Polytope of Type {800}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {800}*1600
Also Known As : 800-gon, {800}. if this polytope has another name.
Group : SmallGroup(1600,7)
Rank : 2
Schlafli Type : {800}
Number of vertices, edges, etc : 800, 800
Order of s₀s₁ : 800
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 : {400}*800
   4-fold quotients : {200}*400
   5-fold quotients : {160}*320
   8-fold quotients : {100}*200
   10-fold quotients : {80}*160
   16-fold quotients : {50}*100
   20-fold quotients : {40}*80
   25-fold quotients : {32}*64
   32-fold quotients : {25}*50
   40-fold quotients : {20}*40
   50-fold quotients : {16}*32
   80-fold quotients : {10}*20
   100-fold quotients : {8}*16
   160-fold quotients : {5}*10
   200-fold quotients : {4}*8
   400-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope