446,851)(447,850)
(448,849);
s1 := Sym(896)!( 1, 2)( 3, 7)( 4, 6)( 8, 9)( 10, 14)( 11, 13)( 15, 16)
( 17, 21)( 18, 20)( 22, 23)( 24, 28)( 25, 27)( 29, 44)( 30, 43)( 31, 49)
( 32, 48)( 33, 47)( 34, 46)( 35, 45)( 36, 51)( 37, 50)( 38, 56)( 39, 55)
( 40, 54)( 41, 53)( 42, 52)( 57, 58)( 59, 63)( 60, 62)( 64, 65)( 66, 70)
( 67, 69)( 71, 72)( 73, 77)( 74, 76)( 78, 79)( 80, 84)( 81, 83)( 85,100)
( 86, 99)( 87,105)( 88,104)( 89,103)( 90,102)( 91,101)( 92,107)( 93,106)
( 94,112)( 95,111)( 96,110)( 97,109)( 98,108)(113,121)(114,120)(115,126)
(116,125)(117,124)(118,123)(119,122)(127,135)(128,134)(129,140)(130,139)
(131,138)(132,137)(133,136)(141,163)(142,162)(143,168)(144,167)(145,166)
(146,165)(147,164)(148,156)(149,155)(150,161)(151,160)(152,159)(153,158)
(154,157)(169,177)(170,176)(171,182)(172,181)(173,180)(174,179)(175,178)
(183,191)(184,190)(185,196)(186,195)(187,194)(188,193)(189,192)(197,219)
(198,218)(199,224)(200,223)(201,222)(202,221)(203,220)(204,212)(205,211)
(206,217)(207,216)(208,215)(209,214)(210,213)(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)(239,296)(240,295)(241,301)(242,300)(243,299)
(244,298)(245,297)(246,303)(247,302)(248,308)(249,307)(250,306)(251,305)
(252,304)(253,324)(254,323)(255,329)(256,328)(257,327)(258,326)(259,325)
(260,331)(261,330)(262,336)(263,335)(264,334)(265,333)(266,332)(267,310)
(268,309)(269,315)(270,314)(271,313)(272,312)(273,311)(274,317)(275,316)
(276,322)(277,321)(278,320)(279,319)(280,318)(337,408)(338,407)(339,413)
(340,412)(341,411)(342,410)(343,409)(344,415)(345,414)(346,420)(347,419)
(348,418)(349,417)(350,416)(351,394)(352,393)(353,399)(354,398)(355,397)
(356,396)(357,395)(358,401)(359,400)(360,406)(361,405)(362,404)(363,403)
(364,402)(365,422)(366,421)(367,427)(368,426)(369,425)(370,424)(371,423)
(372,429)(373,428)(374,434)(375,433)(376,432)(377,431)(378,430)(379,436)
(380,435)(381,441)(382,440)(383,439)(384,438)(385,437)(386,443)(387,442)
(388,448)(389,447)(390,446)(391,445)(392,444)(449,562)(450,561)(451,567)
(452,566)(453,565)(454,564)(455,563)(456,569)(457,568)(458,574)(459,573)
(460,572)(461,571)(462,570)(463,576)(464,575)(465,581)(466,580)(467,579)
(468,578)(469,577)(470,583)(471,582)(472,588)(473,587)(474,586)(475,585)
(476,584)(477,604)(478,603)(479,609)(480,608)(481,607)(482,606)(483,605)
(484,611)(485,610)(486,616)(487,615)(488,614)(489,613)(490,612)(491,590)
(492,589)(493,595)(494,594)(495,593)(496,592)(497,591)(498,597)(499,596)
(500,602)(501,601)(502,600)(503,599)(504,598)(505,618)(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)(519,632)(520,631)(521,637)(522,636)(523,635)
(524,634)(525,633)(526,639)(527,638)(528,644)(529,643)(530,642)(531,641)
(532,640)(533,660)(534,659)(535,665)(536,664)(537,663)(538,662)(539,661)
(540,667)(541,666)(542,672)(543,671)(544,670)(545,669)(546,668)(547,646)
(548,645)(549,651)(550,650)(551,649)(552,648)(553,647)(554,653)(555,652)
(556,658)(557,657)(558,656)(559,655)(560,654)(673,877)(674,876)(675,882)
(676,881)(677,880)(678,879)(679,878)(680,870)(681,869)(682,875)(683,874)
(684,873)(685,872)(686,871)(687,891)(688,890)(689,896)(690,895)(691,894)
(692,893)(693,892)(694,884)(695,883)(696,889)(697,888)(698,887)(699,886)
(700,885)(701,856)(702,855)(703,861)(704,860)(705,859)(706,858)(707,857)
(708,863)(709,862)(710,868)(711,867)(712,866)(713,865)(714,864)(715,842)
(716,841)(717,847)(718,846)(719,845)(720,844)(721,843)(722,849)(723,848)
(724,854)(725,853)(726,852)(727,851)(728,850)(729,814)(730,813)(731,819)
(732,818)(733,817)(734,816)(735,815)(736,821)(737,820)(738,826)(739,825)
(740,824)(741,823)(742,822)(743,828)(744,827)(745,833)(746,832)(747,831)
(748,830)(749,829)(750,835)(751,834)(752,840)(753,839)(754,838)(755,837)
(756,836)(757,807)(758,806)(759,812)(760,811)(761,810)(762,809)(763,808)
(764,800)(765,799)(766,805)(767,804)(768,803)(769,802)(770,801)(771,793)
(772,792)(773,798)(774,797)(775,796)(776,795)(777,794)(778,786)(779,785)
(780,791)(781,790)(782,789)(783,788)(784,787);
s2 := Sym(896)!( 1,225)( 2,226)( 3,227)( 4,228)( 5,229)( 6,230)( 7,231)
( 8,232)( 9,233)( 10,234)( 11,235)( 12,236)( 13,237)( 14,238)( 15,246)
( 16,247)( 17,248)( 18,249)( 19,250)( 20,251)( 21,252)( 22,239)( 23,240)
( 24,241)( 25,242)( 26,243)( 27,244)( 28,245)( 29,260)( 30,261)( 31,262)
( 32,263)( 33,264)( 34,265)( 35,266)( 36,253)( 37,254)( 38,255)( 39,256)
( 40,257)( 41,258)( 42,259)( 43,267)( 44,268)( 45,269)( 46,270)( 47,271)
( 48,272)( 49,273)( 50,274)( 51,275)( 52,276)( 53,277)( 54,278)( 55,279)
( 56,280)( 57,281)( 58,282)( 59,283)( 60,284)( 61,285)( 62,286)( 63,287)
( 64,288)( 65,289)( 66,290)( 67,291)( 68,292)( 69,293)( 70,294)( 71,302)
( 72,303)( 73,304)( 74,305)( 75,306)( 76,307)( 77,308)( 78,295)( 79,296)
( 80,297)( 81,298)( 82,299)( 83,300)( 84,301)( 85,316)( 86,317)( 87,318)
( 88,319)( 89,320)( 90,321)( 91,322)( 92,309)( 93,310)( 94,311)( 95,312)
( 96,313)( 97,314)( 98,315)( 99,323)(100,324)(101,325)(102,326)(103,327)
(104,328)(105,329)(106,330)(107,331)(108,332)(109,333)(110,334)(111,335)
(112,336)(113,365)(114,366)(115,367)(116,368)(117,369)(118,370)(119,371)
(120,372)(121,373)(122,374)(123,375)(124,376)(125,377)(126,378)(127,386)
(128,387)(129,388)(130,389)(131,390)(132,391)(133,392)(134,379)(135,380)
(136,381)(137,382)(138,383)(139,384)(140,385)(141,337)(142,338)(143,339)
(144,340)(145,341)(146,342)(147,343)(148,344)(149,345)(150,346)(151,347)
(152,348)(153,349)(154,350)(155,358)(156,359)(157,360)(158,361)(159,362)
(160,363)(161,364)(162,351)(163,352)(164,353)(165,354)(166,355)(167,356)
(168,357)(169,428)(170,429)(171,430)(172,431)(173,432)(174,433)(175,434)
(176,421)(177,422)(178,423)(179,424)(180,425)(181,426)(182,427)(183,435)
(184,436)(185,437)(186,438)(187,439)(188,440)(189,441)(190,442)(191,443)
(192,444)(193,445)(194,446)(195,447)(196,448)(197,400)(198,401)(199,402)
(200,403)(201,404)(202,405)(203,406)(204,393)(205,394)(206,395)(207,396)
(208,397)(209,398)(210,399)(211,407)(212,408)(213,409)(214,410)(215,411)
(216,412)(217,413)(218,414)(219,415)(220,416)(221,417)(222,418)(223,419)
(224,420)(449,673)(450,674)(451,675)(452,676)(453,677)(454,678)(455,679)
(456,680)(457,681)(458,682)(459,683)(460,684)(461,685)(462,686)(463,694)
(464,695)(465,696)(466,697)(467,698)(468,699)(469,700)(470,687)(471,688)
(472,689)(473,690)(474,691)(475,692)(476,693)(477,708)(478,709)(479,710)
(480,711)(481,712)(482,713)(483,714)(484,701)(485,702)(486,703)(487,704)
(488,705)(489,706)(490,707)(491,715)(492,716)(493,717)(494,718)(495,719)
(496,720)(497,721)(498,722)(499,723)(500,724)(501,725)(502,726)(503,727)
(504,728)(505,729)(506,730)(507,731)(508,732)(509,733)(510,734)(511,735)
(512,736)(513,737)(514,738)(515,739)(516,740)(517,741)(518,742)(519,750)
(520,751)(521,752)(522,753)(523,754)(524,755)(525,756)(526,743)(527,744)
(528,745)(529,746)(530,747)(531,748)(532,749)(533,764)(534,765)(535,766)
(536,767)(537,768)(538,769)(539,770)(540,757)(541,758)(542,759)(543,760)
(544,761)(545,762)(546,763)(547,771)(548,772)(549,773)(550,774)(551,775)
(552,776)(553,777)(554,778)(555,779)(556,780)(557,781)(558,782)(559,783)
(560,784)(561,813)(562,814)(563,815)(564,816)(565,817)(566,818)(567,819)
(568,820)(569,821)(570,822)(571,823)(572,824)(573,825)(574,826)(575,834)
(576,835)(577,836)(578,837)(579,838)(580,839)(581,840)(582,827)(583,828)
(584,829)(585,830)(586,831)(587,832)(588,833)(589,785)(590,786)(591,787)
(592,788)(593,789)(594,790)(595,791)(596,792)(597,793)(598,794)(599,795)
(600,796)(601,797)(602,798)(603,806)(604,807)(605,808)(606,809)(607,810)
(608,811)(609,812)(610,799)(611,800)(612,801)(613,802)(614,803)(615,804)
(616,805)(617,876)(618,877)(619,878)(620,879)(621,880)(622,881)(623,882)
(624,869)(625,870)(626,871)(627,872)(628,873)(629,874)(630,875)(631,883)
(632,884)(633,885)(634,886)(635,887)(636,888)(637,889)(638,890)(639,891)
(640,892)(641,893)(642,894)(643,895)(644,896)(645,848)(646,849)(647,850)
(648,851)(649,852)(650,853)(651,854)(652,841)(653,842)(654,843)(655,844)
(656,845)(657,846)(658,847)(659,855)(660,856)(661,857)(662,858)(663,859)
(664,860)(665,861)(666,862)(667,863)(668,864)(669,865)(670,866)(671,867)
(672,868);
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*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*s2 >;
References : None.
to this polytope