Polytope of Type {4,50}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,50}*1600b
if this polytope has a name.
Group : SmallGroup(1600,5601)
Rank : 3
Schlafli Type : {4,50}
Number of vertices, edges, etc : 16, 400, 200
Order of s0s1s2 : 25
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
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 : {4,25}*800
5-fold quotients : {4,10}*320b
10-fold quotients : {4,5}*160
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,409)( 2,410)( 3,411)( 4,412)( 5,413)( 6,414)( 7,415)( 8,416)
( 9,401)( 10,402)( 11,403)( 12,404)( 13,405)( 14,406)( 15,407)( 16,408)
( 17,425)( 18,426)( 19,427)( 20,428)( 21,429)( 22,430)( 23,431)( 24,432)
( 25,417)( 26,418)( 27,419)( 28,420)( 29,421)( 30,422)( 31,423)( 32,424)
( 33,441)( 34,442)( 35,443)( 36,444)( 37,445)( 38,446)( 39,447)( 40,448)
( 41,433)( 42,434)( 43,435)( 44,436)( 45,437)( 46,438)( 47,439)( 48,440)
( 49,457)( 50,458)( 51,459)( 52,460)( 53,461)( 54,462)( 55,463)( 56,464)
( 57,449)( 58,450)( 59,451)( 60,452)( 61,453)( 62,454)( 63,455)( 64,456)
( 65,473)( 66,474)( 67,475)( 68,476)( 69,477)( 70,478)( 71,479)( 72,480)
( 73,465)( 74,466)( 75,467)( 76,468)( 77,469)( 78,470)( 79,471)( 80,472)
( 81,489)( 82,490)( 83,491)( 84,492)( 85,493)( 86,494)( 87,495)( 88,496)
( 89,481)( 90,482)( 91,483)( 92,484)( 93,485)( 94,486)( 95,487)( 96,488)
( 97,505)( 98,506)( 99,507)(100,508)(101,509)(102,510)(103,511)(104,512)
(105,497)(106,498)(107,499)(108,500)(109,501)(110,502)(111,503)(112,504)
(113,521)(114,522)(115,523)(116,524)(117,525)(118,526)(119,527)(120,528)
(121,513)(122,514)(123,515)(124,516)(125,517)(126,518)(127,519)(128,520)
(129,537)(130,538)(131,539)(132,540)(133,541)(134,542)(135,543)(136,544)
(137,529)(138,530)(139,531)(140,532)(141,533)(142,534)(143,535)(144,536)
(145,553)(146,554)(147,555)(148,556)(149,557)(150,558)(151,559)(152,560)
(153,545)(154,546)(155,547)(156,548)(157,549)(158,550)(159,551)(160,552)
(161,569)(162,570)(163,571)(164,572)(165,573)(166,574)(167,575)(168,576)
(169,561)(170,562)(171,563)(172,564)(173,565)(174,566)(175,567)(176,568)
(177,585)(178,586)(179,587)(180,588)(181,589)(182,590)(183,591)(184,592)
(185,577)(186,578)(187,579)(188,580)(189,581)(190,582)(191,583)(192,584)
(193,601)(194,602)(195,603)(196,604)(197,605)(198,606)(199,607)(200,608)
(201,593)(202,594)(203,595)(204,596)(205,597)(206,598)(207,599)(208,600)
(209,617)(210,618)(211,619)(212,620)(213,621)(214,622)(215,623)(216,624)
(217,609)(218,610)(219,611)(220,612)(221,613)(222,614)(223,615)(224,616)
(225,633)(226,634)(227,635)(228,636)(229,637)(230,638)(231,639)(232,640)
(233,625)(234,626)(235,627)(236,628)(237,629)(238,630)(239,631)(240,632)
(241,649)(242,650)(243,651)(244,652)(245,653)(246,654)(247,655)(248,656)
(249,641)(250,642)(251,643)(252,644)(253,645)(254,646)(255,647)(256,648)
(257,665)(258,666)(259,667)(260,668)(261,669)(262,670)(263,671)(264,672)
(265,657)(266,658)(267,659)(268,660)(269,661)(270,662)(271,663)(272,664)
(273,681)(274,682)(275,683)(276,684)(277,685)(278,686)(279,687)(280,688)
(281,673)(282,674)(283,675)(284,676)(285,677)(286,678)(287,679)(288,680)
(289,697)(290,698)(291,699)(292,700)(293,701)(294,702)(295,703)(296,704)
(297,689)(298,690)(299,691)(300,692)(301,693)(302,694)(303,695)(304,696)
(305,713)(306,714)(307,715)(308,716)(309,717)(310,718)(311,719)(312,720)
(313,705)(314,706)(315,707)(316,708)(317,709)(318,710)(319,711)(320,712)
(321,729)(322,730)(323,731)(324,732)(325,733)(326,734)(327,735)(328,736)
(329,721)(330,722)(331,723)(332,724)(333,725)(334,726)(335,727)(336,728)
(337,745)(338,746)(339,747)(340,748)(341,749)(342,750)(343,751)(344,752)
(345,737)(346,738)(347,739)(348,740)(349,741)(350,742)(351,743)(352,744)
(353,761)(354,762)(355,763)(356,764)(357,765)(358,766)(359,767)(360,768)
(361,753)(362,754)(363,755)(364,756)(365,757)(366,758)(367,759)(368,760)
(369,777)(370,778)(371,779)(372,780)(373,781)(374,782)(375,783)(376,784)
(377,769)(378,770)(379,771)(380,772)(381,773)(382,774)(383,775)(384,776)
(385,793)(386,794)(387,795)(388,796)(389,797)(390,798)(391,799)(392,800)
(393,785)(394,786)(395,787)(396,788)(397,789)(398,790)(399,791)(400,792);;
s1 := ( 3, 4)( 5, 6)( 9, 16)( 10, 15)( 11, 13)( 12, 14)( 17, 65)( 18, 66)
( 19, 68)( 20, 67)( 21, 70)( 22, 69)( 23, 71)( 24, 72)( 25, 80)( 26, 79)
( 27, 77)( 28, 78)( 29, 75)( 30, 76)( 31, 74)( 32, 73)( 33, 49)( 34, 50)
( 35, 52)( 36, 51)( 37, 54)( 38, 53)( 39, 55)( 40, 56)( 41, 64)( 42, 63)
( 43, 61)( 44, 62)( 45, 59)( 46, 60)( 47, 58)( 48, 57)( 81,385)( 82,386)
( 83,388)( 84,387)( 85,390)( 86,389)( 87,391)( 88,392)( 89,400)( 90,399)
( 91,397)( 92,398)( 93,395)( 94,396)( 95,394)( 96,393)( 97,369)( 98,370)
( 99,372)(100,371)(101,374)(102,373)(103,375)(104,376)(105,384)(106,383)
(107,381)(108,382)(109,379)(110,380)(111,378)(112,377)(113,353)(114,354)
(115,356)(116,355)(117,358)(118,357)(119,359)(120,360)(121,368)(122,367)
(123,365)(124,366)(125,363)(126,364)(127,362)(128,361)(129,337)(130,338)
(131,340)(132,339)(133,342)(134,341)(135,343)(136,344)(137,352)(138,351)
(139,349)(140,350)(141,347)(142,348)(143,346)(144,345)(145,321)(146,322)
(147,324)(148,323)(149,326)(150,325)(151,327)(152,328)(153,336)(154,335)
(155,333)(156,334)(157,331)(158,332)(159,330)(160,329)(161,305)(162,306)
(163,308)(164,307)(165,310)(166,309)(167,311)(168,312)(169,320)(170,319)
(171,317)(172,318)(173,315)(174,316)(175,314)(176,313)(177,289)(178,290)
(179,292)(180,291)(181,294)(182,293)(183,295)(184,296)(185,304)(186,303)
(187,301)(188,302)(189,299)(190,300)(191,298)(192,297)(193,273)(194,274)
(195,276)(196,275)(197,278)(198,277)(199,279)(200,280)(201,288)(202,287)
(203,285)(204,286)(205,283)(206,284)(207,282)(208,281)(209,257)(210,258)
(211,260)(212,259)(213,262)(214,261)(215,263)(216,264)(217,272)(218,271)
(219,269)(220,270)(221,267)(222,268)(223,266)(224,265)(225,241)(226,242)
(227,244)(228,243)(229,246)(230,245)(231,247)(232,248)(233,256)(234,255)
(235,253)(236,254)(237,251)(238,252)(239,250)(240,249)(403,404)(405,406)
(409,416)(410,415)(411,413)(412,414)(417,465)(418,466)(419,468)(420,467)
(421,470)(422,469)(423,471)(424,472)(425,480)(426,479)(427,477)(428,478)
(429,475)(430,476)(431,474)(432,473)(433,449)(434,450)(435,452)(436,451)
(437,454)(438,453)(439,455)(440,456)(441,464)(442,463)(443,461)(444,462)
(445,459)(446,460)(447,458)(448,457)(481,785)(482,786)(483,788)(484,787)
(485,790)(486,789)(487,791)(488,792)(489,800)(490,799)(491,797)(492,798)
(493,795)(494,796)(495,794)(496,793)(497,769)(498,770)(499,772)(500,771)
(501,774)(502,773)(503,775)(504,776)(505,784)(506,783)(507,781)(508,782)
(509,779)(510,780)(511,778)(512,777)(513,753)(514,754)(515,756)(516,755)
(517,758)(518,757)(519,759)(520,760)(521,768)(522,767)(523,765)(524,766)
(525,763)(526,764)(527,762)(528,761)(529,737)(530,738)(531,740)(532,739)
(533,742)(534,741)(535,743)(536,744)(537,752)(538,751)(539,749)(540,750)
(541,747)(542,748)(543,746)(544,745)(545,721)(546,722)(547,724)(548,723)
(549,726)(550,725)(551,727)(552,728)(553,736)(554,735)(555,733)(556,734)
(557,731)(558,732)(559,730)(560,729)(561,705)(562,706)(563,708)(564,707)
(565,710)(566,709)(567,711)(568,712)(569,720)(570,719)(571,717)(572,718)
(573,715)(574,716)(575,714)(576,713)(577,689)(578,690)(579,692)(580,691)
(581,694)(582,693)(583,695)(584,696)(585,704)(586,703)(587,701)(588,702)
(589,699)(590,700)(591,698)(592,697)(593,673)(594,674)(595,676)(596,675)
(597,678)(598,677)(599,679)(600,680)(601,688)(602,687)(603,685)(604,686)
(605,683)(606,684)(607,682)(608,681)(609,657)(610,658)(611,660)(612,659)
(613,662)(614,661)(615,663)(616,664)(617,672)(618,671)(619,669)(620,670)
(621,667)(622,668)(623,666)(624,665)(625,641)(626,642)(627,644)(628,643)
(629,646)(630,645)(631,647)(632,648)(633,656)(634,655)(635,653)(636,654)
(637,651)(638,652)(639,650)(640,649);;
s2 := ( 1,481)( 2,490)( 3,491)( 4,484)( 5,496)( 6,487)( 7,486)( 8,493)
( 9,489)( 10,482)( 11,483)( 12,492)( 13,488)( 14,495)( 15,494)( 16,485)
( 17,545)( 18,554)( 19,555)( 20,548)( 21,560)( 22,551)( 23,550)( 24,557)
( 25,553)( 26,546)( 27,547)( 28,556)( 29,552)( 30,559)( 31,558)( 32,549)
( 33,529)( 34,538)( 35,539)( 36,532)( 37,544)( 38,535)( 39,534)( 40,541)
( 41,537)( 42,530)( 43,531)( 44,540)( 45,536)( 46,543)( 47,542)( 48,533)
( 49,513)( 50,522)( 51,523)( 52,516)( 53,528)( 54,519)( 55,518)( 56,525)
( 57,521)( 58,514)( 59,515)( 60,524)( 61,520)( 62,527)( 63,526)( 64,517)
( 65,497)( 66,506)( 67,507)( 68,500)( 69,512)( 70,503)( 71,502)( 72,509)
( 73,505)( 74,498)( 75,499)( 76,508)( 77,504)( 78,511)( 79,510)( 80,501)
( 81,401)( 82,410)( 83,411)( 84,404)( 85,416)( 86,407)( 87,406)( 88,413)
( 89,409)( 90,402)( 91,403)( 92,412)( 93,408)( 94,415)( 95,414)( 96,405)
( 97,465)( 98,474)( 99,475)(100,468)(101,480)(102,471)(103,470)(104,477)
(105,473)(106,466)(107,467)(108,476)(109,472)(110,479)(111,478)(112,469)
(113,449)(114,458)(115,459)(116,452)(117,464)(118,455)(119,454)(120,461)
(121,457)(122,450)(123,451)(124,460)(125,456)(126,463)(127,462)(128,453)
(129,433)(130,442)(131,443)(132,436)(133,448)(134,439)(135,438)(136,445)
(137,441)(138,434)(139,435)(140,444)(141,440)(142,447)(143,446)(144,437)
(145,417)(146,426)(147,427)(148,420)(149,432)(150,423)(151,422)(152,429)
(153,425)(154,418)(155,419)(156,428)(157,424)(158,431)(159,430)(160,421)
(161,785)(162,794)(163,795)(164,788)(165,800)(166,791)(167,790)(168,797)
(169,793)(170,786)(171,787)(172,796)(173,792)(174,799)(175,798)(176,789)
(177,769)(178,778)(179,779)(180,772)(181,784)(182,775)(183,774)(184,781)
(185,777)(186,770)(187,771)(188,780)(189,776)(190,783)(191,782)(192,773)
(193,753)(194,762)(195,763)(196,756)(197,768)(198,759)(199,758)(200,765)
(201,761)(202,754)(203,755)(204,764)(205,760)(206,767)(207,766)(208,757)
(209,737)(210,746)(211,747)(212,740)(213,752)(214,743)(215,742)(216,749)
(217,745)(218,738)(219,739)(220,748)(221,744)(222,751)(223,750)(224,741)
(225,721)(226,730)(227,731)(228,724)(229,736)(230,727)(231,726)(232,733)
(233,729)(234,722)(235,723)(236,732)(237,728)(238,735)(239,734)(240,725)
(241,705)(242,714)(243,715)(244,708)(245,720)(246,711)(247,710)(248,717)
(249,713)(250,706)(251,707)(252,716)(253,712)(254,719)(255,718)(256,709)
(257,689)(258,698)(259,699)(260,692)(261,704)(262,695)(263,694)(264,701)
(265,697)(266,690)(267,691)(268,700)(269,696)(270,703)(271,702)(272,693)
(273,673)(274,682)(275,683)(276,676)(277,688)(278,679)(279,678)(280,685)
(281,681)(282,674)(283,675)(284,684)(285,680)(286,687)(287,686)(288,677)
(289,657)(290,666)(291,667)(292,660)(293,672)(294,663)(295,662)(296,669)
(297,665)(298,658)(299,659)(300,668)(301,664)(302,671)(303,670)(304,661)
(305,641)(306,650)(307,651)(308,644)(309,656)(310,647)(311,646)(312,653)
(313,649)(314,642)(315,643)(316,652)(317,648)(318,655)(319,654)(320,645)
(321,625)(322,634)(323,635)(324,628)(325,640)(326,631)(327,630)(328,637)
(329,633)(330,626)(331,627)(332,636)(333,632)(334,639)(335,638)(336,629)
(337,609)(338,618)(339,619)(340,612)(341,624)(342,615)(343,614)(344,621)
(345,617)(346,610)(347,611)(348,620)(349,616)(350,623)(351,622)(352,613)
(353,593)(354,602)(355,603)(356,596)(357,608)(358,599)(359,598)(360,605)
(361,601)(362,594)(363,595)(364,604)(365,600)(366,607)(367,606)(368,597)
(369,577)(370,586)(371,587)(372,580)(373,592)(374,583)(375,582)(376,589)
(377,585)(378,578)(379,579)(380,588)(381,584)(382,591)(383,590)(384,581)
(385,561)(386,570)(387,571)(388,564)(389,576)(390,567)(391,566)(392,573)
(393,569)(394,562)(395,563)(396,572)(397,568)(398,575)(399,574)(400,565);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1,
s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(800)!( 1,409)( 2,410)( 3,411)( 4,412)( 5,413)( 6,414)( 7,415)
( 8,416)( 9,401)( 10,402)( 11,403)( 12,404)( 13,405)( 14,406)( 15,407)
( 16,408)( 17,425)( 18,426)( 19,427)( 20,428)( 21,429)( 22,430)( 23,431)
( 24,432)( 25,417)( 26,418)( 27,419)( 28,420)( 29,421)( 30,422)( 31,423)
( 32,424)( 33,441)( 34,442)( 35,443)( 36,444)( 37,445)( 38,446)( 39,447)
( 40,448)( 41,433)( 42,434)( 43,435)( 44,436)( 45,437)( 46,438)( 47,439)
( 48,440)( 49,457)( 50,458)( 51,459)( 52,460)( 53,461)( 54,462)( 55,463)
( 56,464)( 57,449)( 58,450)( 59,451)( 60,452)( 61,453)( 62,454)( 63,455)
( 64,456)( 65,473)( 66,474)( 67,475)( 68,476)( 69,477)( 70,478)( 71,479)
( 72,480)( 73,465)( 74,466)( 75,467)( 76,468)( 77,469)( 78,470)( 79,471)
( 80,472)( 81,489)( 82,490)( 83,491)( 84,492)( 85,493)( 86,494)( 87,495)
( 88,496)( 89,481)( 90,482)( 91,483)( 92,484)( 93,485)( 94,486)( 95,487)
( 96,488)( 97,505)( 98,506)( 99,507)(100,508)(101,509)(102,510)(103,511)
(104,512)(105,497)(106,498)(107,499)(108,500)(109,501)(110,502)(111,503)
(112,504)(113,521)(114,522)(115,523)(116,524)(117,525)(118,526)(119,527)
(120,528)(121,513)(122,514)(123,515)(124,516)(125,517)(126,518)(127,519)
(128,520)(129,537)(130,538)(131,539)(132,540)(133,541)(134,542)(135,543)
(136,544)(137,529)(138,530)(139,531)(140,532)(141,533)(142,534)(143,535)
(144,536)(145,553)(146,554)(147,555)(148,556)(149,557)(150,558)(151,559)
(152,560)(153,545)(154,546)(155,547)(156,548)(157,549)(158,550)(159,551)
(160,552)(161,569)(162,570)(163,571)(164,572)(165,573)(166,574)(167,575)
(168,576)(169,561)(170,562)(171,563)(172,564)(173,565)(174,566)(175,567)
(176,568)(177,585)(178,586)(179,587)(180,588)(181,589)(182,590)(183,591)
(184,592)(185,577)(186,578)(187,579)(188,580)(189,581)(190,582)(191,583)
(192,584)(193,601)(194,602)(195,603)(196,604)(197,605)(198,606)(199,607)
(200,608)(201,593)(202,594)(203,595)(204,596)(205,597)(206,598)(207,599)
(208,600)(209,617)(210,618)(211,619)(212,620)(213,621)(214,622)(215,623)
(216,624)(217,609)(218,610)(219,611)(220,612)(221,613)(222,614)(223,615)
(224,616)(225,633)(226,634)(227,635)(228,636)(229,637)(230,638)(231,639)
(232,640)(233,625)(234,626)(235,627)(236,628)(237,629)(238,630)(239,631)
(240,632)(241,649)(242,650)(243,651)(244,652)(245,653)(246,654)(247,655)
(248,656)(249,641)(250,642)(251,643)(252,644)(253,645)(254,646)(255,647)
(256,648)(257,665)(258,666)(259,667)(260,668)(261,669)(262,670)(263,671)
(264,672)(265,657)(266,658)(267,659)(268,660)(269,661)(270,662)(271,663)
(272,664)(273,681)(274,682)(275,683)(276,684)(277,685)(278,686)(279,687)
(280,688)(281,673)(282,674)(283,675)(284,676)(285,677)(286,678)(287,679)
(288,680)(289,697)(290,698)(291,699)(292,700)(293,701)(294,702)(295,703)
(296,704)(297,689)(298,690)(299,691)(300,692)(301,693)(302,694)(303,695)
(304,696)(305,713)(306,714)(307,715)(308,716)(309,717)(310,718)(311,719)
(312,720)(313,705)(314,706)(315,707)(316,708)(317,709)(318,710)(319,711)
(320,712)(321,729)(322,730)(323,731)(324,732)(325,733)(326,734)(327,735)
(328,736)(329,721)(330,722)(331,723)(332,724)(333,725)(334,726)(335,727)
(336,728)(337,745)(338,746)(339,747)(340,748)(341,749)(342,750)(343,751)
(344,752)(345,737)(346,738)(347,739)(348,740)(349,741)(350,742)(351,743)
(352,744)(353,761)(354,762)(355,763)(356,764)(357,765)(358,766)(359,767)
(360,768)(361,753)(362,754)(363,755)(364,756)(365,757)(366,758)(367,759)
(368,760)(369,777)(370,778)(371,779)(372,780)(373,781)(374,782)(375,783)
(376,784)(377,769)(378,770)(379,771)(380,772)(381,773)(382,774)(383,775)
(384,776)(385,793)(386,794)(387,795)(388,796)(389,797)(390,798)(391,799)
(392,800)(393,785)(394,786)(395,787)(396,788)(397,789)(398,790)(399,791)
(400,792);
s1 := Sym(800)!( 3, 4)( 5, 6)( 9, 16)( 10, 15)( 11, 13)( 12, 14)( 17, 65)
( 18, 66)( 19, 68)( 20, 67)( 21, 70)( 22, 69)( 23, 71)( 24, 72)( 25, 80)
( 26, 79)( 27, 77)( 28, 78)( 29, 75)( 30, 76)( 31, 74)( 32, 73)( 33, 49)
( 34, 50)( 35, 52)( 36, 51)( 37, 54)( 38, 53)( 39, 55)( 40, 56)( 41, 64)
( 42, 63)( 43, 61)( 44, 62)( 45, 59)( 46, 60)( 47, 58)( 48, 57)( 81,385)
( 82,386)( 83,388)( 84,387)( 85,390)( 86,389)( 87,391)( 88,392)( 89,400)
( 90,399)( 91,397)( 92,398)( 93,395)( 94,396)( 95,394)( 96,393)( 97,369)
( 98,370)( 99,372)(100,371)(101,374)(102,373)(103,375)(104,376)(105,384)
(106,383)(107,381)(108,382)(109,379)(110,380)(111,378)(112,377)(113,353)
(114,354)(115,356)(116,355)(117,358)(118,357)(119,359)(120,360)(121,368)
(122,367)(123,365)(124,366)(125,363)(126,364)(127,362)(128,361)(129,337)
(130,338)(131,340)(132,339)(133,342)(134,341)(135,343)(136,344)(137,352)
(138,351)(139,349)(140,350)(141,347)(142,348)(143,346)(144,345)(145,321)
(146,322)(147,324)(148,323)(149,326)(150,325)(151,327)(152,328)(153,336)
(154,335)(155,333)(156,334)(157,331)(158,332)(159,330)(160,329)(161,305)
(162,306)(163,308)(164,307)(165,310)(166,309)(167,311)(168,312)(169,320)
(170,319)(171,317)(172,318)(173,315)(174,316)(175,314)(176,313)(177,289)
(178,290)(179,292)(180,291)(181,294)(182,293)(183,295)(184,296)(185,304)
(186,303)(187,301)(188,302)(189,299)(190,300)(191,298)(192,297)(193,273)
(194,274)(195,276)(196,275)(197,278)(198,277)(199,279)(200,280)(201,288)
(202,287)(203,285)(204,286)(205,283)(206,284)(207,282)(208,281)(209,257)
(210,258)(211,260)(212,259)(213,262)(214,261)(215,263)(216,264)(217,272)
(218,271)(219,269)(220,270)(221,267)(222,268)(223,266)(224,265)(225,241)
(226,242)(227,244)(228,243)(229,246)(230,245)(231,247)(232,248)(233,256)
(234,255)(235,253)(236,254)(237,251)(238,252)(239,250)(240,249)(403,404)
(405,406)(409,416)(410,415)(411,413)(412,414)(417,465)(418,466)(419,468)
(420,467)(421,470)(422,469)(423,471)(424,472)(425,480)(426,479)(427,477)
(428,478)(429,475)(430,476)(431,474)(432,473)(433,449)(434,450)(435,452)
(436,451)(437,454)(438,453)(439,455)(440,456)(441,464)(442,463)(443,461)
(444,462)(445,459)(446,460)(447,458)(448,457)(481,785)(482,786)(483,788)
(484,787)(485,790)(486,789)(487,791)(488,792)(489,800)(490,799)(491,797)
(492,798)(493,795)(494,796)(495,794)(496,793)(497,769)(498,770)(499,772)
(500,771)(501,774)(502,773)(503,775)(504,776)(505,784)(506,783)(507,781)
(508,782)(509,779)(510,780)(511,778)(512,777)(513,753)(514,754)(515,756)
(516,755)(517,758)(518,757)(519,759)(520,760)(521,768)(522,767)(523,765)
(524,766)(525,763)(526,764)(527,762)(528,761)(529,737)(530,738)(531,740)
(532,739)(533,742)(534,741)(535,743)(536,744)(537,752)(538,751)(539,749)
(540,750)(541,747)(542,748)(543,746)(544,745)(545,721)(546,722)(547,724)
(548,723)(549,726)(550,725)(551,727)(552,728)(553,736)(554,735)(555,733)
(556,734)(557,731)(558,732)(559,730)(560,729)(561,705)(562,706)(563,708)
(564,707)(565,710)(566,709)(567,711)(568,712)(569,720)(570,719)(571,717)
(572,718)(573,715)(574,716)(575,714)(576,713)(577,689)(578,690)(579,692)
(580,691)(581,694)(582,693)(583,695)(584,696)(585,704)(586,703)(587,701)
(588,702)(589,699)(590,700)(591,698)(592,697)(593,673)(594,674)(595,676)
(596,675)(597,678)(598,677)(599,679)(600,680)(601,688)(602,687)(603,685)
(604,686)(605,683)(606,684)(607,682)(608,681)(609,657)(610,658)(611,660)
(612,659)(613,662)(614,661)(615,663)(616,664)(617,672)(618,671)(619,669)
(620,670)(621,667)(622,668)(623,666)(624,665)(625,641)(626,642)(627,644)
(628,643)(629,646)(630,645)(631,647)(632,648)(633,656)(634,655)(635,653)
(636,654)(637,651)(638,652)(639,650)(640,649);
s2 := Sym(800)!( 1,481)( 2,490)( 3,491)( 4,484)( 5,496)( 6,487)( 7,486)
( 8,493)( 9,489)( 10,482)( 11,483)( 12,492)( 13,488)( 14,495)( 15,494)
( 16,485)( 17,545)( 18,554)( 19,555)( 20,548)( 21,560)( 22,551)( 23,550)
( 24,557)( 25,553)( 26,546)( 27,547)( 28,556)( 29,552)( 30,559)( 31,558)
( 32,549)( 33,529)( 34,538)( 35,539)( 36,532)( 37,544)( 38,535)( 39,534)
( 40,541)( 41,537)( 42,530)( 43,531)( 44,540)( 45,536)( 46,543)( 47,542)
( 48,533)( 49,513)( 50,522)( 51,523)( 52,516)( 53,528)( 54,519)( 55,518)
( 56,525)( 57,521)( 58,514)( 59,515)( 60,524)( 61,520)( 62,527)( 63,526)
( 64,517)( 65,497)( 66,506)( 67,507)( 68,500)( 69,512)( 70,503)( 71,502)
( 72,509)( 73,505)( 74,498)( 75,499)( 76,508)( 77,504)( 78,511)( 79,510)
( 80,501)( 81,401)( 82,410)( 83,411)( 84,404)( 85,416)( 86,407)( 87,406)
( 88,413)( 89,409)( 90,402)( 91,403)( 92,412)( 93,408)( 94,415)( 95,414)
( 96,405)( 97,465)( 98,474)( 99,475)(100,468)(101,480)(102,471)(103,470)
(104,477)(105,473)(106,466)(107,467)(108,476)(109,472)(110,479)(111,478)
(112,469)(113,449)(114,458)(115,459)(116,452)(117,464)(118,455)(119,454)
(120,461)(121,457)(122,450)(123,451)(124,460)(125,456)(126,463)(127,462)
(128,453)(129,433)(130,442)(131,443)(132,436)(133,448)(134,439)(135,438)
(136,445)(137,441)(138,434)(139,435)(140,444)(141,440)(142,447)(143,446)
(144,437)(145,417)(146,426)(147,427)(148,420)(149,432)(150,423)(151,422)
(152,429)(153,425)(154,418)(155,419)(156,428)(157,424)(158,431)(159,430)
(160,421)(161,785)(162,794)(163,795)(164,788)(165,800)(166,791)(167,790)
(168,797)(169,793)(170,786)(171,787)(172,796)(173,792)(174,799)(175,798)
(176,789)(177,769)(178,778)(179,779)(180,772)(181,784)(182,775)(183,774)
(184,781)(185,777)(186,770)(187,771)(188,780)(189,776)(190,783)(191,782)
(192,773)(193,753)(194,762)(195,763)(196,756)(197,768)(198,759)(199,758)
(200,765)(201,761)(202,754)(203,755)(204,764)(205,760)(206,767)(207,766)
(208,757)(209,737)(210,746)(211,747)(212,740)(213,752)(214,743)(215,742)
(216,749)(217,745)(218,738)(219,739)(220,748)(221,744)(222,751)(223,750)
(224,741)(225,721)(226,730)(227,731)(228,724)(229,736)(230,727)(231,726)
(232,733)(233,729)(234,722)(235,723)(236,732)(237,728)(238,735)(239,734)
(240,725)(241,705)(242,714)(243,715)(244,708)(245,720)(246,711)(247,710)
(248,717)(249,713)(250,706)(251,707)(252,716)(253,712)(254,719)(255,718)
(256,709)(257,689)(258,698)(259,699)(260,692)(261,704)(262,695)(263,694)
(264,701)(265,697)(266,690)(267,691)(268,700)(269,696)(270,703)(271,702)
(272,693)(273,673)(274,682)(275,683)(276,676)(277,688)(278,679)(279,678)
(280,685)(281,681)(282,674)(283,675)(284,684)(285,680)(286,687)(287,686)
(288,677)(289,657)(290,666)(291,667)(292,660)(293,672)(294,663)(295,662)
(296,669)(297,665)(298,658)(299,659)(300,668)(301,664)(302,671)(303,670)
(304,661)(305,641)(306,650)(307,651)(308,644)(309,656)(310,647)(311,646)
(312,653)(313,649)(314,642)(315,643)(316,652)(317,648)(318,655)(319,654)
(320,645)(321,625)(322,634)(323,635)(324,628)(325,640)(326,631)(327,630)
(328,637)(329,633)(330,626)(331,627)(332,636)(333,632)(334,639)(335,638)
(336,629)(337,609)(338,618)(339,619)(340,612)(341,624)(342,615)(343,614)
(344,621)(345,617)(346,610)(347,611)(348,620)(349,616)(350,623)(351,622)
(352,613)(353,593)(354,602)(355,603)(356,596)(357,608)(358,599)(359,598)
(360,605)(361,601)(362,594)(363,595)(364,604)(365,600)(366,607)(367,606)
(368,597)(369,577)(370,586)(371,587)(372,580)(373,592)(374,583)(375,582)
(376,589)(377,585)(378,578)(379,579)(380,588)(381,584)(382,591)(383,590)
(384,581)(385,561)(386,570)(387,571)(388,564)(389,576)(390,567)(391,566)
(392,573)(393,569)(394,562)(395,563)(396,572)(397,568)(398,575)(399,574)
(400,565);
poly := sub<Sym(800)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1,
s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1 >;
References : None.
to this polytope