Polytope of Type {4,111}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,111}*1776
if this polytope has a name.
Group : SmallGroup(1776,245)
Rank : 3
Schlafli Type : {4,111}
Number of vertices, edges, etc : 8, 444, 222
Order of s₀s₁s₂ : 222
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {4,111}*888
   4-fold quotients : {2,111}*444
   12-fold quotients : {2,37}*148
   37-fold quotients : {4,3}*48
   74-fold quotients : {4,3}*24
   148-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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