Polytope of Type {8,116}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,116}*1856a
Also Known As : {8,116|2}. if this polytope has another name.
Group : SmallGroup(1856,684)
Rank : 3
Schlafli Type : {8,116}
Number of vertices, edges, etc : 8, 464, 116
Order of s₀s₁s₂ : 232
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 : {4,116}*928, {8,58}*928
   4-fold quotients : {2,116}*464, {4,58}*464
   8-fold quotients : {2,58}*232
   16-fold quotients : {2,29}*116
   29-fold quotients : {8,4}*64a
   58-fold quotients : {4,4}*32, {8,2}*32
   116-fold quotients : {2,4}*16, {4,2}*16
   232-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  1,465)(  2,466)(  3,467)(  4,468)(  5,469)(  6,470)(  7,471)(  8,472)
(  9,473)( 10,474)( 11,475)( 12,476)( 13,477)( 14,478)( 15,479)( 16,480)
( 17,481)( 18,482)( 19,483)( 20,484)( 21,485)( 22,486)( 23,487)( 24,488)
( 25,489)( 26,490)( 27,491)( 28,492)( 29,493)( 30,494)( 31,495)( 32,496)
( 33,497)( 34,498)( 35,499)( 36,500)( 37,501)( 38,502)( 39,503)( 40,504)
( 41,505)( 42,506)( 43,507)( 44,508)( 45,509)( 46,510)( 47,511)( 48,512)
( 49,513)( 50,514)( 51,515)( 52,516)( 53,517)( 54,518)( 55,519)( 56,520)
( 57,521)( 58,522)( 59,523)( 60,524)( 61,525)( 62,526)( 63,527)( 64,528)
( 65,529)( 66,530)( 67,531)( 68,532)( 69,533)( 70,534)( 71,535)( 72,536)
( 73,537)( 74,538)( 75,539)( 76,540)( 77,541)( 78,542)( 79,543)( 80,544)
( 81,545)( 82,546)( 83,547)( 84,548)( 85,549)( 86,550)( 87,551)( 88,552)
( 89,553)( 90,554)( 91,555)( 92,556)( 93,557)( 94,558)( 95,559)( 96,560)
( 97,561)( 98,562)( 99,563)(100,564)(101,565)(102,566)(103,567)(104,568)
(105,569)(106,570)(107,571)(108,572)(109,573)(110,574)(111,575)(112,576)
(113,577)(114,578)(115,579)(116,580)(117,610)(118,611)(119,612)(120,613)
(121,614)(122,615)(123,616)(124,617)(125,618)(126,619)(127,620)(128,621)
(129,622)(130,623)(131,624)(132,625)(133,626)(134,627)(135,628)(136,629)
(137,630)(138,631)(139,632)(140,633)(141,634)(142,635)(143,636)(144,637)
(145,638)(146,581)(147,582)(148,583)(149,584)(150,585)(151,586)(152,587)
(153,588)(154,589)(155,590)(156,591)(157,592)(158,593)(159,594)(160,595)
(161,596)(162,597)(163,598)(164,599)(165,600)(166,601)(167,602)(168,603)
(169,604)(170,605)(171,606)(172,607)(173,608)(174,609)(175,668)(176,669)
(177,670)(178,671)(179,672)(180,673)(181,674)(182,675)(183,676)(184,677)
(185,678)(186,679)(187,680)(188,681)(189,682)(190,683)(191,684)(192,685)
(193,686)(194,687)(195,688)(196,689)(197,690)(198,691)(199,692)(200,693)
(201,694)(202,695)(203,696)(204,639)(205,640)(206,641)(207,642)(208,643)
(209,644)(210,645)(211,646)(212,647)(213,648)(214,649)(215,650)(216,651)
(217,652)(218,653)(219,654)(220,655)(221,656)(222,657)(223,658)(224,659)
(225,660)(226,661)(227,662)(228,663)(229,664)(230,665)(231,666)(232,667)
(233,697)(234,698)(235,699)(236,700)(237,701)(238,702)(239,703)(240,704)
(241,705)(242,706)(243,707)(244,708)(245,709)(246,710)(247,711)(248,712)
(249,713)(250,714)(251,715)(252,716)(253,717)(254,718)(255,719)(256,720)
(257,721)(258,722)(259,723)(260,724)(261,725)(262,726)(263,727)(264,728)
(265,729)(266,730)(267,731)(268,732)(269,733)(270,734)(271,735)(272,736)
(273,737)(274,738)(275,739)(276,740)(277,741)(278,742)(279,743)(280,744)
(281,745)(282,746)(283,747)(284,748)(285,749)(286,750)(287,751)(288,752)
(289,753)(290,754)(291,755)(292,756)(293,757)(294,758)(295,759)(296,760)
(297,761)(298,762)(299,763)(300,764)(301,765)(302,766)(303,767)(304,768)
(305,769)(306,770)(307,771)(308,772)(309,773)(310,774)(311,775)(312,776)
(313,777)(314,778)(315,779)(316,780)(317,781)(318,782)(319,783)(320,784)
(321,785)(322,786)(323,787)(324,788)(325,789)(326,790)(327,791)(328,792)
(329,793)(330,794)(331,795)(332,796)(333,797)(334,798)(335,799)(336,800)
(337,801)(338,802)(339,803)(340,804)(341,805)(342,806)(343,807)(344,808)
(345,809)(346,810)(347,811)(348,812)(349,842)(350,843)(351,844)(352,845)
(353,846)(354,847)(355,848)(356,849)(357,850)(358,851)(359,852)(360,853)
(361,854)(362,855)(363,856)(364,857)(365,858)(366,859)(367,860)(368,861)
(369,862)(370,863)(371,864)(372,865)(373,866)(374,867)(375,868)(376,869)
(377,870)(378,813)(379,814)(380,815)(381,816)(382,817)(383,818)(384,819)
(385,820)(386,821)(387,822)(388,823)(389,824)(390,825)(391,826)(392,827)
(393,828)(394,829)(395,830)(396,831)(397,832)(398,833)(399,834)(400,835)
(401,836)(402,837)(403,838)(404,839)(405,840)(406,841)(407,900)(408,901)
(409,902)(410,903)(411,904)(412,905)(413,906)(414,907)(415,908)(416,909)
(417,910)(418,911)(419,912)(420,913)(421,914)(422,915)(423,916)(424,917)
(425,918)(426,919)(427,920)(428,921)(429,922)(430,923)(431,924)(432,925)
(433,926)(434,927)(435,928)(436,871)(437,872)(438,873)(439,874)(440,875)
(441,876)(442,877)(443,878)(444,879)(445,880)(446,881)(447,882)(448,883)
(449,884)(450,885)(451,886)(452,887)(453,888)(454,889)(455,890)(456,891)
(457,892)(458,893)(459,894)(460,895)(461,896)(462,897)(463,898)(464,899);;
s1 := (  2, 29)(  3, 28)(  4, 27)(  5, 26)(  6, 25)(  7, 24)(  8, 23)(  9, 22)
( 10, 21)( 11, 20)( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 31, 58)( 32, 57)
( 33, 56)( 34, 55)( 35, 54)( 36, 53)( 37, 52)( 38, 51)( 39, 50)( 40, 49)
( 41, 48)( 42, 47)( 43, 46)( 44, 45)( 60, 87)( 61, 86)( 62, 85)( 63, 84)
( 64, 83)( 65, 82)( 66, 81)( 67, 80)( 68, 79)( 69, 78)( 70, 77)( 71, 76)
( 72, 75)( 73, 74)( 89,116)( 90,115)( 91,114)( 92,113)( 93,112)( 94,111)
( 95,110)( 96,109)( 97,108)( 98,107)( 99,106)(100,105)(101,104)(102,103)
(117,146)(118,174)(119,173)(120,172)(121,171)(122,170)(123,169)(124,168)
(125,167)(126,166)(127,165)(128,164)(129,163)(130,162)(131,161)(132,160)
(133,159)(134,158)(135,157)(136,156)(137,155)(138,154)(139,153)(140,152)
(141,151)(142,150)(143,149)(144,148)(145,147)(175,204)(176,232)(177,231)
(178,230)(179,229)(180,228)(181,227)(182,226)(183,225)(184,224)(185,223)
(186,222)(187,221)(188,220)(189,219)(190,218)(191,217)(192,216)(193,215)
(194,214)(195,213)(196,212)(197,211)(198,210)(199,209)(200,208)(201,207)
(202,206)(203,205)(233,291)(234,319)(235,318)(236,317)(237,316)(238,315)
(239,314)(240,313)(241,312)(242,311)(243,310)(244,309)(245,308)(246,307)
(247,306)(248,305)(249,304)(250,303)(251,302)(252,301)(253,300)(254,299)
(255,298)(256,297)(257,296)(258,295)(259,294)(260,293)(261,292)(262,320)
(263,348)(264,347)(265,346)(266,345)(267,344)(268,343)(269,342)(270,341)
(271,340)(272,339)(273,338)(274,337)(275,336)(276,335)(277,334)(278,333)
(279,332)(280,331)(281,330)(282,329)(283,328)(284,327)(285,326)(286,325)
(287,324)(288,323)(289,322)(290,321)(349,436)(350,464)(351,463)(352,462)
(353,461)(354,460)(355,459)(356,458)(357,457)(358,456)(359,455)(360,454)
(361,453)(362,452)(363,451)(364,450)(365,449)(366,448)(367,447)(368,446)
(369,445)(370,444)(371,443)(372,442)(373,441)(374,440)(375,439)(376,438)
(377,437)(378,407)(379,435)(380,434)(381,433)(382,432)(383,431)(384,430)
(385,429)(386,428)(387,427)(388,426)(389,425)(390,424)(391,423)(392,422)
(393,421)(394,420)(395,419)(396,418)(397,417)(398,416)(399,415)(400,414)
(401,413)(402,412)(403,411)(404,410)(405,409)(406,408)(465,581)(466,609)
(467,608)(468,607)(469,606)(470,605)(471,604)(472,603)(473,602)(474,601)
(475,600)(476,599)(477,598)(478,597)(479,596)(480,595)(481,594)(482,593)
(483,592)(484,591)(485,590)(486,589)(487,588)(488,587)(489,586)(490,585)
(491,584)(492,583)(493,582)(494,610)(495,638)(496,637)(497,636)(498,635)
(499,634)(500,633)(501,632)(502,631)(503,630)(504,629)(505,628)(506,627)
(507,626)(508,625)(509,624)(510,623)(511,622)(512,621)(513,620)(514,619)
(515,618)(516,617)(517,616)(518,615)(519,614)(520,613)(521,612)(522,611)
(523,639)(524,667)(525,666)(526,665)(527,664)(528,663)(529,662)(530,661)
(531,660)(532,659)(533,658)(534,657)(535,656)(536,655)(537,654)(538,653)
(539,652)(540,651)(541,650)(542,649)(543,648)(544,647)(545,646)(546,645)
(547,644)(548,643)(549,642)(550,641)(551,640)(552,668)(553,696)(554,695)
(555,694)(556,693)(557,692)(558,691)(559,690)(560,689)(561,688)(562,687)
(563,686)(564,685)(565,684)(566,683)(567,682)(568,681)(569,680)(570,679)
(571,678)(572,677)(573,676)(574,675)(575,674)(576,673)(577,672)(578,671)
(579,670)(580,669)(697,871)(698,899)(699,898)(700,897)(701,896)(702,895)
(703,894)(704,893)(705,892)(706,891)(707,890)(708,889)(709,888)(710,887)
(711,886)(712,885)(713,884)(714,883)(715,882)(716,881)(717,880)(718,879)
(719,878)(720,877)(721,876)(722,875)(723,874)(724,873)(725,872)(726,900)
(727,928)(728,927)(729,926)(730,925)(731,924)(732,923)(733,922)(734,921)
(735,920)(736,919)(737,918)(738,917)(739,916)(740,915)(741,914)(742,913)
(743,912)(744,911)(745,910)(746,909)(747,908)(748,907)(749,906)(750,905)
(751,904)(752,903)(753,902)(754,901)(755,813)(756,841)(757,840)(758,839)
(759,838)(760,837)(761,836)(762,835)(763,834)(764,833)(765,832)(766,831)
(767,830)(768,829)(769,828)(770,827)(771,826)(772,825)(773,824)(774,823)
(775,822)(776,821)(777,820)(778,819)(779,818)(780,817)(781,816)(782,815)
(783,814)(784,842)(785,870)(786,869)(787,868)(788,867)(789,866)(790,865)
(791,864)(792,863)(793,862)(794,861)(795,860)(796,859)(797,858)(798,857)
(799,856)(800,855)(801,854)(802,853)(803,852)(804,851)(805,850)(806,849)
(807,848)(808,847)(809,846)(810,845)(811,844)(812,843);;
s2 := (  1,234)(  2,233)(  3,261)(  4,260)(  5,259)(  6,258)(  7,257)(  8,256)
(  9,255)( 10,254)( 11,253)( 12,252)( 13,251)( 14,250)( 15,249)( 16,248)
( 17,247)( 18,246)( 19,245)( 20,244)( 21,243)( 22,242)( 23,241)( 24,240)
( 25,239)( 26,238)( 27,237)( 28,236)( 29,235)( 30,263)( 31,262)( 32,290)
( 33,289)( 34,288)( 35,287)( 36,286)( 37,285)( 38,284)( 39,283)( 40,282)
( 41,281)( 42,280)( 43,279)( 44,278)( 45,277)( 46,276)( 47,275)( 48,274)
( 49,273)( 50,272)( 51,271)( 52,270)( 53,269)( 54,268)( 55,267)( 56,266)
( 57,265)( 58,264)( 59,292)( 60,291)( 61,319)( 62,318)( 63,317)( 64,316)
( 65,315)( 66,314)( 67,313)( 68,312)( 69,311)( 70,310)( 71,309)( 72,308)
( 73,307)( 74,306)( 75,305)( 76,304)( 77,303)( 78,302)( 79,301)( 80,300)
( 81,299)( 82,298)( 83,297)( 84,296)( 85,295)( 86,294)( 87,293)( 88,321)
( 89,320)( 90,348)( 91,347)( 92,346)( 93,345)( 94,344)( 95,343)( 96,342)
( 97,341)( 98,340)( 99,339)(100,338)(101,337)(102,336)(103,335)(104,334)
(105,333)(106,332)(107,331)(108,330)(109,329)(110,328)(111,327)(112,326)
(113,325)(114,324)(115,323)(116,322)(117,350)(118,349)(119,377)(120,376)
(121,375)(122,374)(123,373)(124,372)(125,371)(126,370)(127,369)(128,368)
(129,367)(130,366)(131,365)(132,364)(133,363)(134,362)(135,361)(136,360)
(137,359)(138,358)(139,357)(140,356)(141,355)(142,354)(143,353)(144,352)
(145,351)(146,379)(147,378)(148,406)(149,405)(150,404)(151,403)(152,402)
(153,401)(154,400)(155,399)(156,398)(157,397)(158,396)(159,395)(160,394)
(161,393)(162,392)(163,391)(164,390)(165,389)(166,388)(167,387)(168,386)
(169,385)(170,384)(171,383)(172,382)(173,381)(174,380)(175,408)(176,407)
(177,435)(178,434)(179,433)(180,432)(181,431)(182,430)(183,429)(184,428)
(185,427)(186,426)(187,425)(188,424)(189,423)(190,422)(191,421)(192,420)
(193,419)(194,418)(195,417)(196,416)(197,415)(198,414)(199,413)(200,412)
(201,411)(202,410)(203,409)(204,437)(205,436)(206,464)(207,463)(208,462)
(209,461)(210,460)(211,459)(212,458)(213,457)(214,456)(215,455)(216,454)
(217,453)(218,452)(219,451)(220,450)(221,449)(222,448)(223,447)(224,446)
(225,445)(226,444)(227,443)(228,442)(229,441)(230,440)(231,439)(232,438)
(465,698)(466,697)(467,725)(468,724)(469,723)(470,722)(471,721)(472,720)
(473,719)(474,718)(475,717)(476,716)(477,715)(478,714)(479,713)(480,712)
(481,711)(482,710)(483,709)(484,708)(485,707)(486,706)(487,705)(488,704)
(489,703)(490,702)(491,701)(492,700)(493,699)(494,727)(495,726)(496,754)
(497,753)(498,752)(499,751)(500,750)(501,749)(502,748)(503,747)(504,746)
(505,745)(506,744)(507,743)(508,742)(509,741)(510,740)(511,739)(512,738)
(513,737)(514,736)(515,735)(516,734)(517,733)(518,732)(519,731)(520,730)
(521,729)(522,728)(523,756)(524,755)(525,783)(526,782)(527,781)(528,780)
(529,779)(530,778)(531,777)(532,776)(533,775)(534,774)(535,773)(536,772)
(537,771)(538,770)(539,769)(540,768)(541,767)(542,766)(543,765)(544,764)
(545,763)(546,762)(547,761)(548,760)(549,759)(550,758)(551,757)(552,785)
(553,784)(554,812)(555,811)(556,810)(557,809)(558,808)(559,807)(560,806)
(561,805)(562,804)(563,803)(564,802)(565,801)(566,800)(567,799)(568,798)
(569,797)(570,796)(571,795)(572,794)(573,793)(574,792)(575,791)(576,790)
(577,789)(578,788)(579,787)(580,786)(581,814)(582,813)(583,841)(584,840)
(585,839)(586,838)(587,837)(588,836)(589,835)(590,834)(591,833)(592,832)
(593,831)(594,830)(595,829)(596,828)(597,827)(598,826)(599,825)(600,824)
(601,823)(602,822)(603,821)(604,820)(605,819)(606,818)(607,817)(608,816)
(609,815)(610,843)(611,842)(612,870)(613,869)(614,868)(615,867)(616,866)
(617,865)(618,864)(619,863)(620,862)(621,861)(622,860)(623,859)(624,858)
(625,857)(626,856)(627,855)(628,854)(629,853)(630,852)(631,851)(632,850)
(633,849)(634,848)(635,847)(636,846)(637,845)(638,844)(639,872)(640,871)
(641,899)(642,898)(643,897)(644,896)(645,895)(646,894)(647,893)(648,892)
(649,891)(650,890)(651,889)(652,888)(653,887)(654,886)(655,885)(656,884)
(657,883)(658,882)(659,881)(660,880)(661,879)(662,878)(663,877)(664,876)
(665,875)(666,874)(667,873)(668,901)(669,900)(670,928)(671,927)(672,926)
(673,925)(674,924)(675,923)(676,922)(677,921)(678,920)(679,919)(680,918)
(681,917)(682,916)(683,915)(684,914)(685,913)(686,912)(687,911)(688,910)
(689,909)(690,908)(691,907)(692,906)(693,905)(694,904)(695,903)(696,902);;
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, 
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*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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(928)!(  1,465)(  2,466)(  3,467)(  4,468)(  5,469)(  6,470)(  7,471)
(  8,472)(  9,473)( 10,474)( 11,475)( 12,476)( 13,477)( 14,478)( 15,479)
( 16,480)( 17,481)( 18,482)( 19,483)( 20,484)( 21,485)( 22,486)( 23,487)
( 24,488)( 25,489)( 26,490)( 27,491)( 28,492)( 29,493)( 30,494)( 31,495)
( 32,496)( 33,497)( 34,498)( 35,499)( 36,500)( 37,501)( 38,502)( 39,503)
( 40,504)( 41,505)( 42,506)( 43,507)( 44,508)( 45,509)( 46,510)( 47,511)
( 48,512)( 49,513)( 50,514)( 51,515)( 52,516)( 53,517)( 54,518)( 55,519)
( 56,520)( 57,521)( 58,522)( 59,523)( 60,524)( 61,525)( 62,526)( 63,527)
( 64,528)( 65,529)( 66,530)( 67,531)( 68,532)( 69,533)( 70,534)( 71,535)
( 72,536)( 73,537)( 74,538)( 75,539)( 76,540)( 77,541)( 78,542)( 79,543)
( 80,544)( 81,545)( 82,546)( 83,547)( 84,548)( 85,549)( 86,550)( 87,551)
( 88,552)( 89,553)( 90,554)( 91,555)( 92,556)( 93,557)( 94,558)( 95,559)
( 96,560)( 97,561)( 98,562)( 99,563)(100,564)(101,565)(102,566)(103,567)
(104,568)(105,569)(106,570)(107,571)(108,572)(109,573)(110,574)(111,575)
(112,576)(113,577)(114,578)(115,579)(116,580)(117,610)(118,611)(119,612)
(120,613)(121,614)(122,615)(123,616)(124,617)(125,618)(126,619)(127,620)
(128,621)(129,622)(130,623)(131,624)(132,625)(133,626)(134,627)(135,628)
(136,629)(137,630)(138,631)(139,632)(140,633)(141,634)(142,635)(143,636)
(144,637)(145,638)(146,581)(147,582)(148,583)(149,584)(150,585)(151,586)
(152,587)(153,588)(154,589)(155,590)(156,591)(157,592)(158,593)(159,594)
(160,595)(161,596)(162,597)(163,598)(164,599)(165,600)(166,601)(167,602)
(168,603)(169,604)(170,605)(171,606)(172,607)(173,608)(174,609)(175,668)
(176,669)(177,670)(178,671)(179,672)(180,673)(181,674)(182,675)(183,676)
(184,677)(185,678)(186,679)(187,680)(188,681)(189,682)(190,683)(191,684)
(192,685)(193,686)(194,687)(195,688)(196,689)(197,690)(198,691)(199,692)
(200,693)(201,694)(202,695)(203,696)(204,639)(205,640)(206,641)(207,642)
(208,643)(209,644)(210,645)(211,646)(212,647)(213,648)(214,649)(215,650)
(216,651)(217,652)(218,653)(219,654)(220,655)(221,656)(222,657)(223,658)
(224,659)(225,660)(226,661)(227,662)(228,663)(229,664)(230,665)(231,666)
(232,667)(233,697)(234,698)(235,699)(236,700)(237,701)(238,702)(239,703)
(240,704)(241,705)(242,706)(243,707)(244,708)(245,709)(246,710)(247,711)
(248,712)(249,713)(250,714)(251,715)(252,716)(253,717)(254,718)(255,719)
(256,720)(257,721)(258,722)(259,723)(260,724)(261,725)(262,726)(263,727)
(264,728)(265,729)(266,730)(267,731)(268,732)(269,733)(270,734)(271,735)
(272,736)(273,737)(274,738)(275,739)(276,740)(277,741)(278,742)(279,743)
(280,744)(281,745)(282,746)(283,747)(284,748)(285,749)(286,750)(287,751)
(288,752)(289,753)(290,754)(291,755)(292,756)(293,757)(294,758)(295,759)
(296,760)(297,761)(298,762)(299,763)(300,764)(301,765)(302,766)(303,767)
(304,768)(305,769)(306,770)(307,771)(308,772)(309,773)(310,774)(311,775)
(312,776)(313,777)(314,778)(315,779)(316,780)(317,781)(318,782)(319,783)
(320,784)(321,785)(322,786)(323,787)(324,788)(325,789)(326,790)(327,791)
(328,792)(329,793)(330,794)(331,795)(332,796)(333,797)(334,798)(335,799)
(336,800)(337,801)(338,802)(339,803)(340,804)(341,805)(342,806)(343,807)
(344,808)(345,809)(346,810)(347,811)(348,812)(349,842)(350,843)(351,844)
(352,845)(353,846)(354,847)(355,848)(356,849)(357,850)(358,851)(359,852)
(360,853)(361,854)(362,855)(363,856)(364,857)(365,858)(366,859)(367,860)
(368,861)(369,862)(370,863)(371,864)(372,865)(373,866)(374,867)(375,868)
(376,869)(377,870)(378,813)(379,814)(380,815)(381,816)(382,817)(383,818)
(384,819)(385,820)(386,821)(387,822)(388,823)(389,824)(390,825)(391,826)
(392,827)(393,828)(394,829)(395,830)(396,831)(397,832)(398,833)(399,834)
(400,835)(401,836)(402,837)(403,838)(404,839)(405,840)(406,841)(407,900)
(408,901)(409,902)(410,903)(411,904)(412,905)(413,906)(414,907)(415,908)
(416,909)(417,910)(418,911)(419,912)(420,913)(421,914)(422,915)(423,916)
(424,917)(425,918)(426,919)(427,920)(428,921)(429,922)(430,923)(431,924)
(432,925)(433,926)(434,927)(435,928)(436,871)(437,872)(438,873)(439,874)
(440,875)(441,876)(442,877)(443,878)(444,879)(445,880)(446,881)(447,882)
(448,883)(449,884)(450,885)(451,886)(452,887)(453,888)(454,889)(455,890)
(456,891)(457,892)(458,893)(459,894)(460,895)(461,896)(462,897)(463,898)
(464,899);
s1 := Sym(928)!(  2, 29)(  3, 28)(  4, 27)(  5, 26)(  6, 25)(  7, 24)(  8, 23)
(  9, 22)( 10, 21)( 11, 20)( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 31, 58)
( 32, 57)( 33, 56)( 34, 55)( 35, 54)( 36, 53)( 37, 52)( 38, 51)( 39, 50)
( 40, 49)( 41, 48)( 42, 47)( 43, 46)( 44, 45)( 60, 87)( 61, 86)( 62, 85)
( 63, 84)( 64, 83)( 65, 82)( 66, 81)( 67, 80)( 68, 79)( 69, 78)( 70, 77)
( 71, 76)( 72, 75)( 73, 74)( 89,116)( 90,115)( 91,114)( 92,113)( 93,112)
( 94,111)( 95,110)( 96,109)( 97,108)( 98,107)( 99,106)(100,105)(101,104)
(102,103)(117,146)(118,174)(119,173)(120,172)(121,171)(122,170)(123,169)
(124,168)(125,167)(126,166)(127,165)(128,164)(129,163)(130,162)(131,161)
(132,160)(133,159)(134,158)(135,157)(136,156)(137,155)(138,154)(139,153)
(140,152)(141,151)(142,150)(143,149)(144,148)(145,147)(175,204)(176,232)
(177,231)(178,230)(179,229)(180,228)(181,227)(182,226)(183,225)(184,224)
(185,223)(186,222)(187,221)(188,220)(189,219)(190,218)(191,217)(192,216)
(193,215)(194,214)(195,213)(196,212)(197,211)(198,210)(199,209)(200,208)
(201,207)(202,206)(203,205)(233,291)(234,319)(235,318)(236,317)(237,316)
(238,315)(239,314)(240,313)(241,312)(242,311)(243,310)(244,309)(245,308)
(246,307)(247,306)(248,305)(249,304)(250,303)(251,302)(252,301)(253,300)
(254,299)(255,298)(256,297)(257,296)(258,295)(259,294)(260,293)(261,292)
(262,320)(263,348)(264,347)(265,346)(266,345)(267,344)(268,343)(269,342)
(270,341)(271,340)(272,339)(273,338)(274,337)(275,336)(276,335)(277,334)
(278,333)(279,332)(280,331)(281,330)(282,329)(283,328)(284,327)(285,326)
(286,325)(287,324)(288,323)(289,322)(290,321)(349,436)(350,464)(351,463)
(352,462)(353,461)(354,460)(355,459)(356,458)(357,457)(358,456)(359,455)
(360,454)(361,453)(362,452)(363,451)(364,450)(365,449)(366,448)(367,447)
(368,446)(369,445)(370,444)(371,443)(372,442)(373,441)(374,440)(375,439)
(376,438)(377,437)(378,407)(379,435)(380,434)(381,433)(382,432)(383,431)
(384,430)(385,429)(386,428)(387,427)(388,426)(389,425)(390,424)(391,423)
(392,422)(393,421)(394,420)(395,419)(396,418)(397,417)(398,416)(399,415)
(400,414)(401,413)(402,412)(403,411)(404,410)(405,409)(406,408)(465,581)
(466,609)(467,608)(468,607)(469,606)(470,605)(471,604)(472,603)(473,602)
(474,601)(475,600)(476,599)(477,598)(478,597)(479,596)(480,595)(481,594)
(482,593)(483,592)(484,591)(485,590)(486,589)(487,588)(488,587)(489,586)
(490,585)(491,584)(492,583)(493,582)(494,610)(495,638)(496,637)(497,636)
(498,635)(499,634)(500,633)(501,632)(502,631)(503,630)(504,629)(505,628)
(506,627)(507,626)(508,625)(509,624)(510,623)(511,622)(512,621)(513,620)
(514,619)(515,618)(516,617)(517,616)(518,615)(519,614)(520,613)(521,612)
(522,611)(523,639)(524,667)(525,666)(526,665)(527,664)(528,663)(529,662)
(530,661)(531,660)(532,659)(533,658)(534,657)(535,656)(536,655)(537,654)
(538,653)(539,652)(540,651)(541,650)(542,649)(543,648)(544,647)(545,646)
(546,645)(547,644)(548,643)(549,642)(550,641)(551,640)(552,668)(553,696)
(554,695)(555,694)(556,693)(557,692)(558,691)(559,690)(560,689)(561,688)
(562,687)(563,686)(564,685)(565,684)(566,683)(567,682)(568,681)(569,680)
(570,679)(571,678)(572,677)(573,676)(574,675)(575,674)(576,673)(577,672)
(578,671)(579,670)(580,669)(697,871)(698,899)(699,898)(700,897)(701,896)
(702,895)(703,894)(704,893)(705,892)(706,891)(707,890)(708,889)(709,888)
(710,887)(711,886)(712,885)(713,884)(714,883)(715,882)(716,881)(717,880)
(718,879)(719,878)(720,877)(721,876)(722,875)(723,874)(724,873)(725,872)
(726,900)(727,928)(728,927)(729,926)(730,925)(731,924)(732,923)(733,922)
(734,921)(735,920)(736,919)(737,918)(738,917)(739,916)(740,915)(741,914)
(742,913)(743,912)(744,911)(745,910)(746,909)(747,908)(748,907)(749,906)
(750,905)(751,904)(752,903)(753,902)(754,901)(755,813)(756,841)(757,840)
(758,839)(759,838)(760,837)(761,836)(762,835)(763,834)(764,833)(765,832)
(766,831)(767,830)(768,829)(769,828)(770,827)(771,826)(772,825)(773,824)
(774,823)(775,822)(776,821)(777,820)(778,819)(779,818)(780,817)(781,816)
(782,815)(783,814)(784,842)(785,870)(786,869)(787,868)(788,867)(789,866)
(790,865)(791,864)(792,863)(793,862)(794,861)(795,860)(796,859)(797,858)
(798,857)(799,856)(800,855)(801,854)(802,853)(803,852)(804,851)(805,850)
(806,849)(807,848)(808,847)(809,846)(810,845)(811,844)(812,843);
s2 := Sym(928)!(  1,234)(  2,233)(  3,261)(  4,260)(  5,259)(  6,258)(  7,257)
(  8,256)(  9,255)( 10,254)( 11,253)( 12,252)( 13,251)( 14,250)( 15,249)
( 16,248)( 17,247)( 18,246)( 19,245)( 20,244)( 21,243)( 22,242)( 23,241)
( 24,240)( 25,239)( 26,238)( 27,237)( 28,236)( 29,235)( 30,263)( 31,262)
( 32,290)( 33,289)( 34,288)( 35,287)( 36,286)( 37,285)( 38,284)( 39,283)
( 40,282)( 41,281)( 42,280)( 43,279)( 44,278)( 45,277)( 46,276)( 47,275)
( 48,274)( 49,273)( 50,272)( 51,271)( 52,270)( 53,269)( 54,268)( 55,267)
( 56,266)( 57,265)( 58,264)( 59,292)( 60,291)( 61,319)( 62,318)( 63,317)
( 64,316)( 65,315)( 66,314)( 67,313)( 68,312)( 69,311)( 70,310)( 71,309)
( 72,308)( 73,307)( 74,306)( 75,305)( 76,304)( 77,303)( 78,302)( 79,301)
( 80,300)( 81,299)( 82,298)( 83,297)( 84,296)( 85,295)( 86,294)( 87,293)
( 88,321)( 89,320)( 90,348)( 91,347)( 92,346)( 93,345)( 94,344)( 95,343)
( 96,342)( 97,341)( 98,340)( 99,339)(100,338)(101,337)(102,336)(103,335)
(104,334)(105,333)(106,332)(107,331)(108,330)(109,329)(110,328)(111,327)
(112,326)(113,325)(114,324)(115,323)(116,322)(117,350)(118,349)(119,377)
(120,376)(121,375)(122,374)(123,373)(124,372)(125,371)(126,370)(127,369)
(128,368)(129,367)(130,366)(131,365)(132,364)(133,363)(134,362)(135,361)
(136,360)(137,359)(138,358)(139,357)(140,356)(141,355)(142,354)(143,353)
(144,352)(145,351)(146,379)(147,378)(148,406)(149,405)(150,404)(151,403)
(152,402)(153,401)(154,400)(155,399)(156,398)(157,397)(158,396)(159,395)
(160,394)(161,393)(162,392)(163,391)(164,390)(165,389)(166,388)(167,387)
(168,386)(169,385)(170,384)(171,383)(172,382)(173,381)(174,380)(175,408)
(176,407)(177,435)(178,434)(179,433)(180,432)(181,431)(182,430)(183,429)
(184,428)(185,427)(186,426)(187,425)(188,424)(189,423)(190,422)(191,421)
(192,420)(193,419)(194,418)(195,417)(196,416)(197,415)(198,414)(199,413)
(200,412)(201,411)(202,410)(203,409)(204,437)(205,436)(206,464)(207,463)
(208,462)(209,461)(210,460)(211,459)(212,458)(213,457)(214,456)(215,455)
(216,454)(217,453)(218,452)(219,451)(220,450)(221,449)(222,448)(223,447)
(224,446)(225,445)(226,444)(227,443)(228,442)(229,441)(230,440)(231,439)
(232,438)(465,698)(466,697)(467,725)(468,724)(469,723)(470,722)(471,721)
(472,720)(473,719)(474,718)(475,717)(476,716)(477,715)(478,714)(479,713)
(480,712)(481,711)(482,710)(483,709)(484,708)(485,707)(486,706)(487,705)
(488,704)(489,703)(490,702)(491,701)(492,700)(493,699)(494,727)(495,726)
(496,754)(497,753)(498,752)(499,751)(500,750)(501,749)(502,748)(503,747)
(504,746)(505,745)(506,744)(507,743)(508,742)(509,741)(510,740)(511,739)
(512,738)(513,737)(514,736)(515,735)(516,734)(517,733)(518,732)(519,731)
(520,730)(521,729)(522,728)(523,756)(524,755)(525,783)(526,782)(527,781)
(528,780)(529,779)(530,778)(531,777)(532,776)(533,775)(534,774)(535,773)
(536,772)(537,771)(538,770)(539,769)(540,768)(541,767)(542,766)(543,765)
(544,764)(545,763)(546,762)(547,761)(548,760)(549,759)(550,758)(551,757)
(552,785)(553,784)(554,812)(555,811)(556,810)(557,809)(558,808)(559,807)
(560,806)(561,805)(562,804)(563,803)(564,802)(565,801)(566,800)(567,799)
(568,798)(569,797)(570,796)(571,795)(572,794)(573,793)(574,792)(575,791)
(576,790)(577,789)(578,788)(579,787)(580,786)(581,814)(582,813)(583,841)
(584,840)(585,839)(586,838)(587,837)(588,836)(589,835)(590,834)(591,833)
(592,832)(593,831)(594,830)(595,829)(596,828)(597,827)(598,826)(599,825)
(600,824)(601,823)(602,822)(603,821)(604,820)(605,819)(606,818)(607,817)
(608,816)(609,815)(610,843)(611,842)(612,870)(613,869)(614,868)(615,867)
(616,866)(617,865)(618,864)(619,863)(620,862)(621,861)(622,860)(623,859)
(624,858)(625,857)(626,856)(627,855)(628,854)(629,853)(630,852)(631,851)
(632,850)(633,849)(634,848)(635,847)(636,846)(637,845)(638,844)(639,872)
(640,871)(641,899)(642,898)(643,897)(644,896)(645,895)(646,894)(647,893)
(648,892)(649,891)(650,890)(651,889)(652,888)(653,887)(654,886)(655,885)
(656,884)(657,883)(658,882)(659,881)(660,880)(661,879)(662,878)(663,877)
(664,876)(665,875)(666,874)(667,873)(668,901)(669,900)(670,928)(671,927)
(672,926)(673,925)(674,924)(675,923)(676,922)(677,921)(678,920)(679,919)
(680,918)(681,917)(682,916)(683,915)(684,914)(685,913)(686,912)(687,911)
(688,910)(689,909)(690,908)(691,907)(692,906)(693,905)(694,904)(695,903)
(696,902);
poly := sub<Sym(928)|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, 
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*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*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope