Polytope of Type {202,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {202,4}*1616
Also Known As : {202,4|2}. if this polytope has another name.
Group : SmallGroup(1616,34)
Rank : 3
Schlafli Type : {202,4}
Number of vertices, edges, etc : 202, 404, 4
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 : {202,2}*808
   4-fold quotients : {101,2}*404
   101-fold quotients : {2,4}*16
   202-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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