Polytope of Type {4,214}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,214}*1712
Also Known As : {4,214|2}. if this polytope has another name.
Group : SmallGroup(1712,34)
Rank : 3
Schlafli Type : {4,214}
Number of vertices, edges, etc : 4, 428, 214
Order of s0s1s2 : 428
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 : {2,214}*856
4-fold quotients : {2,107}*428
107-fold quotients : {4,2}*16
214-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (429,536)(430,537)(431,538)(432,539)(433,540)(434,541)(435,542)(436,543)
(437,544)(438,545)(439,546)(440,547)(441,548)(442,549)(443,550)(444,551)
(445,552)(446,553)(447,554)(448,555)(449,556)(450,557)(451,558)(452,559)
(453,560)(454,561)(455,562)(456,563)(457,564)(458,565)(459,566)(460,567)
(461,568)(462,569)(463,570)(464,571)(465,572)(466,573)(467,574)(468,575)
(469,576)(470,577)(471,578)(472,579)(473,580)(474,581)(475,582)(476,583)
(477,584)(478,585)(479,586)(480,587)(481,588)(482,589)(483,590)(484,591)
(485,592)(486,593)(487,594)(488,595)(489,596)(490,597)(491,598)(492,599)
(493,600)(494,601)(495,602)(496,603)(497,604)(498,605)(499,606)(500,607)
(501,608)(502,609)(503,610)(504,611)(505,612)(506,613)(507,614)(508,615)
(509,616)(510,617)(511,618)(512,619)(513,620)(514,621)(515,622)(516,623)
(517,624)(518,625)(519,626)(520,627)(521,628)(522,629)(523,630)(524,631)
(525,632)(526,633)(527,634)(528,635)(529,636)(530,637)(531,638)(532,639)
(533,640)(534,641)(535,642)(643,750)(644,751)(645,752)(646,753)(647,754)
(648,755)(649,756)(650,757)(651,758)(652,759)(653,760)(654,761)(655,762)
(656,763)(657,764)(658,765)(659,766)(660,767)(661,768)(662,769)(663,770)
(664,771)(665,772)(666,773)(667,774)(668,775)(669,776)(670,777)(671,778)
(672,779)(673,780)(674,781)(675,782)(676,783)(677,784)(678,785)(679,786)
(680,787)(681,788)(682,789)(683,790)(684,791)(685,792)(686,793)(687,794)
(688,795)(689,796)(690,797)(691,798)(692,799)(693,800)(694,801)(695,802)
(696,803)(697,804)(698,805)(699,806)(700,807)(701,808)(702,809)(703,810)
(704,811)(705,812)(706,813)(707,814)(708,815)(709,816)(710,817)(711,818)
(712,819)(713,820)(714,821)(715,822)(716,823)(717,824)(718,825)(719,826)
(720,827)(721,828)(722,829)(723,830)(724,831)(725,832)(726,833)(727,834)
(728,835)(729,836)(730,837)(731,838)(732,839)(733,840)(734,841)(735,842)
(736,843)(737,844)(738,845)(739,846)(740,847)(741,848)(742,849)(743,850)
(744,851)(745,852)(746,853)(747,854)(748,855)(749,856);;
s1 := ( 1,643)( 2,749)( 3,748)( 4,747)( 5,746)( 6,745)( 7,744)( 8,743)
( 9,742)( 10,741)( 11,740)( 12,739)( 13,738)( 14,737)( 15,736)( 16,735)
( 17,734)( 18,733)( 19,732)( 20,731)( 21,730)( 22,729)( 23,728)( 24,727)
( 25,726)( 26,725)( 27,724)( 28,723)( 29,722)( 30,721)( 31,720)( 32,719)
( 33,718)( 34,717)( 35,716)( 36,715)( 37,714)( 38,713)( 39,712)( 40,711)
( 41,710)( 42,709)( 43,708)( 44,707)( 45,706)( 46,705)( 47,704)( 48,703)
( 49,702)( 50,701)( 51,700)( 52,699)( 53,698)( 54,697)( 55,696)( 56,695)
( 57,694)( 58,693)( 59,692)( 60,691)( 61,690)( 62,689)( 63,688)( 64,687)
( 65,686)( 66,685)( 67,684)( 68,683)( 69,682)( 70,681)( 71,680)( 72,679)
( 73,678)( 74,677)( 75,676)( 76,675)( 77,674)( 78,673)( 79,672)( 80,671)
( 81,670)( 82,669)( 83,668)( 84,667)( 85,666)( 86,665)( 87,664)( 88,663)
( 89,662)( 90,661)( 91,660)( 92,659)( 93,658)( 94,657)( 95,656)( 96,655)
( 97,654)( 98,653)( 99,652)(100,651)(101,650)(102,649)(103,648)(104,647)
(105,646)(106,645)(107,644)(108,750)(109,856)(110,855)(111,854)(112,853)
(113,852)(114,851)(115,850)(116,849)(117,848)(118,847)(119,846)(120,845)
(121,844)(122,843)(123,842)(124,841)(125,840)(126,839)(127,838)(128,837)
(129,836)(130,835)(131,834)(132,833)(133,832)(134,831)(135,830)(136,829)
(137,828)(138,827)(139,826)(140,825)(141,824)(142,823)(143,822)(144,821)
(145,820)(146,819)(147,818)(148,817)(149,816)(150,815)(151,814)(152,813)
(153,812)(154,811)(155,810)(156,809)(157,808)(158,807)(159,806)(160,805)
(161,804)(162,803)(163,802)(164,801)(165,800)(166,799)(167,798)(168,797)
(169,796)(170,795)(171,794)(172,793)(173,792)(174,791)(175,790)(176,789)
(177,788)(178,787)(179,786)(180,785)(181,784)(182,783)(183,782)(184,781)
(185,780)(186,779)(187,778)(188,777)(189,776)(190,775)(191,774)(192,773)
(193,772)(194,771)(195,770)(196,769)(197,768)(198,767)(199,766)(200,765)
(201,764)(202,763)(203,762)(204,761)(205,760)(206,759)(207,758)(208,757)
(209,756)(210,755)(211,754)(212,753)(213,752)(214,751)(215,429)(216,535)
(217,534)(218,533)(219,532)(220,531)(221,530)(222,529)(223,528)(224,527)
(225,526)(226,525)(227,524)(228,523)(229,522)(230,521)(231,520)(232,519)
(233,518)(234,517)(235,516)(236,515)(237,514)(238,513)(239,512)(240,511)
(241,510)(242,509)(243,508)(244,507)(245,506)(246,505)(247,504)(248,503)
(249,502)(250,501)(251,500)(252,499)(253,498)(254,497)(255,496)(256,495)
(257,494)(258,493)(259,492)(260,491)(261,490)(262,489)(263,488)(264,487)
(265,486)(266,485)(267,484)(268,483)(269,482)(270,481)(271,480)(272,479)
(273,478)(274,477)(275,476)(276,475)(277,474)(278,473)(279,472)(280,471)
(281,470)(282,469)(283,468)(284,467)(285,466)(286,465)(287,464)(288,463)
(289,462)(290,461)(291,460)(292,459)(293,458)(294,457)(295,456)(296,455)
(297,454)(298,453)(299,452)(300,451)(301,450)(302,449)(303,448)(304,447)
(305,446)(306,445)(307,444)(308,443)(309,442)(310,441)(311,440)(312,439)
(313,438)(314,437)(315,436)(316,435)(317,434)(318,433)(319,432)(320,431)
(321,430)(322,536)(323,642)(324,641)(325,640)(326,639)(327,638)(328,637)
(329,636)(330,635)(331,634)(332,633)(333,632)(334,631)(335,630)(336,629)
(337,628)(338,627)(339,626)(340,625)(341,624)(342,623)(343,622)(344,621)
(345,620)(346,619)(347,618)(348,617)(349,616)(350,615)(351,614)(352,613)
(353,612)(354,611)(355,610)(356,609)(357,608)(358,607)(359,606)(360,605)
(361,604)(362,603)(363,602)(364,601)(365,600)(366,599)(367,598)(368,597)
(369,596)(370,595)(371,594)(372,593)(373,592)(374,591)(375,590)(376,589)
(377,588)(378,587)(379,586)(380,585)(381,584)(382,583)(383,582)(384,581)
(385,580)(386,579)(387,578)(388,577)(389,576)(390,575)(391,574)(392,573)
(393,572)(394,571)(395,570)(396,569)(397,568)(398,567)(399,566)(400,565)
(401,564)(402,563)(403,562)(404,561)(405,560)(406,559)(407,558)(408,557)
(409,556)(410,555)(411,554)(412,553)(413,552)(414,551)(415,550)(416,549)
(417,548)(418,547)(419,546)(420,545)(421,544)(422,543)(423,542)(424,541)
(425,540)(426,539)(427,538)(428,537);;
s2 := ( 1,216)( 2,215)( 3,321)( 4,320)( 5,319)( 6,318)( 7,317)( 8,316)
( 9,315)( 10,314)( 11,313)( 12,312)( 13,311)( 14,310)( 15,309)( 16,308)
( 17,307)( 18,306)( 19,305)( 20,304)( 21,303)( 22,302)( 23,301)( 24,300)
( 25,299)( 26,298)( 27,297)( 28,296)( 29,295)( 30,294)( 31,293)( 32,292)
( 33,291)( 34,290)( 35,289)( 36,288)( 37,287)( 38,286)( 39,285)( 40,284)
( 41,283)( 42,282)( 43,281)( 44,280)( 45,279)( 46,278)( 47,277)( 48,276)
( 49,275)( 50,274)( 51,273)( 52,272)( 53,271)( 54,270)( 55,269)( 56,268)
( 57,267)( 58,266)( 59,265)( 60,264)( 61,263)( 62,262)( 63,261)( 64,260)
( 65,259)( 66,258)( 67,257)( 68,256)( 69,255)( 70,254)( 71,253)( 72,252)
( 73,251)( 74,250)( 75,249)( 76,248)( 77,247)( 78,246)( 79,245)( 80,244)
( 81,243)( 82,242)( 83,241)( 84,240)( 85,239)( 86,238)( 87,237)( 88,236)
( 89,235)( 90,234)( 91,233)( 92,232)( 93,231)( 94,230)( 95,229)( 96,228)
( 97,227)( 98,226)( 99,225)(100,224)(101,223)(102,222)(103,221)(104,220)
(105,219)(106,218)(107,217)(108,323)(109,322)(110,428)(111,427)(112,426)
(113,425)(114,424)(115,423)(116,422)(117,421)(118,420)(119,419)(120,418)
(121,417)(122,416)(123,415)(124,414)(125,413)(126,412)(127,411)(128,410)
(129,409)(130,408)(131,407)(132,406)(133,405)(134,404)(135,403)(136,402)
(137,401)(138,400)(139,399)(140,398)(141,397)(142,396)(143,395)(144,394)
(145,393)(146,392)(147,391)(148,390)(149,389)(150,388)(151,387)(152,386)
(153,385)(154,384)(155,383)(156,382)(157,381)(158,380)(159,379)(160,378)
(161,377)(162,376)(163,375)(164,374)(165,373)(166,372)(167,371)(168,370)
(169,369)(170,368)(171,367)(172,366)(173,365)(174,364)(175,363)(176,362)
(177,361)(178,360)(179,359)(180,358)(181,357)(182,356)(183,355)(184,354)
(185,353)(186,352)(187,351)(188,350)(189,349)(190,348)(191,347)(192,346)
(193,345)(194,344)(195,343)(196,342)(197,341)(198,340)(199,339)(200,338)
(201,337)(202,336)(203,335)(204,334)(205,333)(206,332)(207,331)(208,330)
(209,329)(210,328)(211,327)(212,326)(213,325)(214,324)(429,644)(430,643)
(431,749)(432,748)(433,747)(434,746)(435,745)(436,744)(437,743)(438,742)
(439,741)(440,740)(441,739)(442,738)(443,737)(444,736)(445,735)(446,734)
(447,733)(448,732)(449,731)(450,730)(451,729)(452,728)(453,727)(454,726)
(455,725)(456,724)(457,723)(458,722)(459,721)(460,720)(461,719)(462,718)
(463,717)(464,716)(465,715)(466,714)(467,713)(468,712)(469,711)(470,710)
(471,709)(472,708)(473,707)(474,706)(475,705)(476,704)(477,703)(478,702)
(479,701)(480,700)(481,699)(482,698)(483,697)(484,696)(485,695)(486,694)
(487,693)(488,692)(489,691)(490,690)(491,689)(492,688)(493,687)(494,686)
(495,685)(496,684)(497,683)(498,682)(499,681)(500,680)(501,679)(502,678)
(503,677)(504,676)(505,675)(506,674)(507,673)(508,672)(509,671)(510,670)
(511,669)(512,668)(513,667)(514,666)(515,665)(516,664)(517,663)(518,662)
(519,661)(520,660)(521,659)(522,658)(523,657)(524,656)(525,655)(526,654)
(527,653)(528,652)(529,651)(530,650)(531,649)(532,648)(533,647)(534,646)
(535,645)(536,751)(537,750)(538,856)(539,855)(540,854)(541,853)(542,852)
(543,851)(544,850)(545,849)(546,848)(547,847)(548,846)(549,845)(550,844)
(551,843)(552,842)(553,841)(554,840)(555,839)(556,838)(557,837)(558,836)
(559,835)(560,834)(561,833)(562,832)(563,831)(564,830)(565,829)(566,828)
(567,827)(568,826)(569,825)(570,824)(571,823)(572,822)(573,821)(574,820)
(575,819)(576,818)(577,817)(578,816)(579,815)(580,814)(581,813)(582,812)
(583,811)(584,810)(585,809)(586,808)(587,807)(588,806)(589,805)(590,804)
(591,803)(592,802)(593,801)(594,800)(595,799)(596,798)(597,797)(598,796)
(599,795)(600,794)(601,793)(602,792)(603,791)(604,790)(605,789)(606,788)
(607,787)(608,786)(609,785)(610,784)(611,783)(612,782)(613,781)(614,780)
(615,779)(616,778)(617,777)(618,776)(619,775)(620,774)(621,773)(622,772)
(623,771)(624,770)(625,769)(626,768)(627,767)(628,766)(629,765)(630,764)
(631,763)(632,762)(633,761)(634,760)(635,759)(636,758)(637,757)(638,756)
(639,755)(640,754)(641,753)(642,752);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(856)!(429,536)(430,537)(431,538)(432,539)(433,540)(434,541)(435,542)
(436,543)(437,544)(438,545)(439,546)(440,547)(441,548)(442,549)(443,550)
(444,551)(445,552)(446,553)(447,554)(448,555)(449,556)(450,557)(451,558)
(452,559)(453,560)(454,561)(455,562)(456,563)(457,564)(458,565)(459,566)
(460,567)(461,568)(462,569)(463,570)(464,571)(465,572)(466,573)(467,574)
(468,575)(469,576)(470,577)(471,578)(472,579)(473,580)(474,581)(475,582)
(476,583)(477,584)(478,585)(479,586)(480,587)(481,588)(482,589)(483,590)
(484,591)(485,592)(486,593)(487,594)(488,595)(489,596)(490,597)(491,598)
(492,599)(493,600)(494,601)(495,602)(496,603)(497,604)(498,605)(499,606)
(500,607)(501,608)(502,609)(503,610)(504,611)(505,612)(506,613)(507,614)
(508,615)(509,616)(510,617)(511,618)(512,619)(513,620)(514,621)(515,622)
(516,623)(517,624)(518,625)(519,626)(520,627)(521,628)(522,629)(523,630)
(524,631)(525,632)(526,633)(527,634)(528,635)(529,636)(530,637)(531,638)
(532,639)(533,640)(534,641)(535,642)(643,750)(644,751)(645,752)(646,753)
(647,754)(648,755)(649,756)(650,757)(651,758)(652,759)(653,760)(654,761)
(655,762)(656,763)(657,764)(658,765)(659,766)(660,767)(661,768)(662,769)
(663,770)(664,771)(665,772)(666,773)(667,774)(668,775)(669,776)(670,777)
(671,778)(672,779)(673,780)(674,781)(675,782)(676,783)(677,784)(678,785)
(679,786)(680,787)(681,788)(682,789)(683,790)(684,791)(685,792)(686,793)
(687,794)(688,795)(689,796)(690,797)(691,798)(692,799)(693,800)(694,801)
(695,802)(696,803)(697,804)(698,805)(699,806)(700,807)(701,808)(702,809)
(703,810)(704,811)(705,812)(706,813)(707,814)(708,815)(709,816)(710,817)
(711,818)(712,819)(713,820)(714,821)(715,822)(716,823)(717,824)(718,825)
(719,826)(720,827)(721,828)(722,829)(723,830)(724,831)(725,832)(726,833)
(727,834)(728,835)(729,836)(730,837)(731,838)(732,839)(733,840)(734,841)
(735,842)(736,843)(737,844)(738,845)(739,846)(740,847)(741,848)(742,849)
(743,850)(744,851)(745,852)(746,853)(747,854)(748,855)(749,856);
s1 := Sym(856)!( 1,643)( 2,749)( 3,748)( 4,747)( 5,746)( 6,745)( 7,744)
( 8,743)( 9,742)( 10,741)( 11,740)( 12,739)( 13,738)( 14,737)( 15,736)
( 16,735)( 17,734)( 18,733)( 19,732)( 20,731)( 21,730)( 22,729)( 23,728)
( 24,727)( 25,726)( 26,725)( 27,724)( 28,723)( 29,722)( 30,721)( 31,720)
( 32,719)( 33,718)( 34,717)( 35,716)( 36,715)( 37,714)( 38,713)( 39,712)
( 40,711)( 41,710)( 42,709)( 43,708)( 44,707)( 45,706)( 46,705)( 47,704)
( 48,703)( 49,702)( 50,701)( 51,700)( 52,699)( 53,698)( 54,697)( 55,696)
( 56,695)( 57,694)( 58,693)( 59,692)( 60,691)( 61,690)( 62,689)( 63,688)
( 64,687)( 65,686)( 66,685)( 67,684)( 68,683)( 69,682)( 70,681)( 71,680)
( 72,679)( 73,678)( 74,677)( 75,676)( 76,675)( 77,674)( 78,673)( 79,672)
( 80,671)( 81,670)( 82,669)( 83,668)( 84,667)( 85,666)( 86,665)( 87,664)
( 88,663)( 89,662)( 90,661)( 91,660)( 92,659)( 93,658)( 94,657)( 95,656)
( 96,655)( 97,654)( 98,653)( 99,652)(100,651)(101,650)(102,649)(103,648)
(104,647)(105,646)(106,645)(107,644)(108,750)(109,856)(110,855)(111,854)
(112,853)(113,852)(114,851)(115,850)(116,849)(117,848)(118,847)(119,846)
(120,845)(121,844)(122,843)(123,842)(124,841)(125,840)(126,839)(127,838)
(128,837)(129,836)(130,835)(131,834)(132,833)(133,832)(134,831)(135,830)
(136,829)(137,828)(138,827)(139,826)(140,825)(141,824)(142,823)(143,822)
(144,821)(145,820)(146,819)(147,818)(148,817)(149,816)(150,815)(151,814)
(152,813)(153,812)(154,811)(155,810)(156,809)(157,808)(158,807)(159,806)
(160,805)(161,804)(162,803)(163,802)(164,801)(165,800)(166,799)(167,798)
(168,797)(169,796)(170,795)(171,794)(172,793)(173,792)(174,791)(175,790)
(176,789)(177,788)(178,787)(179,786)(180,785)(181,784)(182,783)(183,782)
(184,781)(185,780)(186,779)(187,778)(188,777)(189,776)(190,775)(191,774)
(192,773)(193,772)(194,771)(195,770)(196,769)(197,768)(198,767)(199,766)
(200,765)(201,764)(202,763)(203,762)(204,761)(205,760)(206,759)(207,758)
(208,757)(209,756)(210,755)(211,754)(212,753)(213,752)(214,751)(215,429)
(216,535)(217,534)(218,533)(219,532)(220,531)(221,530)(222,529)(223,528)
(224,527)(225,526)(226,525)(227,524)(228,523)(229,522)(230,521)(231,520)
(232,519)(233,518)(234,517)(235,516)(236,515)(237,514)(238,513)(239,512)
(240,511)(241,510)(242,509)(243,508)(244,507)(245,506)(246,505)(247,504)
(248,503)(249,502)(250,501)(251,500)(252,499)(253,498)(254,497)(255,496)
(256,495)(257,494)(258,493)(259,492)(260,491)(261,490)(262,489)(263,488)
(264,487)(265,486)(266,485)(267,484)(268,483)(269,482)(270,481)(271,480)
(272,479)(273,478)(274,477)(275,476)(276,475)(277,474)(278,473)(279,472)
(280,471)(281,470)(282,469)(283,468)(284,467)(285,466)(286,465)(287,464)
(288,463)(289,462)(290,461)(291,460)(292,459)(293,458)(294,457)(295,456)
(296,455)(297,454)(298,453)(299,452)(300,451)(301,450)(302,449)(303,448)
(304,447)(305,446)(306,445)(307,444)(308,443)(309,442)(310,441)(311,440)
(312,439)(313,438)(314,437)(315,436)(316,435)(317,434)(318,433)(319,432)
(320,431)(321,430)(322,536)(323,642)(324,641)(325,640)(326,639)(327,638)
(328,637)(329,636)(330,635)(331,634)(332,633)(333,632)(334,631)(335,630)
(336,629)(337,628)(338,627)(339,626)(340,625)(341,624)(342,623)(343,622)
(344,621)(345,620)(346,619)(347,618)(348,617)(349,616)(350,615)(351,614)
(352,613)(353,612)(354,611)(355,610)(356,609)(357,608)(358,607)(359,606)
(360,605)(361,604)(362,603)(363,602)(364,601)(365,600)(366,599)(367,598)
(368,597)(369,596)(370,595)(371,594)(372,593)(373,592)(374,591)(375,590)
(376,589)(377,588)(378,587)(379,586)(380,585)(381,584)(382,583)(383,582)
(384,581)(385,580)(386,579)(387,578)(388,577)(389,576)(390,575)(391,574)
(392,573)(393,572)(394,571)(395,570)(396,569)(397,568)(398,567)(399,566)
(400,565)(401,564)(402,563)(403,562)(404,561)(405,560)(406,559)(407,558)
(408,557)(409,556)(410,555)(411,554)(412,553)(413,552)(414,551)(415,550)
(416,549)(417,548)(418,547)(419,546)(420,545)(421,544)(422,543)(423,542)
(424,541)(425,540)(426,539)(427,538)(428,537);
s2 := Sym(856)!( 1,216)( 2,215)( 3,321)( 4,320)( 5,319)( 6,318)( 7,317)
( 8,316)( 9,315)( 10,314)( 11,313)( 12,312)( 13,311)( 14,310)( 15,309)
( 16,308)( 17,307)( 18,306)( 19,305)( 20,304)( 21,303)( 22,302)( 23,301)
( 24,300)( 25,299)( 26,298)( 27,297)( 28,296)( 29,295)( 30,294)( 31,293)
( 32,292)( 33,291)( 34,290)( 35,289)( 36,288)( 37,287)( 38,286)( 39,285)
( 40,284)( 41,283)( 42,282)( 43,281)( 44,280)( 45,279)( 46,278)( 47,277)
( 48,276)( 49,275)( 50,274)( 51,273)( 52,272)( 53,271)( 54,270)( 55,269)
( 56,268)( 57,267)( 58,266)( 59,265)( 60,264)( 61,263)( 62,262)( 63,261)
( 64,260)( 65,259)( 66,258)( 67,257)( 68,256)( 69,255)( 70,254)( 71,253)
( 72,252)( 73,251)( 74,250)( 75,249)( 76,248)( 77,247)( 78,246)( 79,245)
( 80,244)( 81,243)( 82,242)( 83,241)( 84,240)( 85,239)( 86,238)( 87,237)
( 88,236)( 89,235)( 90,234)( 91,233)( 92,232)( 93,231)( 94,230)( 95,229)
( 96,228)( 97,227)( 98,226)( 99,225)(100,224)(101,223)(102,222)(103,221)
(104,220)(105,219)(106,218)(107,217)(108,323)(109,322)(110,428)(111,427)
(112,426)(113,425)(114,424)(115,423)(116,422)(117,421)(118,420)(119,419)
(120,418)(121,417)(122,416)(123,415)(124,414)(125,413)(126,412)(127,411)
(128,410)(129,409)(130,408)(131,407)(132,406)(133,405)(134,404)(135,403)
(136,402)(137,401)(138,400)(139,399)(140,398)(141,397)(142,396)(143,395)
(144,394)(145,393)(146,392)(147,391)(148,390)(149,389)(150,388)(151,387)
(152,386)(153,385)(154,384)(155,383)(156,382)(157,381)(158,380)(159,379)
(160,378)(161,377)(162,376)(163,375)(164,374)(165,373)(166,372)(167,371)
(168,370)(169,369)(170,368)(171,367)(172,366)(173,365)(174,364)(175,363)
(176,362)(177,361)(178,360)(179,359)(180,358)(181,357)(182,356)(183,355)
(184,354)(185,353)(186,352)(187,351)(188,350)(189,349)(190,348)(191,347)
(192,346)(193,345)(194,344)(195,343)(196,342)(197,341)(198,340)(199,339)
(200,338)(201,337)(202,336)(203,335)(204,334)(205,333)(206,332)(207,331)
(208,330)(209,329)(210,328)(211,327)(212,326)(213,325)(214,324)(429,644)
(430,643)(431,749)(432,748)(433,747)(434,746)(435,745)(436,744)(437,743)
(438,742)(439,741)(440,740)(441,739)(442,738)(443,737)(444,736)(445,735)
(446,734)(447,733)(448,732)(449,731)(450,730)(451,729)(452,728)(453,727)
(454,726)(455,725)(456,724)(457,723)(458,722)(459,721)(460,720)(461,719)
(462,718)(463,717)(464,716)(465,715)(466,714)(467,713)(468,712)(469,711)
(470,710)(471,709)(472,708)(473,707)(474,706)(475,705)(476,704)(477,703)
(478,702)(479,701)(480,700)(481,699)(482,698)(483,697)(484,696)(485,695)
(486,694)(487,693)(488,692)(489,691)(490,690)(491,689)(492,688)(493,687)
(494,686)(495,685)(496,684)(497,683)(498,682)(499,681)(500,680)(501,679)
(502,678)(503,677)(504,676)(505,675)(506,674)(507,673)(508,672)(509,671)
(510,670)(511,669)(512,668)(513,667)(514,666)(515,665)(516,664)(517,663)
(518,662)(519,661)(520,660)(521,659)(522,658)(523,657)(524,656)(525,655)
(526,654)(527,653)(528,652)(529,651)(530,650)(531,649)(532,648)(533,647)
(534,646)(535,645)(536,751)(537,750)(538,856)(539,855)(540,854)(541,853)
(542,852)(543,851)(544,850)(545,849)(546,848)(547,847)(548,846)(549,845)
(550,844)(551,843)(552,842)(553,841)(554,840)(555,839)(556,838)(557,837)
(558,836)(559,835)(560,834)(561,833)(562,832)(563,831)(564,830)(565,829)
(566,828)(567,827)(568,826)(569,825)(570,824)(571,823)(572,822)(573,821)
(574,820)(575,819)(576,818)(577,817)(578,816)(579,815)(580,814)(581,813)
(582,812)(583,811)(584,810)(585,809)(586,808)(587,807)(588,806)(589,805)
(590,804)(591,803)(592,802)(593,801)(594,800)(595,799)(596,798)(597,797)
(598,796)(599,795)(600,794)(601,793)(602,792)(603,791)(604,790)(605,789)
(606,788)(607,787)(608,786)(609,785)(610,784)(611,783)(612,782)(613,781)
(614,780)(615,779)(616,778)(617,777)(618,776)(619,775)(620,774)(621,773)
(622,772)(623,771)(624,770)(625,769)(626,768)(627,767)(628,766)(629,765)
(630,764)(631,763)(632,762)(633,761)(634,760)(635,759)(636,758)(637,757)
(638,756)(639,755)(640,754)(641,753)(642,752);
poly := sub<Sym(856)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope