Polytope of Type {4,212}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,212}*1696
Also Known As : {4,212|2}. if this polytope has another name.
Group : SmallGroup(1696,116)
Rank : 3
Schlafli Type : {4,212}
Number of vertices, edges, etc : 4, 424, 212
Order of s₀s₁s₂ : 212
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 : {2,212}*848, {4,106}*848
   4-fold quotients : {2,106}*424
   8-fold quotients : {2,53}*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 := (  1,425)(  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);;
s1 := (  2, 53)(  3, 52)(  4, 51)(  5, 50)(  6, 49)(  7, 48)(  8, 47)(  9, 46)
( 10, 45)( 11, 44)( 12, 43)( 13, 42)( 14, 41)( 15, 40)( 16, 39)( 17, 38)
( 18, 37)( 19, 36)( 20, 35)( 21, 34)( 22, 33)( 23, 32)( 24, 31)( 25, 30)
( 26, 29)( 27, 28)( 55,106)( 56,105)( 57,104)( 58,103)( 59,102)( 60,101)
( 61,100)( 62, 99)( 63, 98)( 64, 97)( 65, 96)( 66, 95)( 67, 94)( 68, 93)
( 69, 92)( 70, 91)( 71, 90)( 72, 89)( 73, 88)( 74, 87)( 75, 86)( 76, 85)
( 77, 84)( 78, 83)( 79, 82)( 80, 81)(108,159)(109,158)(110,157)(111,156)
(112,155)(113,154)(114,153)(115,152)(116,151)(117,150)(118,149)(119,148)
(120,147)(121,146)(122,145)(123,144)(124,143)(125,142)(126,141)(127,140)
(128,139)(129,138)(130,137)(131,136)(132,135)(133,134)(161,212)(162,211)
(163,210)(164,209)(165,208)(166,207)(167,206)(168,205)(169,204)(170,203)
(171,202)(172,201)(173,200)(174,199)(175,198)(176,197)(177,196)(178,195)
(179,194)(180,193)(181,192)(182,191)(183,190)(184,189)(185,188)(186,187)
(213,266)(214,318)(215,317)(216,316)(217,315)(218,314)(219,313)(220,312)
(221,311)(222,310)(223,309)(224,308)(225,307)(226,306)(227,305)(228,304)
(229,303)(230,302)(231,301)(232,300)(233,299)(234,298)(235,297)(236,296)
(237,295)(238,294)(239,293)(240,292)(241,291)(242,290)(243,289)(244,288)
(245,287)(246,286)(247,285)(248,284)(249,283)(250,282)(251,281)(252,280)
(253,279)(254,278)(255,277)(256,276)(257,275)(258,274)(259,273)(260,272)
(261,271)(262,270)(263,269)(264,268)(265,267)(319,372)(320,424)(321,423)
(322,422)(323,421)(324,420)(325,419)(326,418)(327,417)(328,416)(329,415)
(330,414)(331,413)(332,412)(333,411)(334,410)(335,409)(336,408)(337,407)
(338,406)(339,405)(340,404)(341,403)(342,402)(343,401)(344,400)(345,399)
(346,398)(347,397)(348,396)(349,395)(350,394)(351,393)(352,392)(353,391)
(354,390)(355,389)(356,388)(357,387)(358,386)(359,385)(360,384)(361,383)
(362,382)(363,381)(364,380)(365,379)(366,378)(367,377)(368,376)(369,375)
(370,374)(371,373)(425,531)(426,583)(427,582)(428,581)(429,580)(430,579)
(431,578)(432,577)(433,576)(434,575)(435,574)(436,573)(437,572)(438,571)
(439,570)(440,569)(441,568)(442,567)(443,566)(444,565)(445,564)(446,563)
(447,562)(448,561)(449,560)(450,559)(451,558)(452,557)(453,556)(454,555)
(455,554)(456,553)(457,552)(458,551)(459,550)(460,549)(461,548)(462,547)
(463,546)(464,545)(465,544)(466,543)(467,542)(468,541)(469,540)(470,539)
(471,538)(472,537)(473,536)(474,535)(475,534)(476,533)(477,532)(478,584)
(479,636)(480,635)(481,634)(482,633)(483,632)(484,631)(485,630)(486,629)
(487,628)(488,627)(489,626)(490,625)(491,624)(492,623)(493,622)(494,621)
(495,620)(496,619)(497,618)(498,617)(499,616)(500,615)(501,614)(502,613)
(503,612)(504,611)(505,610)(506,609)(507,608)(508,607)(509,606)(510,605)
(511,604)(512,603)(513,602)(514,601)(515,600)(516,599)(517,598)(518,597)
(519,596)(520,595)(521,594)(522,593)(523,592)(524,591)(525,590)(526,589)
(527,588)(528,587)(529,586)(530,585)(637,796)(638,848)(639,847)(640,846)
(641,845)(642,844)(643,843)(644,842)(645,841)(646,840)(647,839)(648,838)
(649,837)(650,836)(651,835)(652,834)(653,833)(654,832)(655,831)(656,830)
(657,829)(658,828)(659,827)(660,826)(661,825)(662,824)(663,823)(664,822)
(665,821)(666,820)(667,819)(668,818)(669,817)(670,816)(671,815)(672,814)
(673,813)(674,812)(675,811)(676,810)(677,809)(678,808)(679,807)(680,806)
(681,805)(682,804)(683,803)(684,802)(685,801)(686,800)(687,799)(688,798)
(689,797)(690,743)(691,795)(692,794)(693,793)(694,792)(695,791)(696,790)
(697,789)(698,788)(699,787)(700,786)(701,785)(702,784)(703,783)(704,782)
(705,781)(706,780)(707,779)(708,778)(709,777)(710,776)(711,775)(712,774)
(713,773)(714,772)(715,771)(716,770)(717,769)(718,768)(719,767)(720,766)
(721,765)(722,764)(723,763)(724,762)(725,761)(726,760)(727,759)(728,758)
(729,757)(730,756)(731,755)(732,754)(733,753)(734,752)(735,751)(736,750)
(737,749)(738,748)(739,747)(740,746)(741,745)(742,744);;
s2 := (  1,214)(  2,213)(  3,265)(  4,264)(  5,263)(  6,262)(  7,261)(  8,260)
(  9,259)( 10,258)( 11,257)( 12,256)( 13,255)( 14,254)( 15,253)( 16,252)
( 17,251)( 18,250)( 19,249)( 20,248)( 21,247)( 22,246)( 23,245)( 24,244)
( 25,243)( 26,242)( 27,241)( 28,240)( 29,239)( 30,238)( 31,237)( 32,236)
( 33,235)( 34,234)( 35,233)( 36,232)( 37,231)( 38,230)( 39,229)( 40,228)
( 41,227)( 42,226)( 43,225)( 44,224)( 45,223)( 46,222)( 47,221)( 48,220)
( 49,219)( 50,218)( 51,217)( 52,216)( 53,215)( 54,267)( 55,266)( 56,318)
( 57,317)( 58,316)( 59,315)( 60,314)( 61,313)( 62,312)( 63,311)( 64,310)
( 65,309)( 66,308)( 67,307)( 68,306)( 69,305)( 70,304)( 71,303)( 72,302)
( 73,301)( 74,300)( 75,299)( 76,298)( 77,297)( 78,296)( 79,295)( 80,294)
( 81,293)( 82,292)( 83,291)( 84,290)( 85,289)( 86,288)( 87,287)( 88,286)
( 89,285)( 90,284)( 91,283)( 92,282)( 93,281)( 94,280)( 95,279)( 96,278)
( 97,277)( 98,276)( 99,275)(100,274)(101,273)(102,272)(103,271)(104,270)
(105,269)(106,268)(107,320)(108,319)(109,371)(110,370)(111,369)(112,368)
(113,367)(114,366)(115,365)(116,364)(117,363)(118,362)(119,361)(120,360)
(121,359)(122,358)(123,357)(124,356)(125,355)(126,354)(127,353)(128,352)
(129,351)(130,350)(131,349)(132,348)(133,347)(134,346)(135,345)(136,344)
(137,343)(138,342)(139,341)(140,340)(141,339)(142,338)(143,337)(144,336)
(145,335)(146,334)(147,333)(148,332)(149,331)(150,330)(151,329)(152,328)
(153,327)(154,326)(155,325)(156,324)(157,323)(158,322)(159,321)(160,373)
(161,372)(162,424)(163,423)(164,422)(165,421)(166,420)(167,419)(168,418)
(169,417)(170,416)(171,415)(172,414)(173,413)(174,412)(175,411)(176,410)
(177,409)(178,408)(179,407)(180,406)(181,405)(182,404)(183,403)(184,402)
(185,401)(186,400)(187,399)(188,398)(189,397)(190,396)(191,395)(192,394)
(193,393)(194,392)(195,391)(196,390)(197,389)(198,388)(199,387)(200,386)
(201,385)(202,384)(203,383)(204,382)(205,381)(206,380)(207,379)(208,378)
(209,377)(210,376)(211,375)(212,374)(425,638)(426,637)(427,689)(428,688)
(429,687)(430,686)(431,685)(432,684)(433,683)(434,682)(435,681)(436,680)
(437,679)(438,678)(439,677)(440,676)(441,675)(442,674)(443,673)(444,672)
(445,671)(446,670)(447,669)(448,668)(449,667)(450,666)(451,665)(452,664)
(453,663)(454,662)(455,661)(456,660)(457,659)(458,658)(459,657)(460,656)
(461,655)(462,654)(463,653)(464,652)(465,651)(466,650)(467,649)(468,648)
(469,647)(470,646)(471,645)(472,644)(473,643)(474,642)(475,641)(476,640)
(477,639)(478,691)(479,690)(480,742)(481,741)(482,740)(483,739)(484,738)
(485,737)(486,736)(487,735)(488,734)(489,733)(490,732)(491,731)(492,730)
(493,729)(494,728)(495,727)(496,726)(497,725)(498,724)(499,723)(500,722)
(501,721)(502,720)(503,719)(504,718)(505,717)(506,716)(507,715)(508,714)
(509,713)(510,712)(511,711)(512,710)(513,709)(514,708)(515,707)(516,706)
(517,705)(518,704)(519,703)(520,702)(521,701)(522,700)(523,699)(524,698)
(525,697)(526,696)(527,695)(528,694)(529,693)(530,692)(531,744)(532,743)
(533,795)(534,794)(535,793)(536,792)(537,791)(538,790)(539,789)(540,788)
(541,787)(542,786)(543,785)(544,784)(545,783)(546,782)(547,781)(548,780)
(549,779)(550,778)(551,777)(552,776)(553,775)(554,774)(555,773)(556,772)
(557,771)(558,770)(559,769)(560,768)(561,767)(562,766)(563,765)(564,764)
(565,763)(566,762)(567,761)(568,760)(569,759)(570,758)(571,757)(572,756)
(573,755)(574,754)(575,753)(576,752)(577,751)(578,750)(579,749)(580,748)
(581,747)(582,746)(583,745)(584,797)(585,796)(586,848)(587,847)(588,846)
(589,845)(590,844)(591,843)(592,842)(593,841)(594,840)(595,839)(596,838)
(597,837)(598,836)(599,835)(600,834)(601,833)(602,832)(603,831)(604,830)
(605,829)(606,828)(607,827)(608,826)(609,825)(610,824)(611,823)(612,822)
(613,821)(614,820)(615,819)(616,818)(617,817)(618,816)(619,815)(620,814)
(621,813)(622,812)(623,811)(624,810)(625,809)(626,808)(627,807)(628,806)
(629,805)(630,804)(631,803)(632,802)(633,801)(634,800)(635,799)(636,798);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope