Polytope of Type {8,116}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,116}*1856b
if this polytope has a name.
Group : SmallGroup(1856,718)
Rank : 3
Schlafli Type : {8,116}
Number of vertices, edges, etc : 8, 464, 116
Order of s₀s₁s₂ : 232
Order of s₀s₁s₂s₁ : 4
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
   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}*64b
   58-fold quotients : {4,4}*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)( 59,552)( 60,553)( 61,554)( 62,555)( 63,556)( 64,557)
( 65,558)( 66,559)( 67,560)( 68,561)( 69,562)( 70,563)( 71,564)( 72,565)
( 73,566)( 74,567)( 75,568)( 76,569)( 77,570)( 78,571)( 79,572)( 80,573)
( 81,574)( 82,575)( 83,576)( 84,577)( 85,578)( 86,579)( 87,580)( 88,523)
( 89,524)( 90,525)( 91,526)( 92,527)( 93,528)( 94,529)( 95,530)( 96,531)
( 97,532)( 98,533)( 99,534)(100,535)(101,536)(102,537)(103,538)(104,539)
(105,540)(106,541)(107,542)(108,543)(109,544)(110,545)(111,546)(112,547)
(113,548)(114,549)(115,550)(116,551)(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)(175,639)(176,640)
(177,641)(178,642)(179,643)(180,644)(181,645)(182,646)(183,647)(184,648)
(185,649)(186,650)(187,651)(188,652)(189,653)(190,654)(191,655)(192,656)
(193,657)(194,658)(195,659)(196,660)(197,661)(198,662)(199,663)(200,664)
(201,665)(202,666)(203,667)(204,668)(205,669)(206,670)(207,671)(208,672)
(209,673)(210,674)(211,675)(212,676)(213,677)(214,678)(215,679)(216,680)
(217,681)(218,682)(219,683)(220,684)(221,685)(222,686)(223,687)(224,688)
(225,689)(226,690)(227,691)(228,692)(229,693)(230,694)(231,695)(232,696)
(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)(291,784)(292,785)(293,786)(294,787)(295,788)(296,789)
(297,790)(298,791)(299,792)(300,793)(301,794)(302,795)(303,796)(304,797)
(305,798)(306,799)(307,800)(308,801)(309,802)(310,803)(311,804)(312,805)
(313,806)(314,807)(315,808)(316,809)(317,810)(318,811)(319,812)(320,755)
(321,756)(322,757)(323,758)(324,759)(325,760)(326,761)(327,762)(328,763)
(329,764)(330,765)(331,766)(332,767)(333,768)(334,769)(335,770)(336,771)
(337,772)(338,773)(339,774)(340,775)(341,776)(342,777)(343,778)(344,779)
(345,780)(346,781)(347,782)(348,783)(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)(407,871)(408,872)
(409,873)(410,874)(411,875)(412,876)(413,877)(414,878)(415,879)(416,880)
(417,881)(418,882)(419,883)(420,884)(421,885)(422,886)(423,887)(424,888)
(425,889)(426,890)(427,891)(428,892)(429,893)(430,894)(431,895)(432,896)
(433,897)(434,898)(435,899)(436,900)(437,901)(438,902)(439,903)(440,904)
(441,905)(442,906)(443,907)(444,908)(445,909)(446,910)(447,911)(448,912)
(449,913)(450,914)(451,915)(452,916)(453,917)(454,918)(455,919)(456,920)
(457,921)(458,922)(459,923)(460,924)(461,925)(462,926)(463,927)(464,928);;
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)(697,900)(698,928)(699,927)(700,926)(701,925)(702,924)
(703,923)(704,922)(705,921)(706,920)(707,919)(708,918)(709,917)(710,916)
(711,915)(712,914)(713,913)(714,912)(715,911)(716,910)(717,909)(718,908)
(719,907)(720,906)(721,905)(722,904)(723,903)(724,902)(725,901)(726,871)
(727,899)(728,898)(729,897)(730,896)(731,895)(732,894)(733,893)(734,892)
(735,891)(736,890)(737,889)(738,888)(739,887)(740,886)(741,885)(742,884)
(743,883)(744,882)(745,881)(746,880)(747,879)(748,878)(749,877)(750,876)
(751,875)(752,874)(753,873)(754,872)(755,842)(756,870)(757,869)(758,868)
(759,867)(760,866)(761,865)(762,864)(763,863)(764,862)(765,861)(766,860)
(767,859)(768,858)(769,857)(770,856)(771,855)(772,854)(773,853)(774,852)
(775,851)(776,850)(777,849)(778,848)(779,847)(780,846)(781,845)(782,844)
(783,843)(784,813)(785,841)(786,840)(787,839)(788,838)(789,837)(790,836)
(791,835)(792,834)(793,833)(794,832)(795,831)(796,830)(797,829)(798,828)
(799,827)(800,826)(801,825)(802,824)(803,823)(804,822)(805,821)(806,820)
(807,819)(808,818)(809,817)(810,816)(811,815)(812,814);;
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)(117,379)(118,378)(119,406)(120,405)
(121,404)(122,403)(123,402)(124,401)(125,400)(126,399)(127,398)(128,397)
(129,396)(130,395)(131,394)(132,393)(133,392)(134,391)(135,390)(136,389)
(137,388)(138,387)(139,386)(140,385)(141,384)(142,383)(143,382)(144,381)
(145,380)(146,350)(147,349)(148,377)(149,376)(150,375)(151,374)(152,373)
(153,372)(154,371)(155,370)(156,369)(157,368)(158,367)(159,366)(160,365)
(161,364)(162,363)(163,362)(164,361)(165,360)(166,359)(167,358)(168,357)
(169,356)(170,355)(171,354)(172,353)(173,352)(174,351)(175,437)(176,436)
(177,464)(178,463)(179,462)(180,461)(181,460)(182,459)(183,458)(184,457)
(185,456)(186,455)(187,454)(188,453)(189,452)(190,451)(191,450)(192,449)
(193,448)(194,447)(195,446)(196,445)(197,444)(198,443)(199,442)(200,441)
(201,440)(202,439)(203,438)(204,408)(205,407)(206,435)(207,434)(208,433)
(209,432)(210,431)(211,430)(212,429)(213,428)(214,427)(215,426)(216,425)
(217,424)(218,423)(219,422)(220,421)(221,420)(222,419)(223,418)(224,417)
(225,416)(226,415)(227,414)(228,413)(229,412)(230,411)(231,410)(232,409)
(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)(581,843)(582,842)(583,870)(584,869)
(585,868)(586,867)(587,866)(588,865)(589,864)(590,863)(591,862)(592,861)
(593,860)(594,859)(595,858)(596,857)(597,856)(598,855)(599,854)(600,853)
(601,852)(602,851)(603,850)(604,849)(605,848)(606,847)(607,846)(608,845)
(609,844)(610,814)(611,813)(612,841)(613,840)(614,839)(615,838)(616,837)
(617,836)(618,835)(619,834)(620,833)(621,832)(622,831)(623,830)(624,829)
(625,828)(626,827)(627,826)(628,825)(629,824)(630,823)(631,822)(632,821)
(633,820)(634,819)(635,818)(636,817)(637,816)(638,815)(639,901)(640,900)
(641,928)(642,927)(643,926)(644,925)(645,924)(646,923)(647,922)(648,921)
(649,920)(650,919)(651,918)(652,917)(653,916)(654,915)(655,914)(656,913)
(657,912)(658,911)(659,910)(660,909)(661,908)(662,907)(663,906)(664,905)
(665,904)(666,903)(667,902)(668,872)(669,871)(670,899)(671,898)(672,897)
(673,896)(674,895)(675,894)(676,893)(677,892)(678,891)(679,890)(680,889)
(681,888)(682,887)(683,886)(684,885)(685,884)(686,883)(687,882)(688,881)
(689,880)(690,879)(691,878)(692,877)(693,876)(694,875)(695,874)(696,873);;
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, 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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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)( 59,552)( 60,553)( 61,554)( 62,555)( 63,556)
( 64,557)( 65,558)( 66,559)( 67,560)( 68,561)( 69,562)( 70,563)( 71,564)
( 72,565)( 73,566)( 74,567)( 75,568)( 76,569)( 77,570)( 78,571)( 79,572)
( 80,573)( 81,574)( 82,575)( 83,576)( 84,577)( 85,578)( 86,579)( 87,580)
( 88,523)( 89,524)( 90,525)( 91,526)( 92,527)( 93,528)( 94,529)( 95,530)
( 96,531)( 97,532)( 98,533)( 99,534)(100,535)(101,536)(102,537)(103,538)
(104,539)(105,540)(106,541)(107,542)(108,543)(109,544)(110,545)(111,546)
(112,547)(113,548)(114,549)(115,550)(116,551)(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)(175,639)
(176,640)(177,641)(178,642)(179,643)(180,644)(181,645)(182,646)(183,647)
(184,648)(185,649)(186,650)(187,651)(188,652)(189,653)(190,654)(191,655)
(192,656)(193,657)(194,658)(195,659)(196,660)(197,661)(198,662)(199,663)
(200,664)(201,665)(202,666)(203,667)(204,668)(205,669)(206,670)(207,671)
(208,672)(209,673)(210,674)(211,675)(212,676)(213,677)(214,678)(215,679)
(216,680)(217,681)(218,682)(219,683)(220,684)(221,685)(222,686)(223,687)
(224,688)(225,689)(226,690)(227,691)(228,692)(229,693)(230,694)(231,695)
(232,696)(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)(291,784)(292,785)(293,786)(294,787)(295,788)
(296,789)(297,790)(298,791)(299,792)(300,793)(301,794)(302,795)(303,796)
(304,797)(305,798)(306,799)(307,800)(308,801)(309,802)(310,803)(311,804)
(312,805)(313,806)(314,807)(315,808)(316,809)(317,810)(318,811)(319,812)
(320,755)(321,756)(322,757)(323,758)(324,759)(325,760)(326,761)(327,762)
(328,763)(329,764)(330,765)(331,766)(332,767)(333,768)(334,769)(335,770)
(336,771)(337,772)(338,773)(339,774)(340,775)(341,776)(342,777)(343,778)
(344,779)(345,780)(346,781)(347,782)(348,783)(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)(407,871)
(408,872)(409,873)(410,874)(411,875)(412,876)(413,877)(414,878)(415,879)
(416,880)(417,881)(418,882)(419,883)(420,884)(421,885)(422,886)(423,887)
(424,888)(425,889)(426,890)(427,891)(428,892)(429,893)(430,894)(431,895)
(432,896)(433,897)(434,898)(435,899)(436,900)(437,901)(438,902)(439,903)
(440,904)(441,905)(442,906)(443,907)(444,908)(445,909)(446,910)(447,911)
(448,912)(449,913)(450,914)(451,915)(452,916)(453,917)(454,918)(455,919)
(456,920)(457,921)(458,922)(459,923)(460,924)(461,925)(462,926)(463,927)
(464,928);
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)(697,900)(698,928)(699,927)(700,926)(701,925)
(702,924)(703,923)(704,922)(705,921)(706,920)(707,919)(708,918)(709,917)
(710,916)(711,915)(712,914)(713,913)(714,912)(715,911)(716,910)(717,909)
(718,908)(719,907)(720,906)(721,905)(722,904)(723,903)(724,902)(725,901)
(726,871)(727,899)(728,898)(729,897)(730,896)(731,895)(732,894)(733,893)
(734,892)(735,891)(736,890)(737,889)(738,888)(739,887)(740,886)(741,885)
(742,884)(743,883)(744,882)(745,881)(746,880)(747,879)(748,878)(749,877)
(750,876)(751,875)(752,874)(753,873)(754,872)(755,842)(756,870)(757,869)
(758,868)(759,867)(760,866)(761,865)(762,864)(763,863)(764,862)(765,861)
(766,860)(767,859)(768,858)(769,857)(770,856)(771,855)(772,854)(773,853)
(774,852)(775,851)(776,850)(777,849)(778,848)(779,847)(780,846)(781,845)
(782,844)(783,843)(784,813)(785,841)(786,840)(787,839)(788,838)(789,837)
(790,836)(791,835)(792,834)(793,833)(794,832)(795,831)(796,830)(797,829)
(798,828)(799,827)(800,826)(801,825)(802,824)(803,823)(804,822)(805,821)
(806,820)(807,819)(808,818)(809,817)(810,816)(811,815)(812,814);
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)(117,379)(118,378)(119,406)
(120,405)(121,404)(122,403)(123,402)(124,401)(125,400)(126,399)(127,398)
(128,397)(129,396)(130,395)(131,394)(132,393)(133,392)(134,391)(135,390)
(136,389)(137,388)(138,387)(139,386)(140,385)(141,384)(142,383)(143,382)
(144,381)(145,380)(146,350)(147,349)(148,377)(149,376)(150,375)(151,374)
(152,373)(153,372)(154,371)(155,370)(156,369)(157,368)(158,367)(159,366)
(160,365)(161,364)(162,363)(163,362)(164,361)(165,360)(166,359)(167,358)
(168,357)(169,356)(170,355)(171,354)(172,353)(173,352)(174,351)(175,437)
(176,436)(177,464)(178,463)(179,462)(180,461)(181,460)(182,459)(183,458)
(184,457)(185,456)(186,455)(187,454)(188,453)(189,452)(190,451)(191,450)
(192,449)(193,448)(194,447)(195,446)(196,445)(197,444)(198,443)(199,442)
(200,441)(201,440)(202,439)(203,438)(204,408)(205,407)(206,435)(207,434)
(208,433)(209,432)(210,431)(211,430)(212,429)(213,428)(214,427)(215,426)
(216,425)(217,424)(218,423)(219,422)(220,421)(221,420)(222,419)(223,418)
(224,417)(225,416)(226,415)(227,414)(228,413)(229,412)(230,411)(231,410)
(232,409)(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)(581,843)(582,842)(583,870)
(584,869)(585,868)(586,867)(587,866)(588,865)(589,864)(590,863)(591,862)
(592,861)(593,860)(594,859)(595,858)(596,857)(597,856)(598,855)(599,854)
(600,853)(601,852)(602,851)(603,850)(604,849)(605,848)(606,847)(607,846)
(608,845)(609,844)(610,814)(611,813)(612,841)(613,840)(614,839)(615,838)
(616,837)(617,836)(618,835)(619,834)(620,833)(621,832)(622,831)(623,830)
(624,829)(625,828)(626,827)(627,826)(628,825)(629,824)(630,823)(631,822)
(632,821)(633,820)(634,819)(635,818)(636,817)(637,816)(638,815)(639,901)
(640,900)(641,928)(642,927)(643,926)(644,925)(645,924)(646,923)(647,922)
(648,921)(649,920)(650,919)(651,918)(652,917)(653,916)(654,915)(655,914)
(656,913)(657,912)(658,911)(659,910)(660,909)(661,908)(662,907)(663,906)
(664,905)(665,904)(666,903)(667,902)(668,872)(669,871)(670,899)(671,898)
(672,897)(673,896)(674,895)(675,894)(676,893)(677,892)(678,891)(679,890)
(680,889)(681,888)(682,887)(683,886)(684,885)(685,884)(686,883)(687,882)
(688,881)(689,880)(690,879)(691,878)(692,877)(693,876)(694,875)(695,874)
(696,873);
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, 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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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