Polytope of Type {56,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {56,8}*1792h
if this polytope has a name.
Group : SmallGroup(1792,90329)
Rank : 3
Schlafli Type : {56,8}
Number of vertices, edges, etc : 112, 448, 16
Order of s0s1s2 : 56
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Petrie
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 : {28,8}*896b
4-fold quotients : {28,4}*448
7-fold quotients : {8,8}*256g
8-fold quotients : {28,4}*224
14-fold quotients : {4,8}*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 := ( 1,225)( 2,231)( 3,230)( 4,229)( 5,228)( 6,227)( 7,226)( 8,232)
( 9,238)( 10,237)( 11,236)( 12,235)( 13,234)( 14,233)( 15,246)( 16,252)
( 17,251)( 18,250)( 19,249)( 20,248)( 21,247)( 22,239)( 23,245)( 24,244)
( 25,243)( 26,242)( 27,241)( 28,240)( 29,260)( 30,266)( 31,265)( 32,264)
( 33,263)( 34,262)( 35,261)( 36,253)( 37,259)( 38,258)( 39,257)( 40,256)
( 41,255)( 42,254)( 43,267)( 44,273)( 45,272)( 46,271)( 47,270)( 48,269)
( 49,268)( 50,274)( 51,280)( 52,279)( 53,278)( 54,277)( 55,276)( 56,275)
( 57,288)( 58,294)( 59,293)( 60,292)( 61,291)( 62,290)( 63,289)( 64,281)
( 65,287)( 66,286)( 67,285)( 68,284)( 69,283)( 70,282)( 71,295)( 72,301)
( 73,300)( 74,299)( 75,298)( 76,297)( 77,296)( 78,302)( 79,308)( 80,307)
( 81,306)( 82,305)( 83,304)( 84,303)( 85,309)( 86,315)( 87,314)( 88,313)
( 89,312)( 90,311)( 91,310)( 92,316)( 93,322)( 94,321)( 95,320)( 96,319)
( 97,318)( 98,317)( 99,330)(100,336)(101,335)(102,334)(103,333)(104,332)
(105,331)(106,323)(107,329)(108,328)(109,327)(110,326)(111,325)(112,324)
(113,365)(114,371)(115,370)(116,369)(117,368)(118,367)(119,366)(120,372)
(121,378)(122,377)(123,376)(124,375)(125,374)(126,373)(127,386)(128,392)
(129,391)(130,390)(131,389)(132,388)(133,387)(134,379)(135,385)(136,384)
(137,383)(138,382)(139,381)(140,380)(141,337)(142,343)(143,342)(144,341)
(145,340)(146,339)(147,338)(148,344)(149,350)(150,349)(151,348)(152,347)
(153,346)(154,345)(155,358)(156,364)(157,363)(158,362)(159,361)(160,360)
(161,359)(162,351)(163,357)(164,356)(165,355)(166,354)(167,353)(168,352)
(169,421)(170,427)(171,426)(172,425)(173,424)(174,423)(175,422)(176,428)
(177,434)(178,433)(179,432)(180,431)(181,430)(182,429)(183,442)(184,448)
(185,447)(186,446)(187,445)(188,444)(189,443)(190,435)(191,441)(192,440)
(193,439)(194,438)(195,437)(196,436)(197,393)(198,399)(199,398)(200,397)
(201,396)(202,395)(203,394)(204,400)(205,406)(206,405)(207,404)(208,403)
(209,402)(210,401)(211,414)(212,420)(213,419)(214,418)(215,417)(216,416)
(217,415)(218,407)(219,413)(220,412)(221,411)(222,410)(223,409)(224,408)
(449,673)(450,679)(451,678)(452,677)(453,676)(454,675)(455,674)(456,680)
(457,686)(458,685)(459,684)(460,683)(461,682)(462,681)(463,694)(464,700)
(465,699)(466,698)(467,697)(468,696)(469,695)(470,687)(471,693)(472,692)
(473,691)(474,690)(475,689)(476,688)(477,708)(478,714)(479,713)(480,712)
(481,711)(482,710)(483,709)(484,701)(485,707)(486,706)(487,705)(488,704)
(489,703)(490,702)(491,715)(492,721)(493,720)(494,719)(495,718)(496,717)
(497,716)(498,722)(499,728)(500,727)(501,726)(502,725)(503,724)(504,723)
(505,736)(506,742)(507,741)(508,740)(509,739)(510,738)(511,737)(512,729)
(513,735)(514,734)(515,733)(516,732)(517,731)(518,730)(519,743)(520,749)
(521,748)(522,747)(523,746)(524,745)(525,744)(526,750)(527,756)(528,755)
(529,754)(530,753)(531,752)(532,751)(533,757)(534,763)(535,762)(536,761)
(537,760)(538,759)(539,758)(540,764)(541,770)(542,769)(543,768)(544,767)
(545,766)(546,765)(547,778)(548,784)(549,783)(550,782)(551,781)(552,780)
(553,779)(554,771)(555,777)(556,776)(557,775)(558,774)(559,773)(560,772)
(561,813)(562,819)(563,818)(564,817)(565,816)(566,815)(567,814)(568,820)
(569,826)(570,825)(571,824)(572,823)(573,822)(574,821)(575,834)(576,840)
(577,839)(578,838)(579,837)(580,836)(581,835)(582,827)(583,833)(584,832)
(585,831)(586,830)(587,829)(588,828)(589,785)(590,791)(591,790)(592,789)
(593,788)(594,787)(595,786)(596,792)(597,798)(598,797)(599,796)(600,795)
(601,794)(602,793)(603,806)(604,812)(605,811)(606,810)(607,809)(608,808)
(609,807)(610,799)(611,805)(612,804)(613,803)(614,802)(615,801)(616,800)
(617,869)(618,875)(619,874)(620,873)(621,872)(622,871)(623,870)(624,876)
(625,882)(626,881)(627,880)(628,879)(629,878)(630,877)(631,890)(632,896)
(633,895)(634,894)(635,893)(636,892)(637,891)(638,883)(639,889)(640,888)
(641,887)(642,886)(643,885)(644,884)(645,841)(646,847)(647,846)(648,845)
(649,844)(650,843)(651,842)(652,848)(653,854)(654,853)(655,852)(656,851)
(657,850)(658,849)(659,862)(660,868)(661,867)(662,866)(663,865)(664,864)
(665,863)(666,855)(667,861)(668,860)(669,859)(670,858)(671,857)(672,856);;
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, 65)( 58, 64)( 59, 70)( 60, 69)( 61, 68)( 62, 67)
( 63, 66)( 71, 79)( 72, 78)( 73, 84)( 74, 83)( 75, 82)( 76, 81)( 77, 80)
( 85,107)( 86,106)( 87,112)( 88,111)( 89,110)( 90,109)( 91,108)( 92,100)
( 93, 99)( 94,105)( 95,104)( 96,103)( 97,102)( 98,101)(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)(169,170)(171,175)(172,174)(176,177)(178,182)(179,181)
(183,184)(185,189)(186,188)(190,191)(192,196)(193,195)(197,212)(198,211)
(199,217)(200,216)(201,215)(202,214)(203,213)(204,219)(205,218)(206,224)
(207,223)(208,222)(209,221)(210,220)(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)(505,625)(506,624)(507,630)(508,629)
(509,628)(510,627)(511,626)(512,618)(513,617)(514,623)(515,622)(516,621)
(517,620)(518,619)(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)
(533,667)(534,666)(535,672)(536,671)(537,670)(538,669)(539,668)(540,660)
(541,659)(542,665)(543,664)(544,663)(545,662)(546,661)(547,653)(548,652)
(549,658)(550,657)(551,656)(552,655)(553,654)(554,646)(555,645)(556,651)
(557,650)(558,649)(559,648)(560,647)(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 := ( 1,673)( 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);;
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*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(896)!( 1,225)( 2,231)( 3,230)( 4,229)( 5,228)( 6,227)( 7,226)
( 8,232)( 9,238)( 10,237)( 11,236)( 12,235)( 13,234)( 14,233)( 15,246)
( 16,252)( 17,251)( 18,250)( 19,249)( 20,248)( 21,247)( 22,239)( 23,245)
( 24,244)( 25,243)( 26,242)( 27,241)( 28,240)( 29,260)( 30,266)( 31,265)
( 32,264)( 33,263)( 34,262)( 35,261)( 36,253)( 37,259)( 38,258)( 39,257)
( 40,256)( 41,255)( 42,254)( 43,267)( 44,273)( 45,272)( 46,271)( 47,270)
( 48,269)( 49,268)( 50,274)( 51,280)( 52,279)( 53,278)( 54,277)( 55,276)
( 56,275)( 57,288)( 58,294)( 59,293)( 60,292)( 61,291)( 62,290)( 63,289)
( 64,281)( 65,287)( 66,286)( 67,285)( 68,284)( 69,283)( 70,282)( 71,295)
( 72,301)( 73,300)( 74,299)( 75,298)( 76,297)( 77,296)( 78,302)( 79,308)
( 80,307)( 81,306)( 82,305)( 83,304)( 84,303)( 85,309)( 86,315)( 87,314)
( 88,313)( 89,312)( 90,311)( 91,310)( 92,316)( 93,322)( 94,321)( 95,320)
( 96,319)( 97,318)( 98,317)( 99,330)(100,336)(101,335)(102,334)(103,333)
(104,332)(105,331)(106,323)(107,329)(108,328)(109,327)(110,326)(111,325)
(112,324)(113,365)(114,371)(115,370)(116,369)(117,368)(118,367)(119,366)
(120,372)(121,378)(122,377)(123,376)(124,375)(125,374)(126,373)(127,386)
(128,392)(129,391)(130,390)(131,389)(132,388)(133,387)(134,379)(135,385)
(136,384)(137,383)(138,382)(139,381)(140,380)(141,337)(142,343)(143,342)
(144,341)(145,340)(146,339)(147,338)(148,344)(149,350)(150,349)(151,348)
(152,347)(153,346)(154,345)(155,358)(156,364)(157,363)(158,362)(159,361)
(160,360)(161,359)(162,351)(163,357)(164,356)(165,355)(166,354)(167,353)
(168,352)(169,421)(170,427)(171,426)(172,425)(173,424)(174,423)(175,422)
(176,428)(177,434)(178,433)(179,432)(180,431)(181,430)(182,429)(183,442)
(184,448)(185,447)(186,446)(187,445)(188,444)(189,443)(190,435)(191,441)
(192,440)(193,439)(194,438)(195,437)(196,436)(197,393)(198,399)(199,398)
(200,397)(201,396)(202,395)(203,394)(204,400)(205,406)(206,405)(207,404)
(208,403)(209,402)(210,401)(211,414)(212,420)(213,419)(214,418)(215,417)
(216,416)(217,415)(218,407)(219,413)(220,412)(221,411)(222,410)(223,409)
(224,408)(449,673)(450,679)(451,678)(452,677)(453,676)(454,675)(455,674)
(456,680)(457,686)(458,685)(459,684)(460,683)(461,682)(462,681)(463,694)
(464,700)(465,699)(466,698)(467,697)(468,696)(469,695)(470,687)(471,693)
(472,692)(473,691)(474,690)(475,689)(476,688)(477,708)(478,714)(479,713)
(480,712)(481,711)(482,710)(483,709)(484,701)(485,707)(486,706)(487,705)
(488,704)(489,703)(490,702)(491,715)(492,721)(493,720)(494,719)(495,718)
(496,717)(497,716)(498,722)(499,728)(500,727)(501,726)(502,725)(503,724)
(504,723)(505,736)(506,742)(507,741)(508,740)(509,739)(510,738)(511,737)
(512,729)(513,735)(514,734)(515,733)(516,732)(517,731)(518,730)(519,743)
(520,749)(521,748)(522,747)(523,746)(524,745)(525,744)(526,750)(527,756)
(528,755)(529,754)(530,753)(531,752)(532,751)(533,757)(534,763)(535,762)
(536,761)(537,760)(538,759)(539,758)(540,764)(541,770)(542,769)(543,768)
(544,767)(545,766)(546,765)(547,778)(548,784)(549,783)(550,782)(551,781)
(552,780)(553,779)(554,771)(555,777)(556,776)(557,775)(558,774)(559,773)
(560,772)(561,813)(562,819)(563,818)(564,817)(565,816)(566,815)(567,814)
(568,820)(569,826)(570,825)(571,824)(572,823)(573,822)(574,821)(575,834)
(576,840)(577,839)(578,838)(579,837)(580,836)(581,835)(582,827)(583,833)
(584,832)(585,831)(586,830)(587,829)(588,828)(589,785)(590,791)(591,790)
(592,789)(593,788)(594,787)(595,786)(596,792)(597,798)(598,797)(599,796)
(600,795)(601,794)(602,793)(603,806)(604,812)(605,811)(606,810)(607,809)
(608,808)(609,807)(610,799)(611,805)(612,804)(613,803)(614,802)(615,801)
(616,800)(617,869)(618,875)(619,874)(620,873)(621,872)(622,871)(623,870)
(624,876)(625,882)(626,881)(627,880)(628,879)(629,878)(630,877)(631,890)
(632,896)(633,895)(634,894)(635,893)(636,892)(637,891)(638,883)(639,889)
(640,888)(641,887)(642,886)(643,885)(644,884)(645,841)(646,847)(647,846)
(648,845)(649,844)(650,843)(651,842)(652,848)(653,854)(654,853)(655,852)
(656,851)(657,850)(658,849)(659,862)(660,868)(661,867)(662,866)(663,865)
(664,864)(665,863)(666,855)(667,861)(668,860)(669,859)(670,858)(671,857)
(672,856);
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, 65)( 58, 64)( 59, 70)( 60, 69)( 61, 68)
( 62, 67)( 63, 66)( 71, 79)( 72, 78)( 73, 84)( 74, 83)( 75, 82)( 76, 81)
( 77, 80)( 85,107)( 86,106)( 87,112)( 88,111)( 89,110)( 90,109)( 91,108)
( 92,100)( 93, 99)( 94,105)( 95,104)( 96,103)( 97,102)( 98,101)(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)(169,170)(171,175)(172,174)(176,177)(178,182)
(179,181)(183,184)(185,189)(186,188)(190,191)(192,196)(193,195)(197,212)
(198,211)(199,217)(200,216)(201,215)(202,214)(203,213)(204,219)(205,218)
(206,224)(207,223)(208,222)(209,221)(210,220)(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)(505,625)(506,624)(507,630)
(508,629)(509,628)(510,627)(511,626)(512,618)(513,617)(514,623)(515,622)
(516,621)(517,620)(518,619)(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)(533,667)(534,666)(535,672)(536,671)(537,670)(538,669)(539,668)
(540,660)(541,659)(542,665)(543,664)(544,663)(545,662)(546,661)(547,653)
(548,652)(549,658)(550,657)(551,656)(552,655)(553,654)(554,646)(555,645)
(556,651)(557,650)(558,649)(559,648)(560,647)(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)!( 1,673)( 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);
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*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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*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 >;
References : None.
to this polytope