Polytope of Type {218,4}

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

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope