Polytope of Type {64,14}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {64,14}*1792
Also Known As : {64,14|2}. if this polytope has another name.
Group : SmallGroup(1792,90609)
Rank : 3
Schlafli Type : {64,14}
Number of vertices, edges, etc : 64, 448, 14
Order of s0s1s2 : 448
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 : {32,14}*896
4-fold quotients : {16,14}*448
7-fold quotients : {64,2}*256
8-fold quotients : {8,14}*224
14-fold quotients : {32,2}*128
16-fold quotients : {4,14}*112
28-fold quotients : {16,2}*64
32-fold quotients : {2,14}*56
56-fold quotients : {8,2}*32
64-fold quotients : {2,7}*28
112-fold quotients : {4,2}*16
224-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 15, 22)( 16, 23)( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 29, 43)
( 30, 44)( 31, 45)( 32, 46)( 33, 47)( 34, 48)( 35, 49)( 36, 50)( 37, 51)
( 38, 52)( 39, 53)( 40, 54)( 41, 55)( 42, 56)( 57, 85)( 58, 86)( 59, 87)
( 60, 88)( 61, 89)( 62, 90)( 63, 91)( 64, 92)( 65, 93)( 66, 94)( 67, 95)
( 68, 96)( 69, 97)( 70, 98)( 71,106)( 72,107)( 73,108)( 74,109)( 75,110)
( 76,111)( 77,112)( 78, 99)( 79,100)( 80,101)( 81,102)( 82,103)( 83,104)
( 84,105)(113,169)(114,170)(115,171)(116,172)(117,173)(118,174)(119,175)
(120,176)(121,177)(122,178)(123,179)(124,180)(125,181)(126,182)(127,190)
(128,191)(129,192)(130,193)(131,194)(132,195)(133,196)(134,183)(135,184)
(136,185)(137,186)(138,187)(139,188)(140,189)(141,211)(142,212)(143,213)
(144,214)(145,215)(146,216)(147,217)(148,218)(149,219)(150,220)(151,221)
(152,222)(153,223)(154,224)(155,197)(156,198)(157,199)(158,200)(159,201)
(160,202)(161,203)(162,204)(163,205)(164,206)(165,207)(166,208)(167,209)
(168,210)(239,246)(240,247)(241,248)(242,249)(243,250)(244,251)(245,252)
(253,267)(254,268)(255,269)(256,270)(257,271)(258,272)(259,273)(260,274)
(261,275)(262,276)(263,277)(264,278)(265,279)(266,280)(281,309)(282,310)
(283,311)(284,312)(285,313)(286,314)(287,315)(288,316)(289,317)(290,318)
(291,319)(292,320)(293,321)(294,322)(295,330)(296,331)(297,332)(298,333)
(299,334)(300,335)(301,336)(302,323)(303,324)(304,325)(305,326)(306,327)
(307,328)(308,329)(337,393)(338,394)(339,395)(340,396)(341,397)(342,398)
(343,399)(344,400)(345,401)(346,402)(347,403)(348,404)(349,405)(350,406)
(351,414)(352,415)(353,416)(354,417)(355,418)(356,419)(357,420)(358,407)
(359,408)(360,409)(361,410)(362,411)(363,412)(364,413)(365,435)(366,436)
(367,437)(368,438)(369,439)(370,440)(371,441)(372,442)(373,443)(374,444)
(375,445)(376,446)(377,447)(378,448)(379,421)(380,422)(381,423)(382,424)
(383,425)(384,426)(385,427)(386,428)(387,429)(388,430)(389,431)(390,432)
(391,433)(392,434)(449,561)(450,562)(451,563)(452,564)(453,565)(454,566)
(455,567)(456,568)(457,569)(458,570)(459,571)(460,572)(461,573)(462,574)
(463,582)(464,583)(465,584)(466,585)(467,586)(468,587)(469,588)(470,575)
(471,576)(472,577)(473,578)(474,579)(475,580)(476,581)(477,603)(478,604)
(479,605)(480,606)(481,607)(482,608)(483,609)(484,610)(485,611)(486,612)
(487,613)(488,614)(489,615)(490,616)(491,589)(492,590)(493,591)(494,592)
(495,593)(496,594)(497,595)(498,596)(499,597)(500,598)(501,599)(502,600)
(503,601)(504,602)(505,645)(506,646)(507,647)(508,648)(509,649)(510,650)
(511,651)(512,652)(513,653)(514,654)(515,655)(516,656)(517,657)(518,658)
(519,666)(520,667)(521,668)(522,669)(523,670)(524,671)(525,672)(526,659)
(527,660)(528,661)(529,662)(530,663)(531,664)(532,665)(533,617)(534,618)
(535,619)(536,620)(537,621)(538,622)(539,623)(540,624)(541,625)(542,626)
(543,627)(544,628)(545,629)(546,630)(547,638)(548,639)(549,640)(550,641)
(551,642)(552,643)(553,644)(554,631)(555,632)(556,633)(557,634)(558,635)
(559,636)(560,637)(673,785)(674,786)(675,787)(676,788)(677,789)(678,790)
(679,791)(680,792)(681,793)(682,794)(683,795)(684,796)(685,797)(686,798)
(687,806)(688,807)(689,808)(690,809)(691,810)(692,811)(693,812)(694,799)
(695,800)(696,801)(697,802)(698,803)(699,804)(700,805)(701,827)(702,828)
(703,829)(704,830)(705,831)(706,832)(707,833)(708,834)(709,835)(710,836)
(711,837)(712,838)(713,839)(714,840)(715,813)(716,814)(717,815)(718,816)
(719,817)(720,818)(721,819)(722,820)(723,821)(724,822)(725,823)(726,824)
(727,825)(728,826)(729,869)(730,870)(731,871)(732,872)(733,873)(734,874)
(735,875)(736,876)(737,877)(738,878)(739,879)(740,880)(741,881)(742,882)
(743,890)(744,891)(745,892)(746,893)(747,894)(748,895)(749,896)(750,883)
(751,884)(752,885)(753,886)(754,887)(755,888)(756,889)(757,841)(758,842)
(759,843)(760,844)(761,845)(762,846)(763,847)(764,848)(765,849)(766,850)
(767,851)(768,852)(769,853)(770,854)(771,862)(772,863)(773,864)(774,865)
(775,866)(776,867)(777,868)(778,855)(779,856)(780,857)(781,858)(782,859)
(783,860)(784,861);;
s1 := ( 1,673)( 2,679)( 3,678)( 4,677)( 5,676)( 6,675)( 7,674)( 8,680)
( 9,686)( 10,685)( 11,684)( 12,683)( 13,682)( 14,681)( 15,694)( 16,700)
( 17,699)( 18,698)( 19,697)( 20,696)( 21,695)( 22,687)( 23,693)( 24,692)
( 25,691)( 26,690)( 27,689)( 28,688)( 29,715)( 30,721)( 31,720)( 32,719)
( 33,718)( 34,717)( 35,716)( 36,722)( 37,728)( 38,727)( 39,726)( 40,725)
( 41,724)( 42,723)( 43,701)( 44,707)( 45,706)( 46,705)( 47,704)( 48,703)
( 49,702)( 50,708)( 51,714)( 52,713)( 53,712)( 54,711)( 55,710)( 56,709)
( 57,757)( 58,763)( 59,762)( 60,761)( 61,760)( 62,759)( 63,758)( 64,764)
( 65,770)( 66,769)( 67,768)( 68,767)( 69,766)( 70,765)( 71,778)( 72,784)
( 73,783)( 74,782)( 75,781)( 76,780)( 77,779)( 78,771)( 79,777)( 80,776)
( 81,775)( 82,774)( 83,773)( 84,772)( 85,729)( 86,735)( 87,734)( 88,733)
( 89,732)( 90,731)( 91,730)( 92,736)( 93,742)( 94,741)( 95,740)( 96,739)
( 97,738)( 98,737)( 99,750)(100,756)(101,755)(102,754)(103,753)(104,752)
(105,751)(106,743)(107,749)(108,748)(109,747)(110,746)(111,745)(112,744)
(113,841)(114,847)(115,846)(116,845)(117,844)(118,843)(119,842)(120,848)
(121,854)(122,853)(123,852)(124,851)(125,850)(126,849)(127,862)(128,868)
(129,867)(130,866)(131,865)(132,864)(133,863)(134,855)(135,861)(136,860)
(137,859)(138,858)(139,857)(140,856)(141,883)(142,889)(143,888)(144,887)
(145,886)(146,885)(147,884)(148,890)(149,896)(150,895)(151,894)(152,893)
(153,892)(154,891)(155,869)(156,875)(157,874)(158,873)(159,872)(160,871)
(161,870)(162,876)(163,882)(164,881)(165,880)(166,879)(167,878)(168,877)
(169,785)(170,791)(171,790)(172,789)(173,788)(174,787)(175,786)(176,792)
(177,798)(178,797)(179,796)(180,795)(181,794)(182,793)(183,806)(184,812)
(185,811)(186,810)(187,809)(188,808)(189,807)(190,799)(191,805)(192,804)
(193,803)(194,802)(195,801)(196,800)(197,827)(198,833)(199,832)(200,831)
(201,830)(202,829)(203,828)(204,834)(205,840)(206,839)(207,838)(208,837)
(209,836)(210,835)(211,813)(212,819)(213,818)(214,817)(215,816)(216,815)
(217,814)(218,820)(219,826)(220,825)(221,824)(222,823)(223,822)(224,821)
(225,449)(226,455)(227,454)(228,453)(229,452)(230,451)(231,450)(232,456)
(233,462)(234,461)(235,460)(236,459)(237,458)(238,457)(239,470)(240,476)
(241,475)(242,474)(243,473)(244,472)(245,471)(246,463)(247,469)(248,468)
(249,467)(250,466)(251,465)(252,464)(253,491)(254,497)(255,496)(256,495)
(257,494)(258,493)(259,492)(260,498)(261,504)(262,503)(263,502)(264,501)
(265,500)(266,499)(267,477)(268,483)(269,482)(270,481)(271,480)(272,479)
(273,478)(274,484)(275,490)(276,489)(277,488)(278,487)(279,486)(280,485)
(281,533)(282,539)(283,538)(284,537)(285,536)(286,535)(287,534)(288,540)
(289,546)(290,545)(291,544)(292,543)(293,542)(294,541)(295,554)(296,560)
(297,559)(298,558)(299,557)(300,556)(301,555)(302,547)(303,553)(304,552)
(305,551)(306,550)(307,549)(308,548)(309,505)(310,511)(311,510)(312,509)
(313,508)(314,507)(315,506)(316,512)(317,518)(318,517)(319,516)(320,515)
(321,514)(322,513)(323,526)(324,532)(325,531)(326,530)(327,529)(328,528)
(329,527)(330,519)(331,525)(332,524)(333,523)(334,522)(335,521)(336,520)
(337,617)(338,623)(339,622)(340,621)(341,620)(342,619)(343,618)(344,624)
(345,630)(346,629)(347,628)(348,627)(349,626)(350,625)(351,638)(352,644)
(353,643)(354,642)(355,641)(356,640)(357,639)(358,631)(359,637)(360,636)
(361,635)(362,634)(363,633)(364,632)(365,659)(366,665)(367,664)(368,663)
(369,662)(370,661)(371,660)(372,666)(373,672)(374,671)(375,670)(376,669)
(377,668)(378,667)(379,645)(380,651)(381,650)(382,649)(383,648)(384,647)
(385,646)(386,652)(387,658)(388,657)(389,656)(390,655)(391,654)(392,653)
(393,561)(394,567)(395,566)(396,565)(397,564)(398,563)(399,562)(400,568)
(401,574)(402,573)(403,572)(404,571)(405,570)(406,569)(407,582)(408,588)
(409,587)(410,586)(411,585)(412,584)(413,583)(414,575)(415,581)(416,580)
(417,579)(418,578)(419,577)(420,576)(421,603)(422,609)(423,608)(424,607)
(425,606)(426,605)(427,604)(428,610)(429,616)(430,615)(431,614)(432,613)
(433,612)(434,611)(435,589)(436,595)(437,594)(438,593)(439,592)(440,591)
(441,590)(442,596)(443,602)(444,601)(445,600)(446,599)(447,598)(448,597);;
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)
( 57,282)( 58,281)( 59,287)( 60,286)( 61,285)( 62,284)( 63,283)( 64,289)
( 65,288)( 66,294)( 67,293)( 68,292)( 69,291)( 70,290)( 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)( 99,324)(100,323)(101,329)(102,328)(103,327)(104,326)
(105,325)(106,331)(107,330)(108,336)(109,335)(110,334)(111,333)(112,332)
(113,338)(114,337)(115,343)(116,342)(117,341)(118,340)(119,339)(120,345)
(121,344)(122,350)(123,349)(124,348)(125,347)(126,346)(127,352)(128,351)
(129,357)(130,356)(131,355)(132,354)(133,353)(134,359)(135,358)(136,364)
(137,363)(138,362)(139,361)(140,360)(141,366)(142,365)(143,371)(144,370)
(145,369)(146,368)(147,367)(148,373)(149,372)(150,378)(151,377)(152,376)
(153,375)(154,374)(155,380)(156,379)(157,385)(158,384)(159,383)(160,382)
(161,381)(162,387)(163,386)(164,392)(165,391)(166,390)(167,389)(168,388)
(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)
(505,730)(506,729)(507,735)(508,734)(509,733)(510,732)(511,731)(512,737)
(513,736)(514,742)(515,741)(516,740)(517,739)(518,738)(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)(547,772)(548,771)(549,777)(550,776)(551,775)(552,774)
(553,773)(554,779)(555,778)(556,784)(557,783)(558,782)(559,781)(560,780)
(561,786)(562,785)(563,791)(564,790)(565,789)(566,788)(567,787)(568,793)
(569,792)(570,798)(571,797)(572,796)(573,795)(574,794)(575,800)(576,799)
(577,805)(578,804)(579,803)(580,802)(581,801)(582,807)(583,806)(584,812)
(585,811)(586,810)(587,809)(588,808)(589,814)(590,813)(591,819)(592,818)
(593,817)(594,816)(595,815)(596,821)(597,820)(598,826)(599,825)(600,824)
(601,823)(602,822)(603,828)(604,827)(605,833)(606,832)(607,831)(608,830)
(609,829)(610,835)(611,834)(612,840)(613,839)(614,838)(615,837)(616,836)
(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,
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(896)!( 15, 22)( 16, 23)( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)
( 29, 43)( 30, 44)( 31, 45)( 32, 46)( 33, 47)( 34, 48)( 35, 49)( 36, 50)
( 37, 51)( 38, 52)( 39, 53)( 40, 54)( 41, 55)( 42, 56)( 57, 85)( 58, 86)
( 59, 87)( 60, 88)( 61, 89)( 62, 90)( 63, 91)( 64, 92)( 65, 93)( 66, 94)
( 67, 95)( 68, 96)( 69, 97)( 70, 98)( 71,106)( 72,107)( 73,108)( 74,109)
( 75,110)( 76,111)( 77,112)( 78, 99)( 79,100)( 80,101)( 81,102)( 82,103)
( 83,104)( 84,105)(113,169)(114,170)(115,171)(116,172)(117,173)(118,174)
(119,175)(120,176)(121,177)(122,178)(123,179)(124,180)(125,181)(126,182)
(127,190)(128,191)(129,192)(130,193)(131,194)(132,195)(133,196)(134,183)
(135,184)(136,185)(137,186)(138,187)(139,188)(140,189)(141,211)(142,212)
(143,213)(144,214)(145,215)(146,216)(147,217)(148,218)(149,219)(150,220)
(151,221)(152,222)(153,223)(154,224)(155,197)(156,198)(157,199)(158,200)
(159,201)(160,202)(161,203)(162,204)(163,205)(164,206)(165,207)(166,208)
(167,209)(168,210)(239,246)(240,247)(241,248)(242,249)(243,250)(244,251)
(245,252)(253,267)(254,268)(255,269)(256,270)(257,271)(258,272)(259,273)
(260,274)(261,275)(262,276)(263,277)(264,278)(265,279)(266,280)(281,309)
(282,310)(283,311)(284,312)(285,313)(286,314)(287,315)(288,316)(289,317)
(290,318)(291,319)(292,320)(293,321)(294,322)(295,330)(296,331)(297,332)
(298,333)(299,334)(300,335)(301,336)(302,323)(303,324)(304,325)(305,326)
(306,327)(307,328)(308,329)(337,393)(338,394)(339,395)(340,396)(341,397)
(342,398)(343,399)(344,400)(345,401)(346,402)(347,403)(348,404)(349,405)
(350,406)(351,414)(352,415)(353,416)(354,417)(355,418)(356,419)(357,420)
(358,407)(359,408)(360,409)(361,410)(362,411)(363,412)(364,413)(365,435)
(366,436)(367,437)(368,438)(369,439)(370,440)(371,441)(372,442)(373,443)
(374,444)(375,445)(376,446)(377,447)(378,448)(379,421)(380,422)(381,423)
(382,424)(383,425)(384,426)(385,427)(386,428)(387,429)(388,430)(389,431)
(390,432)(391,433)(392,434)(449,561)(450,562)(451,563)(452,564)(453,565)
(454,566)(455,567)(456,568)(457,569)(458,570)(459,571)(460,572)(461,573)
(462,574)(463,582)(464,583)(465,584)(466,585)(467,586)(468,587)(469,588)
(470,575)(471,576)(472,577)(473,578)(474,579)(475,580)(476,581)(477,603)
(478,604)(479,605)(480,606)(481,607)(482,608)(483,609)(484,610)(485,611)
(486,612)(487,613)(488,614)(489,615)(490,616)(491,589)(492,590)(493,591)
(494,592)(495,593)(496,594)(497,595)(498,596)(499,597)(500,598)(501,599)
(502,600)(503,601)(504,602)(505,645)(506,646)(507,647)(508,648)(509,649)
(510,650)(511,651)(512,652)(513,653)(514,654)(515,655)(516,656)(517,657)
(518,658)(519,666)(520,667)(521,668)(522,669)(523,670)(524,671)(525,672)
(526,659)(527,660)(528,661)(529,662)(530,663)(531,664)(532,665)(533,617)
(534,618)(535,619)(536,620)(537,621)(538,622)(539,623)(540,624)(541,625)
(542,626)(543,627)(544,628)(545,629)(546,630)(547,638)(548,639)(549,640)
(550,641)(551,642)(552,643)(553,644)(554,631)(555,632)(556,633)(557,634)
(558,635)(559,636)(560,637)(673,785)(674,786)(675,787)(676,788)(677,789)
(678,790)(679,791)(680,792)(681,793)(682,794)(683,795)(684,796)(685,797)
(686,798)(687,806)(688,807)(689,808)(690,809)(691,810)(692,811)(693,812)
(694,799)(695,800)(696,801)(697,802)(698,803)(699,804)(700,805)(701,827)
(702,828)(703,829)(704,830)(705,831)(706,832)(707,833)(708,834)(709,835)
(710,836)(711,837)(712,838)(713,839)(714,840)(715,813)(716,814)(717,815)
(718,816)(719,817)(720,818)(721,819)(722,820)(723,821)(724,822)(725,823)
(726,824)(727,825)(728,826)(729,869)(730,870)(731,871)(732,872)(733,873)
(734,874)(735,875)(736,876)(737,877)(738,878)(739,879)(740,880)(741,881)
(742,882)(743,890)(744,891)(745,892)(746,893)(747,894)(748,895)(749,896)
(750,883)(751,884)(752,885)(753,886)(754,887)(755,888)(756,889)(757,841)
(758,842)(759,843)(760,844)(761,845)(762,846)(763,847)(764,848)(765,849)
(766,850)(767,851)(768,852)(769,853)(770,854)(771,862)(772,863)(773,864)
(774,865)(775,866)(776,867)(777,868)(778,855)(779,856)(780,857)(781,858)
(782,859)(783,860)(784,861);
s1 := Sym(896)!( 1,673)( 2,679)( 3,678)( 4,677)( 5,676)( 6,675)( 7,674)
( 8,680)( 9,686)( 10,685)( 11,684)( 12,683)( 13,682)( 14,681)( 15,694)
( 16,700)( 17,699)( 18,698)( 19,697)( 20,696)( 21,695)( 22,687)( 23,693)
( 24,692)( 25,691)( 26,690)( 27,689)( 28,688)( 29,715)( 30,721)( 31,720)
( 32,719)( 33,718)( 34,717)( 35,716)( 36,722)( 37,728)( 38,727)( 39,726)
( 40,725)( 41,724)( 42,723)( 43,701)( 44,707)( 45,706)( 46,705)( 47,704)
( 48,703)( 49,702)( 50,708)( 51,714)( 52,713)( 53,712)( 54,711)( 55,710)
( 56,709)( 57,757)( 58,763)( 59,762)( 60,761)( 61,760)( 62,759)( 63,758)
( 64,764)( 65,770)( 66,769)( 67,768)( 68,767)( 69,766)( 70,765)( 71,778)
( 72,784)( 73,783)( 74,782)( 75,781)( 76,780)( 77,779)( 78,771)( 79,777)
( 80,776)( 81,775)( 82,774)( 83,773)( 84,772)( 85,729)( 86,735)( 87,734)
( 88,733)( 89,732)( 90,731)( 91,730)( 92,736)( 93,742)( 94,741)( 95,740)
( 96,739)( 97,738)( 98,737)( 99,750)(100,756)(101,755)(102,754)(103,753)
(104,752)(105,751)(106,743)(107,749)(108,748)(109,747)(110,746)(111,745)
(112,744)(113,841)(114,847)(115,846)(116,845)(117,844)(118,843)(119,842)
(120,848)(121,854)(122,853)(123,852)(124,851)(125,850)(126,849)(127,862)
(128,868)(129,867)(130,866)(131,865)(132,864)(133,863)(134,855)(135,861)
(136,860)(137,859)(138,858)(139,857)(140,856)(141,883)(142,889)(143,888)
(144,887)(145,886)(146,885)(147,884)(148,890)(149,896)(150,895)(151,894)
(152,893)(153,892)(154,891)(155,869)(156,875)(157,874)(158,873)(159,872)
(160,871)(161,870)(162,876)(163,882)(164,881)(165,880)(166,879)(167,878)
(168,877)(169,785)(170,791)(171,790)(172,789)(173,788)(174,787)(175,786)
(176,792)(177,798)(178,797)(179,796)(180,795)(181,794)(182,793)(183,806)
(184,812)(185,811)(186,810)(187,809)(188,808)(189,807)(190,799)(191,805)
(192,804)(193,803)(194,802)(195,801)(196,800)(197,827)(198,833)(199,832)
(200,831)(201,830)(202,829)(203,828)(204,834)(205,840)(206,839)(207,838)
(208,837)(209,836)(210,835)(211,813)(212,819)(213,818)(214,817)(215,816)
(216,815)(217,814)(218,820)(219,826)(220,825)(221,824)(222,823)(223,822)
(224,821)(225,449)(226,455)(227,454)(228,453)(229,452)(230,451)(231,450)
(232,456)(233,462)(234,461)(235,460)(236,459)(237,458)(238,457)(239,470)
(240,476)(241,475)(242,474)(243,473)(244,472)(245,471)(246,463)(247,469)
(248,468)(249,467)(250,466)(251,465)(252,464)(253,491)(254,497)(255,496)
(256,495)(257,494)(258,493)(259,492)(260,498)(261,504)(262,503)(263,502)
(264,501)(265,500)(266,499)(267,477)(268,483)(269,482)(270,481)(271,480)
(272,479)(273,478)(274,484)(275,490)(276,489)(277,488)(278,487)(279,486)
(280,485)(281,533)(282,539)(283,538)(284,537)(285,536)(286,535)(287,534)
(288,540)(289,546)(290,545)(291,544)(292,543)(293,542)(294,541)(295,554)
(296,560)(297,559)(298,558)(299,557)(300,556)(301,555)(302,547)(303,553)
(304,552)(305,551)(306,550)(307,549)(308,548)(309,505)(310,511)(311,510)
(312,509)(313,508)(314,507)(315,506)(316,512)(317,518)(318,517)(319,516)
(320,515)(321,514)(322,513)(323,526)(324,532)(325,531)(326,530)(327,529)
(328,528)(329,527)(330,519)(331,525)(332,524)(333,523)(334,522)(335,521)
(336,520)(337,617)(338,623)(339,622)(340,621)(341,620)(342,619)(343,618)
(344,624)(345,630)(346,629)(347,628)(348,627)(349,626)(350,625)(351,638)
(352,644)(353,643)(354,642)(355,641)(356,640)(357,639)(358,631)(359,637)
(360,636)(361,635)(362,634)(363,633)(364,632)(365,659)(366,665)(367,664)
(368,663)(369,662)(370,661)(371,660)(372,666)(373,672)(374,671)(375,670)
(376,669)(377,668)(378,667)(379,645)(380,651)(381,650)(382,649)(383,648)
(384,647)(385,646)(386,652)(387,658)(388,657)(389,656)(390,655)(391,654)
(392,653)(393,561)(394,567)(395,566)(396,565)(397,564)(398,563)(399,562)
(400,568)(401,574)(402,573)(403,572)(404,571)(405,570)(406,569)(407,582)
(408,588)(409,587)(410,586)(411,585)(412,584)(413,583)(414,575)(415,581)
(416,580)(417,579)(418,578)(419,577)(420,576)(421,603)(422,609)(423,608)
(424,607)(425,606)(426,605)(427,604)(428,610)(429,616)(430,615)(431,614)
(432,613)(433,612)(434,611)(435,589)(436,595)(437,594)(438,593)(439,592)
(440,591)(441,590)(442,596)(443,602)(444,601)(445,600)(446,599)(447,598)
(448,597);
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)( 57,282)( 58,281)( 59,287)( 60,286)( 61,285)( 62,284)( 63,283)
( 64,289)( 65,288)( 66,294)( 67,293)( 68,292)( 69,291)( 70,290)( 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)( 99,324)(100,323)(101,329)(102,328)(103,327)
(104,326)(105,325)(106,331)(107,330)(108,336)(109,335)(110,334)(111,333)
(112,332)(113,338)(114,337)(115,343)(116,342)(117,341)(118,340)(119,339)
(120,345)(121,344)(122,350)(123,349)(124,348)(125,347)(126,346)(127,352)
(128,351)(129,357)(130,356)(131,355)(132,354)(133,353)(134,359)(135,358)
(136,364)(137,363)(138,362)(139,361)(140,360)(141,366)(142,365)(143,371)
(144,370)(145,369)(146,368)(147,367)(148,373)(149,372)(150,378)(151,377)
(152,376)(153,375)(154,374)(155,380)(156,379)(157,385)(158,384)(159,383)
(160,382)(161,381)(162,387)(163,386)(164,392)(165,391)(166,390)(167,389)
(168,388)(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)(505,730)(506,729)(507,735)(508,734)(509,733)(510,732)(511,731)
(512,737)(513,736)(514,742)(515,741)(516,740)(517,739)(518,738)(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)(547,772)(548,771)(549,777)(550,776)(551,775)
(552,774)(553,773)(554,779)(555,778)(556,784)(557,783)(558,782)(559,781)
(560,780)(561,786)(562,785)(563,791)(564,790)(565,789)(566,788)(567,787)
(568,793)(569,792)(570,798)(571,797)(572,796)(573,795)(574,794)(575,800)
(576,799)(577,805)(578,804)(579,803)(580,802)(581,801)(582,807)(583,806)
(584,812)(585,811)(586,810)(587,809)(588,808)(589,814)(590,813)(591,819)
(592,818)(593,817)(594,816)(595,815)(596,821)(597,820)(598,826)(599,825)
(600,824)(601,823)(602,822)(603,828)(604,827)(605,833)(606,832)(607,831)
(608,830)(609,829)(610,835)(611,834)(612,840)(613,839)(614,838)(615,837)
(616,836)(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,
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope