Polytope of Type {4,218}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,218}*1744
Also Known As : {4,218|2}. if this polytope has another name.
Group : SmallGroup(1744,34)
Rank : 3
Schlafli Type : {4,218}
Number of vertices, edges, etc : 4, 436, 218
Order of s₀s₁s₂ : 436
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 : {2,218}*872
   4-fold quotients : {2,109}*436
   109-fold quotients : {4,2}*16
   218-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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