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