Polytope of Type {864}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {864}*1728
Also Known As : 864-gon, {864}. if this polytope has another name.
Group : SmallGroup(1728,8)
Rank : 2
Schlafli Type : {864}
Number of vertices, edges, etc : 864, 864
Order of s₀s₁ : 864
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 : {432}*864
   3-fold quotients : {288}*576
   4-fold quotients : {216}*432
   6-fold quotients : {144}*288
   8-fold quotients : {108}*216
   9-fold quotients : {96}*192
   12-fold quotients : {72}*144
   16-fold quotients : {54}*108
   18-fold quotients : {48}*96
   24-fold quotients : {36}*72
   27-fold quotients : {32}*64
   32-fold quotients : {27}*54
   36-fold quotients : {24}*48
   48-fold quotients : {18}*36
   54-fold quotients : {16}*32
   72-fold quotients : {12}*24
   96-fold quotients : {9}*18
   108-fold quotients : {8}*16
   144-fold quotients : {6}*12
   216-fold quotients : {4}*8
   288-fold quotients : {3}*6
   432-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

References : None.
to this polytope