Polytope of Type {4,202}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,202}*1616
Also Known As : {4,202|2}. if this polytope has another name.
Group : SmallGroup(1616,34)
Rank : 3
Schlafli Type : {4,202}
Number of vertices, edges, etc : 4, 404, 202
Order of s0s1s2 : 404
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
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 : {2,202}*808
4-fold quotients : {2,101}*404
101-fold quotients : {4,2}*16
202-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (405,506)(406,507)(407,508)(408,509)(409,510)(410,511)(411,512)(412,513)
(413,514)(414,515)(415,516)(416,517)(417,518)(418,519)(419,520)(420,521)
(421,522)(422,523)(423,524)(424,525)(425,526)(426,527)(427,528)(428,529)
(429,530)(430,531)(431,532)(432,533)(433,534)(434,535)(435,536)(436,537)
(437,538)(438,539)(439,540)(440,541)(441,542)(442,543)(443,544)(444,545)
(445,546)(446,547)(447,548)(448,549)(449,550)(450,551)(451,552)(452,553)
(453,554)(454,555)(455,556)(456,557)(457,558)(458,559)(459,560)(460,561)
(461,562)(462,563)(463,564)(464,565)(465,566)(466,567)(467,568)(468,569)
(469,570)(470,571)(471,572)(472,573)(473,574)(474,575)(475,576)(476,577)
(477,578)(478,579)(479,580)(480,581)(481,582)(482,583)(483,584)(484,585)
(485,586)(486,587)(487,588)(488,589)(489,590)(490,591)(491,592)(492,593)
(493,594)(494,595)(495,596)(496,597)(497,598)(498,599)(499,600)(500,601)
(501,602)(502,603)(503,604)(504,605)(505,606)(607,708)(608,709)(609,710)
(610,711)(611,712)(612,713)(613,714)(614,715)(615,716)(616,717)(617,718)
(618,719)(619,720)(620,721)(621,722)(622,723)(623,724)(624,725)(625,726)
(626,727)(627,728)(628,729)(629,730)(630,731)(631,732)(632,733)(633,734)
(634,735)(635,736)(636,737)(637,738)(638,739)(639,740)(640,741)(641,742)
(642,743)(643,744)(644,745)(645,746)(646,747)(647,748)(648,749)(649,750)
(650,751)(651,752)(652,753)(653,754)(654,755)(655,756)(656,757)(657,758)
(658,759)(659,760)(660,761)(661,762)(662,763)(663,764)(664,765)(665,766)
(666,767)(667,768)(668,769)(669,770)(670,771)(671,772)(672,773)(673,774)
(674,775)(675,776)(676,777)(677,778)(678,779)(679,780)(680,781)(681,782)
(682,783)(683,784)(684,785)(685,786)(686,787)(687,788)(688,789)(689,790)
(690,791)(691,792)(692,793)(693,794)(694,795)(695,796)(696,797)(697,798)
(698,799)(699,800)(700,801)(701,802)(702,803)(703,804)(704,805)(705,806)
(706,807)(707,808);;
s1 := ( 1,607)( 2,707)( 3,706)( 4,705)( 5,704)( 6,703)( 7,702)( 8,701)
( 9,700)( 10,699)( 11,698)( 12,697)( 13,696)( 14,695)( 15,694)( 16,693)
( 17,692)( 18,691)( 19,690)( 20,689)( 21,688)( 22,687)( 23,686)( 24,685)
( 25,684)( 26,683)( 27,682)( 28,681)( 29,680)( 30,679)( 31,678)( 32,677)
( 33,676)( 34,675)( 35,674)( 36,673)( 37,672)( 38,671)( 39,670)( 40,669)
( 41,668)( 42,667)( 43,666)( 44,665)( 45,664)( 46,663)( 47,662)( 48,661)
( 49,660)( 50,659)( 51,658)( 52,657)( 53,656)( 54,655)( 55,654)( 56,653)
( 57,652)( 58,651)( 59,650)( 60,649)( 61,648)( 62,647)( 63,646)( 64,645)
( 65,644)( 66,643)( 67,642)( 68,641)( 69,640)( 70,639)( 71,638)( 72,637)
( 73,636)( 74,635)( 75,634)( 76,633)( 77,632)( 78,631)( 79,630)( 80,629)
( 81,628)( 82,627)( 83,626)( 84,625)( 85,624)( 86,623)( 87,622)( 88,621)
( 89,620)( 90,619)( 91,618)( 92,617)( 93,616)( 94,615)( 95,614)( 96,613)
( 97,612)( 98,611)( 99,610)(100,609)(101,608)(102,708)(103,808)(104,807)
(105,806)(106,805)(107,804)(108,803)(109,802)(110,801)(111,800)(112,799)
(113,798)(114,797)(115,796)(116,795)(117,794)(118,793)(119,792)(120,791)
(121,790)(122,789)(123,788)(124,787)(125,786)(126,785)(127,784)(128,783)
(129,782)(130,781)(131,780)(132,779)(133,778)(134,777)(135,776)(136,775)
(137,774)(138,773)(139,772)(140,771)(141,770)(142,769)(143,768)(144,767)
(145,766)(146,765)(147,764)(148,763)(149,762)(150,761)(151,760)(152,759)
(153,758)(154,757)(155,756)(156,755)(157,754)(158,753)(159,752)(160,751)
(161,750)(162,749)(163,748)(164,747)(165,746)(166,745)(167,744)(168,743)
(169,742)(170,741)(171,740)(172,739)(173,738)(174,737)(175,736)(176,735)
(177,734)(178,733)(179,732)(180,731)(181,730)(182,729)(183,728)(184,727)
(185,726)(186,725)(187,724)(188,723)(189,722)(190,721)(191,720)(192,719)
(193,718)(194,717)(195,716)(196,715)(197,714)(198,713)(199,712)(200,711)
(201,710)(202,709)(203,405)(204,505)(205,504)(206,503)(207,502)(208,501)
(209,500)(210,499)(211,498)(212,497)(213,496)(214,495)(215,494)(216,493)
(217,492)(218,491)(219,490)(220,489)(221,488)(222,487)(223,486)(224,485)
(225,484)(226,483)(227,482)(228,481)(229,480)(230,479)(231,478)(232,477)
(233,476)(234,475)(235,474)(236,473)(237,472)(238,471)(239,470)(240,469)
(241,468)(242,467)(243,466)(244,465)(245,464)(246,463)(247,462)(248,461)
(249,460)(250,459)(251,458)(252,457)(253,456)(254,455)(255,454)(256,453)
(257,452)(258,451)(259,450)(260,449)(261,448)(262,447)(263,446)(264,445)
(265,444)(266,443)(267,442)(268,441)(269,440)(270,439)(271,438)(272,437)
(273,436)(274,435)(275,434)(276,433)(277,432)(278,431)(279,430)(280,429)
(281,428)(282,427)(283,426)(284,425)(285,424)(286,423)(287,422)(288,421)
(289,420)(290,419)(291,418)(292,417)(293,416)(294,415)(295,414)(296,413)
(297,412)(298,411)(299,410)(300,409)(301,408)(302,407)(303,406)(304,506)
(305,606)(306,605)(307,604)(308,603)(309,602)(310,601)(311,600)(312,599)
(313,598)(314,597)(315,596)(316,595)(317,594)(318,593)(319,592)(320,591)
(321,590)(322,589)(323,588)(324,587)(325,586)(326,585)(327,584)(328,583)
(329,582)(330,581)(331,580)(332,579)(333,578)(334,577)(335,576)(336,575)
(337,574)(338,573)(339,572)(340,571)(341,570)(342,569)(343,568)(344,567)
(345,566)(346,565)(347,564)(348,563)(349,562)(350,561)(351,560)(352,559)
(353,558)(354,557)(355,556)(356,555)(357,554)(358,553)(359,552)(360,551)
(361,550)(362,549)(363,548)(364,547)(365,546)(366,545)(367,544)(368,543)
(369,542)(370,541)(371,540)(372,539)(373,538)(374,537)(375,536)(376,535)
(377,534)(378,533)(379,532)(380,531)(381,530)(382,529)(383,528)(384,527)
(385,526)(386,525)(387,524)(388,523)(389,522)(390,521)(391,520)(392,519)
(393,518)(394,517)(395,516)(396,515)(397,514)(398,513)(399,512)(400,511)
(401,510)(402,509)(403,508)(404,507);;
s2 := ( 1,204)( 2,203)( 3,303)( 4,302)( 5,301)( 6,300)( 7,299)( 8,298)
( 9,297)( 10,296)( 11,295)( 12,294)( 13,293)( 14,292)( 15,291)( 16,290)
( 17,289)( 18,288)( 19,287)( 20,286)( 21,285)( 22,284)( 23,283)( 24,282)
( 25,281)( 26,280)( 27,279)( 28,278)( 29,277)( 30,276)( 31,275)( 32,274)
( 33,273)( 34,272)( 35,271)( 36,270)( 37,269)( 38,268)( 39,267)( 40,266)
( 41,265)( 42,264)( 43,263)( 44,262)( 45,261)( 46,260)( 47,259)( 48,258)
( 49,257)( 50,256)( 51,255)( 52,254)( 53,253)( 54,252)( 55,251)( 56,250)
( 57,249)( 58,248)( 59,247)( 60,246)( 61,245)( 62,244)( 63,243)( 64,242)
( 65,241)( 66,240)( 67,239)( 68,238)( 69,237)( 70,236)( 71,235)( 72,234)
( 73,233)( 74,232)( 75,231)( 76,230)( 77,229)( 78,228)( 79,227)( 80,226)
( 81,225)( 82,224)( 83,223)( 84,222)( 85,221)( 86,220)( 87,219)( 88,218)
( 89,217)( 90,216)( 91,215)( 92,214)( 93,213)( 94,212)( 95,211)( 96,210)
( 97,209)( 98,208)( 99,207)(100,206)(101,205)(102,305)(103,304)(104,404)
(105,403)(106,402)(107,401)(108,400)(109,399)(110,398)(111,397)(112,396)
(113,395)(114,394)(115,393)(116,392)(117,391)(118,390)(119,389)(120,388)
(121,387)(122,386)(123,385)(124,384)(125,383)(126,382)(127,381)(128,380)
(129,379)(130,378)(131,377)(132,376)(133,375)(134,374)(135,373)(136,372)
(137,371)(138,370)(139,369)(140,368)(141,367)(142,366)(143,365)(144,364)
(145,363)(146,362)(147,361)(148,360)(149,359)(150,358)(151,357)(152,356)
(153,355)(154,354)(155,353)(156,352)(157,351)(158,350)(159,349)(160,348)
(161,347)(162,346)(163,345)(164,344)(165,343)(166,342)(167,341)(168,340)
(169,339)(170,338)(171,337)(172,336)(173,335)(174,334)(175,333)(176,332)
(177,331)(178,330)(179,329)(180,328)(181,327)(182,326)(183,325)(184,324)
(185,323)(186,322)(187,321)(188,320)(189,319)(190,318)(191,317)(192,316)
(193,315)(194,314)(195,313)(196,312)(197,311)(198,310)(199,309)(200,308)
(201,307)(202,306)(405,608)(406,607)(407,707)(408,706)(409,705)(410,704)
(411,703)(412,702)(413,701)(414,700)(415,699)(416,698)(417,697)(418,696)
(419,695)(420,694)(421,693)(422,692)(423,691)(424,690)(425,689)(426,688)
(427,687)(428,686)(429,685)(430,684)(431,683)(432,682)(433,681)(434,680)
(435,679)(436,678)(437,677)(438,676)(439,675)(440,674)(441,673)(442,672)
(443,671)(444,670)(445,669)(446,668)(447,667)(448,666)(449,665)(450,664)
(451,663)(452,662)(453,661)(454,660)(455,659)(456,658)(457,657)(458,656)
(459,655)(460,654)(461,653)(462,652)(463,651)(464,650)(465,649)(466,648)
(467,647)(468,646)(469,645)(470,644)(471,643)(472,642)(473,641)(474,640)
(475,639)(476,638)(477,637)(478,636)(479,635)(480,634)(481,633)(482,632)
(483,631)(484,630)(485,629)(486,628)(487,627)(488,626)(489,625)(490,624)
(491,623)(492,622)(493,621)(494,620)(495,619)(496,618)(497,617)(498,616)
(499,615)(500,614)(501,613)(502,612)(503,611)(504,610)(505,609)(506,709)
(507,708)(508,808)(509,807)(510,806)(511,805)(512,804)(513,803)(514,802)
(515,801)(516,800)(517,799)(518,798)(519,797)(520,796)(521,795)(522,794)
(523,793)(524,792)(525,791)(526,790)(527,789)(528,788)(529,787)(530,786)
(531,785)(532,784)(533,783)(534,782)(535,781)(536,780)(537,779)(538,778)
(539,777)(540,776)(541,775)(542,774)(543,773)(544,772)(545,771)(546,770)
(547,769)(548,768)(549,767)(550,766)(551,765)(552,764)(553,763)(554,762)
(555,761)(556,760)(557,759)(558,758)(559,757)(560,756)(561,755)(562,754)
(563,753)(564,752)(565,751)(566,750)(567,749)(568,748)(569,747)(570,746)
(571,745)(572,744)(573,743)(574,742)(575,741)(576,740)(577,739)(578,738)
(579,737)(580,736)(581,735)(582,734)(583,733)(584,732)(585,731)(586,730)
(587,729)(588,728)(589,727)(590,726)(591,725)(592,724)(593,723)(594,722)
(595,721)(596,720)(597,719)(598,718)(599,717)(600,716)(601,715)(602,714)
(603,713)(604,712)(605,711)(606,710);;
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, 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*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*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*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(808)!(405,506)(406,507)(407,508)(408,509)(409,510)(410,511)(411,512)
(412,513)(413,514)(414,515)(415,516)(416,517)(417,518)(418,519)(419,520)
(420,521)(421,522)(422,523)(423,524)(424,525)(425,526)(426,527)(427,528)
(428,529)(429,530)(430,531)(431,532)(432,533)(433,534)(434,535)(435,536)
(436,537)(437,538)(438,539)(439,540)(440,541)(441,542)(442,543)(443,544)
(444,545)(445,546)(446,547)(447,548)(448,549)(449,550)(450,551)(451,552)
(452,553)(453,554)(454,555)(455,556)(456,557)(457,558)(458,559)(459,560)
(460,561)(461,562)(462,563)(463,564)(464,565)(465,566)(466,567)(467,568)
(468,569)(469,570)(470,571)(471,572)(472,573)(473,574)(474,575)(475,576)
(476,577)(477,578)(478,579)(479,580)(480,581)(481,582)(482,583)(483,584)
(484,585)(485,586)(486,587)(487,588)(488,589)(489,590)(490,591)(491,592)
(492,593)(493,594)(494,595)(495,596)(496,597)(497,598)(498,599)(499,600)
(500,601)(501,602)(502,603)(503,604)(504,605)(505,606)(607,708)(608,709)
(609,710)(610,711)(611,712)(612,713)(613,714)(614,715)(615,716)(616,717)
(617,718)(618,719)(619,720)(620,721)(621,722)(622,723)(623,724)(624,725)
(625,726)(626,727)(627,728)(628,729)(629,730)(630,731)(631,732)(632,733)
(633,734)(634,735)(635,736)(636,737)(637,738)(638,739)(639,740)(640,741)
(641,742)(642,743)(643,744)(644,745)(645,746)(646,747)(647,748)(648,749)
(649,750)(650,751)(651,752)(652,753)(653,754)(654,755)(655,756)(656,757)
(657,758)(658,759)(659,760)(660,761)(661,762)(662,763)(663,764)(664,765)
(665,766)(666,767)(667,768)(668,769)(669,770)(670,771)(671,772)(672,773)
(673,774)(674,775)(675,776)(676,777)(677,778)(678,779)(679,780)(680,781)
(681,782)(682,783)(683,784)(684,785)(685,786)(686,787)(687,788)(688,789)
(689,790)(690,791)(691,792)(692,793)(693,794)(694,795)(695,796)(696,797)
(697,798)(698,799)(699,800)(700,801)(701,802)(702,803)(703,804)(704,805)
(705,806)(706,807)(707,808);
s1 := Sym(808)!( 1,607)( 2,707)( 3,706)( 4,705)( 5,704)( 6,703)( 7,702)
( 8,701)( 9,700)( 10,699)( 11,698)( 12,697)( 13,696)( 14,695)( 15,694)
( 16,693)( 17,692)( 18,691)( 19,690)( 20,689)( 21,688)( 22,687)( 23,686)
( 24,685)( 25,684)( 26,683)( 27,682)( 28,681)( 29,680)( 30,679)( 31,678)
( 32,677)( 33,676)( 34,675)( 35,674)( 36,673)( 37,672)( 38,671)( 39,670)
( 40,669)( 41,668)( 42,667)( 43,666)( 44,665)( 45,664)( 46,663)( 47,662)
( 48,661)( 49,660)( 50,659)( 51,658)( 52,657)( 53,656)( 54,655)( 55,654)
( 56,653)( 57,652)( 58,651)( 59,650)( 60,649)( 61,648)( 62,647)( 63,646)
( 64,645)( 65,644)( 66,643)( 67,642)( 68,641)( 69,640)( 70,639)( 71,638)
( 72,637)( 73,636)( 74,635)( 75,634)( 76,633)( 77,632)( 78,631)( 79,630)
( 80,629)( 81,628)( 82,627)( 83,626)( 84,625)( 85,624)( 86,623)( 87,622)
( 88,621)( 89,620)( 90,619)( 91,618)( 92,617)( 93,616)( 94,615)( 95,614)
( 96,613)( 97,612)( 98,611)( 99,610)(100,609)(101,608)(102,708)(103,808)
(104,807)(105,806)(106,805)(107,804)(108,803)(109,802)(110,801)(111,800)
(112,799)(113,798)(114,797)(115,796)(116,795)(117,794)(118,793)(119,792)
(120,791)(121,790)(122,789)(123,788)(124,787)(125,786)(126,785)(127,784)
(128,783)(129,782)(130,781)(131,780)(132,779)(133,778)(134,777)(135,776)
(136,775)(137,774)(138,773)(139,772)(140,771)(141,770)(142,769)(143,768)
(144,767)(145,766)(146,765)(147,764)(148,763)(149,762)(150,761)(151,760)
(152,759)(153,758)(154,757)(155,756)(156,755)(157,754)(158,753)(159,752)
(160,751)(161,750)(162,749)(163,748)(164,747)(165,746)(166,745)(167,744)
(168,743)(169,742)(170,741)(171,740)(172,739)(173,738)(174,737)(175,736)
(176,735)(177,734)(178,733)(179,732)(180,731)(181,730)(182,729)(183,728)
(184,727)(185,726)(186,725)(187,724)(188,723)(189,722)(190,721)(191,720)
(192,719)(193,718)(194,717)(195,716)(196,715)(197,714)(198,713)(199,712)
(200,711)(201,710)(202,709)(203,405)(204,505)(205,504)(206,503)(207,502)
(208,501)(209,500)(210,499)(211,498)(212,497)(213,496)(214,495)(215,494)
(216,493)(217,492)(218,491)(219,490)(220,489)(221,488)(222,487)(223,486)
(224,485)(225,484)(226,483)(227,482)(228,481)(229,480)(230,479)(231,478)
(232,477)(233,476)(234,475)(235,474)(236,473)(237,472)(238,471)(239,470)
(240,469)(241,468)(242,467)(243,466)(244,465)(245,464)(246,463)(247,462)
(248,461)(249,460)(250,459)(251,458)(252,457)(253,456)(254,455)(255,454)
(256,453)(257,452)(258,451)(259,450)(260,449)(261,448)(262,447)(263,446)
(264,445)(265,444)(266,443)(267,442)(268,441)(269,440)(270,439)(271,438)
(272,437)(273,436)(274,435)(275,434)(276,433)(277,432)(278,431)(279,430)
(280,429)(281,428)(282,427)(283,426)(284,425)(285,424)(286,423)(287,422)
(288,421)(289,420)(290,419)(291,418)(292,417)(293,416)(294,415)(295,414)
(296,413)(297,412)(298,411)(299,410)(300,409)(301,408)(302,407)(303,406)
(304,506)(305,606)(306,605)(307,604)(308,603)(309,602)(310,601)(311,600)
(312,599)(313,598)(314,597)(315,596)(316,595)(317,594)(318,593)(319,592)
(320,591)(321,590)(322,589)(323,588)(324,587)(325,586)(326,585)(327,584)
(328,583)(329,582)(330,581)(331,580)(332,579)(333,578)(334,577)(335,576)
(336,575)(337,574)(338,573)(339,572)(340,571)(341,570)(342,569)(343,568)
(344,567)(345,566)(346,565)(347,564)(348,563)(349,562)(350,561)(351,560)
(352,559)(353,558)(354,557)(355,556)(356,555)(357,554)(358,553)(359,552)
(360,551)(361,550)(362,549)(363,548)(364,547)(365,546)(366,545)(367,544)
(368,543)(369,542)(370,541)(371,540)(372,539)(373,538)(374,537)(375,536)
(376,535)(377,534)(378,533)(379,532)(380,531)(381,530)(382,529)(383,528)
(384,527)(385,526)(386,525)(387,524)(388,523)(389,522)(390,521)(391,520)
(392,519)(393,518)(394,517)(395,516)(396,515)(397,514)(398,513)(399,512)
(400,511)(401,510)(402,509)(403,508)(404,507);
s2 := Sym(808)!( 1,204)( 2,203)( 3,303)( 4,302)( 5,301)( 6,300)( 7,299)
( 8,298)( 9,297)( 10,296)( 11,295)( 12,294)( 13,293)( 14,292)( 15,291)
( 16,290)( 17,289)( 18,288)( 19,287)( 20,286)( 21,285)( 22,284)( 23,283)
( 24,282)( 25,281)( 26,280)( 27,279)( 28,278)( 29,277)( 30,276)( 31,275)
( 32,274)( 33,273)( 34,272)( 35,271)( 36,270)( 37,269)( 38,268)( 39,267)
( 40,266)( 41,265)( 42,264)( 43,263)( 44,262)( 45,261)( 46,260)( 47,259)
( 48,258)( 49,257)( 50,256)( 51,255)( 52,254)( 53,253)( 54,252)( 55,251)
( 56,250)( 57,249)( 58,248)( 59,247)( 60,246)( 61,245)( 62,244)( 63,243)
( 64,242)( 65,241)( 66,240)( 67,239)( 68,238)( 69,237)( 70,236)( 71,235)
( 72,234)( 73,233)( 74,232)( 75,231)( 76,230)( 77,229)( 78,228)( 79,227)
( 80,226)( 81,225)( 82,224)( 83,223)( 84,222)( 85,221)( 86,220)( 87,219)
( 88,218)( 89,217)( 90,216)( 91,215)( 92,214)( 93,213)( 94,212)( 95,211)
( 96,210)( 97,209)( 98,208)( 99,207)(100,206)(101,205)(102,305)(103,304)
(104,404)(105,403)(106,402)(107,401)(108,400)(109,399)(110,398)(111,397)
(112,396)(113,395)(114,394)(115,393)(116,392)(117,391)(118,390)(119,389)
(120,388)(121,387)(122,386)(123,385)(124,384)(125,383)(126,382)(127,381)
(128,380)(129,379)(130,378)(131,377)(132,376)(133,375)(134,374)(135,373)
(136,372)(137,371)(138,370)(139,369)(140,368)(141,367)(142,366)(143,365)
(144,364)(145,363)(146,362)(147,361)(148,360)(149,359)(150,358)(151,357)
(152,356)(153,355)(154,354)(155,353)(156,352)(157,351)(158,350)(159,349)
(160,348)(161,347)(162,346)(163,345)(164,344)(165,343)(166,342)(167,341)
(168,340)(169,339)(170,338)(171,337)(172,336)(173,335)(174,334)(175,333)
(176,332)(177,331)(178,330)(179,329)(180,328)(181,327)(182,326)(183,325)
(184,324)(185,323)(186,322)(187,321)(188,320)(189,319)(190,318)(191,317)
(192,316)(193,315)(194,314)(195,313)(196,312)(197,311)(198,310)(199,309)
(200,308)(201,307)(202,306)(405,608)(406,607)(407,707)(408,706)(409,705)
(410,704)(411,703)(412,702)(413,701)(414,700)(415,699)(416,698)(417,697)
(418,696)(419,695)(420,694)(421,693)(422,692)(423,691)(424,690)(425,689)
(426,688)(427,687)(428,686)(429,685)(430,684)(431,683)(432,682)(433,681)
(434,680)(435,679)(436,678)(437,677)(438,676)(439,675)(440,674)(441,673)
(442,672)(443,671)(444,670)(445,669)(446,668)(447,667)(448,666)(449,665)
(450,664)(451,663)(452,662)(453,661)(454,660)(455,659)(456,658)(457,657)
(458,656)(459,655)(460,654)(461,653)(462,652)(463,651)(464,650)(465,649)
(466,648)(467,647)(468,646)(469,645)(470,644)(471,643)(472,642)(473,641)
(474,640)(475,639)(476,638)(477,637)(478,636)(479,635)(480,634)(481,633)
(482,632)(483,631)(484,630)(485,629)(486,628)(487,627)(488,626)(489,625)
(490,624)(491,623)(492,622)(493,621)(494,620)(495,619)(496,618)(497,617)
(498,616)(499,615)(500,614)(501,613)(502,612)(503,611)(504,610)(505,609)
(506,709)(507,708)(508,808)(509,807)(510,806)(511,805)(512,804)(513,803)
(514,802)(515,801)(516,800)(517,799)(518,798)(519,797)(520,796)(521,795)
(522,794)(523,793)(524,792)(525,791)(526,790)(527,789)(528,788)(529,787)
(530,786)(531,785)(532,784)(533,783)(534,782)(535,781)(536,780)(537,779)
(538,778)(539,777)(540,776)(541,775)(542,774)(543,773)(544,772)(545,771)
(546,770)(547,769)(548,768)(549,767)(550,766)(551,765)(552,764)(553,763)
(554,762)(555,761)(556,760)(557,759)(558,758)(559,757)(560,756)(561,755)
(562,754)(563,753)(564,752)(565,751)(566,750)(567,749)(568,748)(569,747)
(570,746)(571,745)(572,744)(573,743)(574,742)(575,741)(576,740)(577,739)
(578,738)(579,737)(580,736)(581,735)(582,734)(583,733)(584,732)(585,731)
(586,730)(587,729)(588,728)(589,727)(590,726)(591,725)(592,724)(593,723)
(594,722)(595,721)(596,720)(597,719)(598,718)(599,717)(600,716)(601,715)
(602,714)(603,713)(604,712)(605,711)(606,710);
poly := sub<Sym(808)|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, 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*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*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*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