Polytope of Type {890}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {890}*1780
Also Known As : 890-gon, {890}. if this polytope has another name.
Group : SmallGroup(1780,14)
Rank : 2
Schlafli Type : {890}
Number of vertices, edges, etc : 890, 890
Order of s₀s₁ : 890
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 : {445}*890
   5-fold quotients : {178}*356
   10-fold quotients : {89}*178
   89-fold quotients : {10}*20
   178-fold quotients : {5}*10
   445-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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