Polytope of Type {212,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {212,4}*1696
Also Known As : {212,4|2}. if this polytope has another name.
Group : SmallGroup(1696,116)
Rank : 3
Schlafli Type : {212,4}
Number of vertices, edges, etc : 212, 424, 4
Order of s₀s₁s₂ : 212
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {212,2}*848, {106,4}*848
   4-fold quotients : {106,2}*424
   8-fold quotients : {53,2}*212
   53-fold quotients : {4,4}*32
   106-fold quotients : {2,4}*16, {4,2}*16
   212-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope