Polytope of Type {840}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {840}*1680
Also Known As : 840-gon, {840}. if this polytope has another name.
Group : SmallGroup(1680,376)
Rank : 2
Schlafli Type : {840}
Number of vertices, edges, etc : 840, 840
Order of s₀s₁ : 840
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
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 : {420}*840
   3-fold quotients : {280}*560
   4-fold quotients : {210}*420
   5-fold quotients : {168}*336
   6-fold quotients : {140}*280
   7-fold quotients : {120}*240
   8-fold quotients : {105}*210
   10-fold quotients : {84}*168
   12-fold quotients : {70}*140
   14-fold quotients : {60}*120
   15-fold quotients : {56}*112
   20-fold quotients : {42}*84
   21-fold quotients : {40}*80
   24-fold quotients : {35}*70
   28-fold quotients : {30}*60
   30-fold quotients : {28}*56
   35-fold quotients : {24}*48
   40-fold quotients : {21}*42
   42-fold quotients : {20}*40
   56-fold quotients : {15}*30
   60-fold quotients : {14}*28
   70-fold quotients : {12}*24
   84-fold quotients : {10}*20
   105-fold quotients : {8}*16
   120-fold quotients : {7}*14
   140-fold quotients : {6}*12
   168-fold quotients : {5}*10
   210-fold quotients : {4}*8
   280-fold quotients : {3}*6
   420-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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