Polytope of Type {226,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {226,4}*1808
Also Known As : {226,4|2}. if this polytope has another name.
Group : SmallGroup(1808,34)
Rank : 3
Schlafli Type : {226,4}
Number of vertices, edges, etc : 226, 452, 4
Order of s₀s₁s₂ : 452
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 : {226,2}*904
   4-fold quotients : {113,2}*452
   113-fold quotients : {2,4}*16
   226-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope