Polytope of Type {4,206}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,206}*1648
Also Known As : {4,206|2}. if this polytope has another name.
Group : SmallGroup(1648,34)
Rank : 3
Schlafli Type : {4,206}
Number of vertices, edges, etc : 4, 412, 206
Order of s₀s₁s₂ : 412
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 : {2,206}*824
   4-fold quotients : {2,103}*412
   103-fold quotients : {4,2}*16
   206-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (413,516)(414,517)(415,518)(416,519)(417,520)(418,521)(419,522)(420,523)
(421,524)(422,525)(423,526)(424,527)(425,528)(426,529)(427,530)(428,531)
(429,532)(430,533)(431,534)(432,535)(433,536)(434,537)(435,538)(436,539)
(437,540)(438,541)(439,542)(440,543)(441,544)(442,545)(443,546)(444,547)
(445,548)(446,549)(447,550)(448,551)(449,552)(450,553)(451,554)(452,555)
(453,556)(454,557)(455,558)(456,559)(457,560)(458,561)(459,562)(460,563)
(461,564)(462,565)(463,566)(464,567)(465,568)(466,569)(467,570)(468,571)
(469,572)(470,573)(471,574)(472,575)(473,576)(474,577)(475,578)(476,579)
(477,580)(478,581)(479,582)(480,583)(481,584)(482,585)(483,586)(484,587)
(485,588)(486,589)(487,590)(488,591)(489,592)(490,593)(491,594)(492,595)
(493,596)(494,597)(495,598)(496,599)(497,600)(498,601)(499,602)(500,603)
(501,604)(502,605)(503,606)(504,607)(505,608)(506,609)(507,610)(508,611)
(509,612)(510,613)(511,614)(512,615)(513,616)(514,617)(515,618)(619,722)
(620,723)(621,724)(622,725)(623,726)(624,727)(625,728)(626,729)(627,730)
(628,731)(629,732)(630,733)(631,734)(632,735)(633,736)(634,737)(635,738)
(636,739)(637,740)(638,741)(639,742)(640,743)(641,744)(642,745)(643,746)
(644,747)(645,748)(646,749)(647,750)(648,751)(649,752)(650,753)(651,754)
(652,755)(653,756)(654,757)(655,758)(656,759)(657,760)(658,761)(659,762)
(660,763)(661,764)(662,765)(663,766)(664,767)(665,768)(666,769)(667,770)
(668,771)(669,772)(670,773)(671,774)(672,775)(673,776)(674,777)(675,778)
(676,779)(677,780)(678,781)(679,782)(680,783)(681,784)(682,785)(683,786)
(684,787)(685,788)(686,789)(687,790)(688,791)(689,792)(690,793)(691,794)
(692,795)(693,796)(694,797)(695,798)(696,799)(697,800)(698,801)(699,802)
(700,803)(701,804)(702,805)(703,806)(704,807)(705,808)(706,809)(707,810)
(708,811)(709,812)(710,813)(711,814)(712,815)(713,816)(714,817)(715,818)
(716,819)(717,820)(718,821)(719,822)(720,823)(721,824);;
s1 := (  1,619)(  2,721)(  3,720)(  4,719)(  5,718)(  6,717)(  7,716)(  8,715)
(  9,714)( 10,713)( 11,712)( 12,711)( 13,710)( 14,709)( 15,708)( 16,707)
( 17,706)( 18,705)( 19,704)( 20,703)( 21,702)( 22,701)( 23,700)( 24,699)
( 25,698)( 26,697)( 27,696)( 28,695)( 29,694)( 30,693)( 31,692)( 32,691)
( 33,690)( 34,689)( 35,688)( 36,687)( 37,686)( 38,685)( 39,684)( 40,683)
( 41,682)( 42,681)( 43,680)( 44,679)( 45,678)( 46,677)( 47,676)( 48,675)
( 49,674)( 50,673)( 51,672)( 52,671)( 53,670)( 54,669)( 55,668)( 56,667)
( 57,666)( 58,665)( 59,664)( 60,663)( 61,662)( 62,661)( 63,660)( 64,659)
( 65,658)( 66,657)( 67,656)( 68,655)( 69,654)( 70,653)( 71,652)( 72,651)
( 73,650)( 74,649)( 75,648)( 76,647)( 77,646)( 78,645)( 79,644)( 80,643)
( 81,642)( 82,641)( 83,640)( 84,639)( 85,638)( 86,637)( 87,636)( 88,635)
( 89,634)( 90,633)( 91,632)( 92,631)( 93,630)( 94,629)( 95,628)( 96,627)
( 97,626)( 98,625)( 99,624)(100,623)(101,622)(102,621)(103,620)(104,722)
(105,824)(106,823)(107,822)(108,821)(109,820)(110,819)(111,818)(112,817)
(113,816)(114,815)(115,814)(116,813)(117,812)(118,811)(119,810)(120,809)
(121,808)(122,807)(123,806)(124,805)(125,804)(126,803)(127,802)(128,801)
(129,800)(130,799)(131,798)(132,797)(133,796)(134,795)(135,794)(136,793)
(137,792)(138,791)(139,790)(140,789)(141,788)(142,787)(143,786)(144,785)
(145,784)(146,783)(147,782)(148,781)(149,780)(150,779)(151,778)(152,777)
(153,776)(154,775)(155,774)(156,773)(157,772)(158,771)(159,770)(160,769)
(161,768)(162,767)(163,766)(164,765)(165,764)(166,763)(167,762)(168,761)
(169,760)(170,759)(171,758)(172,757)(173,756)(174,755)(175,754)(176,753)
(177,752)(178,751)(179,750)(180,749)(181,748)(182,747)(183,746)(184,745)
(185,744)(186,743)(187,742)(188,741)(189,740)(190,739)(191,738)(192,737)
(193,736)(194,735)(195,734)(196,733)(197,732)(198,731)(199,730)(200,729)
(201,728)(202,727)(203,726)(204,725)(205,724)(206,723)(207,413)(208,515)
(209,514)(210,513)(211,512)(212,511)(213,510)(214,509)(215,508)(216,507)
(217,506)(218,505)(219,504)(220,503)(221,502)(222,501)(223,500)(224,499)
(225,498)(226,497)(227,496)(228,495)(229,494)(230,493)(231,492)(232,491)
(233,490)(234,489)(235,488)(236,487)(237,486)(238,485)(239,484)(240,483)
(241,482)(242,481)(243,480)(244,479)(245,478)(246,477)(247,476)(248,475)
(249,474)(250,473)(251,472)(252,471)(253,470)(254,469)(255,468)(256,467)
(257,466)(258,465)(259,464)(260,463)(261,462)(262,461)(263,460)(264,459)
(265,458)(266,457)(267,456)(268,455)(269,454)(270,453)(271,452)(272,451)
(273,450)(274,449)(275,448)(276,447)(277,446)(278,445)(279,444)(280,443)
(281,442)(282,441)(283,440)(284,439)(285,438)(286,437)(287,436)(288,435)
(289,434)(290,433)(291,432)(292,431)(293,430)(294,429)(295,428)(296,427)
(297,426)(298,425)(299,424)(300,423)(301,422)(302,421)(303,420)(304,419)
(305,418)(306,417)(307,416)(308,415)(309,414)(310,516)(311,618)(312,617)
(313,616)(314,615)(315,614)(316,613)(317,612)(318,611)(319,610)(320,609)
(321,608)(322,607)(323,606)(324,605)(325,604)(326,603)(327,602)(328,601)
(329,600)(330,599)(331,598)(332,597)(333,596)(334,595)(335,594)(336,593)
(337,592)(338,591)(339,590)(340,589)(341,588)(342,587)(343,586)(344,585)
(345,584)(346,583)(347,582)(348,581)(349,580)(350,579)(351,578)(352,577)
(353,576)(354,575)(355,574)(356,573)(357,572)(358,571)(359,570)(360,569)
(361,568)(362,567)(363,566)(364,565)(365,564)(366,563)(367,562)(368,561)
(369,560)(370,559)(371,558)(372,557)(373,556)(374,555)(375,554)(376,553)
(377,552)(378,551)(379,550)(380,549)(381,548)(382,547)(383,546)(384,545)
(385,544)(386,543)(387,542)(388,541)(389,540)(390,539)(391,538)(392,537)
(393,536)(394,535)(395,534)(396,533)(397,532)(398,531)(399,530)(400,529)
(401,528)(402,527)(403,526)(404,525)(405,524)(406,523)(407,522)(408,521)
(409,520)(410,519)(411,518)(412,517);;
s2 := (  1,208)(  2,207)(  3,309)(  4,308)(  5,307)(  6,306)(  7,305)(  8,304)
(  9,303)( 10,302)( 11,301)( 12,300)( 13,299)( 14,298)( 15,297)( 16,296)
( 17,295)( 18,294)( 19,293)( 20,292)( 21,291)( 22,290)( 23,289)( 24,288)
( 25,287)( 26,286)( 27,285)( 28,284)( 29,283)( 30,282)( 31,281)( 32,280)
( 33,279)( 34,278)( 35,277)( 36,276)( 37,275)( 38,274)( 39,273)( 40,272)
( 41,271)( 42,270)( 43,269)( 44,268)( 45,267)( 46,266)( 47,265)( 48,264)
( 49,263)( 50,262)( 51,261)( 52,260)( 53,259)( 54,258)( 55,257)( 56,256)
( 57,255)( 58,254)( 59,253)( 60,252)( 61,251)( 62,250)( 63,249)( 64,248)
( 65,247)( 66,246)( 67,245)( 68,244)( 69,243)( 70,242)( 71,241)( 72,240)
( 73,239)( 74,238)( 75,237)( 76,236)( 77,235)( 78,234)( 79,233)( 80,232)
( 81,231)( 82,230)( 83,229)( 84,228)( 85,227)( 86,226)( 87,225)( 88,224)
( 89,223)( 90,222)( 91,221)( 92,220)( 93,219)( 94,218)( 95,217)( 96,216)
( 97,215)( 98,214)( 99,213)(100,212)(101,211)(102,210)(103,209)(104,311)
(105,310)(106,412)(107,411)(108,410)(109,409)(110,408)(111,407)(112,406)
(113,405)(114,404)(115,403)(116,402)(117,401)(118,400)(119,399)(120,398)
(121,397)(122,396)(123,395)(124,394)(125,393)(126,392)(127,391)(128,390)
(129,389)(130,388)(131,387)(132,386)(133,385)(134,384)(135,383)(136,382)
(137,381)(138,380)(139,379)(140,378)(141,377)(142,376)(143,375)(144,374)
(145,373)(146,372)(147,371)(148,370)(149,369)(150,368)(151,367)(152,366)
(153,365)(154,364)(155,363)(156,362)(157,361)(158,360)(159,359)(160,358)
(161,357)(162,356)(163,355)(164,354)(165,353)(166,352)(167,351)(168,350)
(169,349)(170,348)(171,347)(172,346)(173,345)(174,344)(175,343)(176,342)
(177,341)(178,340)(179,339)(180,338)(181,337)(182,336)(183,335)(184,334)
(185,333)(186,332)(187,331)(188,330)(189,329)(190,328)(191,327)(192,326)
(193,325)(194,324)(195,323)(196,322)(197,321)(198,320)(199,319)(200,318)
(201,317)(202,316)(203,315)(204,314)(205,313)(206,312)(413,620)(414,619)
(415,721)(416,720)(417,719)(418,718)(419,717)(420,716)(421,715)(422,714)
(423,713)(424,712)(425,711)(426,710)(427,709)(428,708)(429,707)(430,706)
(431,705)(432,704)(433,703)(434,702)(435,701)(436,700)(437,699)(438,698)
(439,697)(440,696)(441,695)(442,694)(443,693)(444,692)(445,691)(446,690)
(447,689)(448,688)(449,687)(450,686)(451,685)(452,684)(453,683)(454,682)
(455,681)(456,680)(457,679)(458,678)(459,677)(460,676)(461,675)(462,674)
(463,673)(464,672)(465,671)(466,670)(467,669)(468,668)(469,667)(470,666)
(471,665)(472,664)(473,663)(474,662)(475,661)(476,660)(477,659)(478,658)
(479,657)(480,656)(481,655)(482,654)(483,653)(484,652)(485,651)(486,650)
(487,649)(488,648)(489,647)(490,646)(491,645)(492,644)(493,643)(494,642)
(495,641)(496,640)(497,639)(498,638)(499,637)(500,636)(501,635)(502,634)
(503,633)(504,632)(505,631)(506,630)(507,629)(508,628)(509,627)(510,626)
(511,625)(512,624)(513,623)(514,622)(515,621)(516,723)(517,722)(518,824)
(519,823)(520,822)(521,821)(522,820)(523,819)(524,818)(525,817)(526,816)
(527,815)(528,814)(529,813)(530,812)(531,811)(532,810)(533,809)(534,808)
(535,807)(536,806)(537,805)(538,804)(539,803)(540,802)(541,801)(542,800)
(543,799)(544,798)(545,797)(546,796)(547,795)(548,794)(549,793)(550,792)
(551,791)(552,790)(553,789)(554,788)(555,787)(556,786)(557,785)(558,784)
(559,783)(560,782)(561,781)(562,780)(563,779)(564,778)(565,777)(566,776)
(567,775)(568,774)(569,773)(570,772)(571,771)(572,770)(573,769)(574,768)
(575,767)(576,766)(577,765)(578,764)(579,763)(580,762)(581,761)(582,760)
(583,759)(584,758)(585,757)(586,756)(587,755)(588,754)(589,753)(590,752)
(591,751)(592,750)(593,749)(594,748)(595,747)(596,746)(597,745)(598,744)
(599,743)(600,742)(601,741)(602,740)(603,739)(604,738)(605,737)(606,736)
(607,735)(608,734)(609,733)(610,732)(611,731)(612,730)(613,729)(614,728)
(615,727)(616,726)(617,725)(618,724);;
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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(824)!(413,516)(414,517)(415,518)(416,519)(417,520)(418,521)(419,522)
(420,523)(421,524)(422,525)(423,526)(424,527)(425,528)(426,529)(427,530)
(428,531)(429,532)(430,533)(431,534)(432,535)(433,536)(434,537)(435,538)
(436,539)(437,540)(438,541)(439,542)(440,543)(441,544)(442,545)(443,546)
(444,547)(445,548)(446,549)(447,550)(448,551)(449,552)(450,553)(451,554)
(452,555)(453,556)(454,557)(455,558)(456,559)(457,560)(458,561)(459,562)
(460,563)(461,564)(462,565)(463,566)(464,567)(465,568)(466,569)(467,570)
(468,571)(469,572)(470,573)(471,574)(472,575)(473,576)(474,577)(475,578)
(476,579)(477,580)(478,581)(479,582)(480,583)(481,584)(482,585)(483,586)
(484,587)(485,588)(486,589)(487,590)(488,591)(489,592)(490,593)(491,594)
(492,595)(493,596)(494,597)(495,598)(496,599)(497,600)(498,601)(499,602)
(500,603)(501,604)(502,605)(503,606)(504,607)(505,608)(506,609)(507,610)
(508,611)(509,612)(510,613)(511,614)(512,615)(513,616)(514,617)(515,618)
(619,722)(620,723)(621,724)(622,725)(623,726)(624,727)(625,728)(626,729)
(627,730)(628,731)(629,732)(630,733)(631,734)(632,735)(633,736)(634,737)
(635,738)(636,739)(637,740)(638,741)(639,742)(640,743)(641,744)(642,745)
(643,746)(644,747)(645,748)(646,749)(647,750)(648,751)(649,752)(650,753)
(651,754)(652,755)(653,756)(654,757)(655,758)(656,759)(657,760)(658,761)
(659,762)(660,763)(661,764)(662,765)(663,766)(664,767)(665,768)(666,769)
(667,770)(668,771)(669,772)(670,773)(671,774)(672,775)(673,776)(674,777)
(675,778)(676,779)(677,780)(678,781)(679,782)(680,783)(681,784)(682,785)
(683,786)(684,787)(685,788)(686,789)(687,790)(688,791)(689,792)(690,793)
(691,794)(692,795)(693,796)(694,797)(695,798)(696,799)(697,800)(698,801)
(699,802)(700,803)(701,804)(702,805)(703,806)(704,807)(705,808)(706,809)
(707,810)(708,811)(709,812)(710,813)(711,814)(712,815)(713,816)(714,817)
(715,818)(716,819)(717,820)(718,821)(719,822)(720,823)(721,824);
s1 := Sym(824)!(  1,619)(  2,721)(  3,720)(  4,719)(  5,718)(  6,717)(  7,716)
(  8,715)(  9,714)( 10,713)( 11,712)( 12,711)( 13,710)( 14,709)( 15,708)
( 16,707)( 17,706)( 18,705)( 19,704)( 20,703)( 21,702)( 22,701)( 23,700)
( 24,699)( 25,698)( 26,697)( 27,696)( 28,695)( 29,694)( 30,693)( 31,692)
( 32,691)( 33,690)( 34,689)( 35,688)( 36,687)( 37,686)( 38,685)( 39,684)
( 40,683)( 41,682)( 42,681)( 43,680)( 44,679)( 45,678)( 46,677)( 47,676)
( 48,675)( 49,674)( 50,673)( 51,672)( 52,671)( 53,670)( 54,669)( 55,668)
( 56,667)( 57,666)( 58,665)( 59,664)( 60,663)( 61,662)( 62,661)( 63,660)
( 64,659)( 65,658)( 66,657)( 67,656)( 68,655)( 69,654)( 70,653)( 71,652)
( 72,651)( 73,650)( 74,649)( 75,648)( 76,647)( 77,646)( 78,645)( 79,644)
( 80,643)( 81,642)( 82,641)( 83,640)( 84,639)( 85,638)( 86,637)( 87,636)
( 88,635)( 89,634)( 90,633)( 91,632)( 92,631)( 93,630)( 94,629)( 95,628)
( 96,627)( 97,626)( 98,625)( 99,624)(100,623)(101,622)(102,621)(103,620)
(104,722)(105,824)(106,823)(107,822)(108,821)(109,820)(110,819)(111,818)
(112,817)(113,816)(114,815)(115,814)(116,813)(117,812)(118,811)(119,810)
(120,809)(121,808)(122,807)(123,806)(124,805)(125,804)(126,803)(127,802)
(128,801)(129,800)(130,799)(131,798)(132,797)(133,796)(134,795)(135,794)
(136,793)(137,792)(138,791)(139,790)(140,789)(141,788)(142,787)(143,786)
(144,785)(145,784)(146,783)(147,782)(148,781)(149,780)(150,779)(151,778)
(152,777)(153,776)(154,775)(155,774)(156,773)(157,772)(158,771)(159,770)
(160,769)(161,768)(162,767)(163,766)(164,765)(165,764)(166,763)(167,762)
(168,761)(169,760)(170,759)(171,758)(172,757)(173,756)(174,755)(175,754)
(176,753)(177,752)(178,751)(179,750)(180,749)(181,748)(182,747)(183,746)
(184,745)(185,744)(186,743)(187,742)(188,741)(189,740)(190,739)(191,738)
(192,737)(193,736)(194,735)(195,734)(196,733)(197,732)(198,731)(199,730)
(200,729)(201,728)(202,727)(203,726)(204,725)(205,724)(206,723)(207,413)
(208,515)(209,514)(210,513)(211,512)(212,511)(213,510)(214,509)(215,508)
(216,507)(217,506)(218,505)(219,504)(220,503)(221,502)(222,501)(223,500)
(224,499)(225,498)(226,497)(227,496)(228,495)(229,494)(230,493)(231,492)
(232,491)(233,490)(234,489)(235,488)(236,487)(237,486)(238,485)(239,484)
(240,483)(241,482)(242,481)(243,480)(244,479)(245,478)(246,477)(247,476)
(248,475)(249,474)(250,473)(251,472)(252,471)(253,470)(254,469)(255,468)
(256,467)(257,466)(258,465)(259,464)(260,463)(261,462)(262,461)(263,460)
(264,459)(265,458)(266,457)(267,456)(268,455)(269,454)(270,453)(271,452)
(272,451)(273,450)(274,449)(275,448)(276,447)(277,446)(278,445)(279,444)
(280,443)(281,442)(282,441)(283,440)(284,439)(285,438)(286,437)(287,436)
(288,435)(289,434)(290,433)(291,432)(292,431)(293,430)(294,429)(295,428)
(296,427)(297,426)(298,425)(299,424)(300,423)(301,422)(302,421)(303,420)
(304,419)(305,418)(306,417)(307,416)(308,415)(309,414)(310,516)(311,618)
(312,617)(313,616)(314,615)(315,614)(316,613)(317,612)(318,611)(319,610)
(320,609)(321,608)(322,607)(323,606)(324,605)(325,604)(326,603)(327,602)
(328,601)(329,600)(330,599)(331,598)(332,597)(333,596)(334,595)(335,594)
(336,593)(337,592)(338,591)(339,590)(340,589)(341,588)(342,587)(343,586)
(344,585)(345,584)(346,583)(347,582)(348,581)(349,580)(350,579)(351,578)
(352,577)(353,576)(354,575)(355,574)(356,573)(357,572)(358,571)(359,570)
(360,569)(361,568)(362,567)(363,566)(364,565)(365,564)(366,563)(367,562)
(368,561)(369,560)(370,559)(371,558)(372,557)(373,556)(374,555)(375,554)
(376,553)(377,552)(378,551)(379,550)(380,549)(381,548)(382,547)(383,546)
(384,545)(385,544)(386,543)(387,542)(388,541)(389,540)(390,539)(391,538)
(392,537)(393,536)(394,535)(395,534)(396,533)(397,532)(398,531)(399,530)
(400,529)(401,528)(402,527)(403,526)(404,525)(405,524)(406,523)(407,522)
(408,521)(409,520)(410,519)(411,518)(412,517);
s2 := Sym(824)!(  1,208)(  2,207)(  3,309)(  4,308)(  5,307)(  6,306)(  7,305)
(  8,304)(  9,303)( 10,302)( 11,301)( 12,300)( 13,299)( 14,298)( 15,297)
( 16,296)( 17,295)( 18,294)( 19,293)( 20,292)( 21,291)( 22,290)( 23,289)
( 24,288)( 25,287)( 26,286)( 27,285)( 28,284)( 29,283)( 30,282)( 31,281)
( 32,280)( 33,279)( 34,278)( 35,277)( 36,276)( 37,275)( 38,274)( 39,273)
( 40,272)( 41,271)( 42,270)( 43,269)( 44,268)( 45,267)( 46,266)( 47,265)
( 48,264)( 49,263)( 50,262)( 51,261)( 52,260)( 53,259)( 54,258)( 55,257)
( 56,256)( 57,255)( 58,254)( 59,253)( 60,252)( 61,251)( 62,250)( 63,249)
( 64,248)( 65,247)( 66,246)( 67,245)( 68,244)( 69,243)( 70,242)( 71,241)
( 72,240)( 73,239)( 74,238)( 75,237)( 76,236)( 77,235)( 78,234)( 79,233)
( 80,232)( 81,231)( 82,230)( 83,229)( 84,228)( 85,227)( 86,226)( 87,225)
( 88,224)( 89,223)( 90,222)( 91,221)( 92,220)( 93,219)( 94,218)( 95,217)
( 96,216)( 97,215)( 98,214)( 99,213)(100,212)(101,211)(102,210)(103,209)
(104,311)(105,310)(106,412)(107,411)(108,410)(109,409)(110,408)(111,407)
(112,406)(113,405)(114,404)(115,403)(116,402)(117,401)(118,400)(119,399)
(120,398)(121,397)(122,396)(123,395)(124,394)(125,393)(126,392)(127,391)
(128,390)(129,389)(130,388)(131,387)(132,386)(133,385)(134,384)(135,383)
(136,382)(137,381)(138,380)(139,379)(140,378)(141,377)(142,376)(143,375)
(144,374)(145,373)(146,372)(147,371)(148,370)(149,369)(150,368)(151,367)
(152,366)(153,365)(154,364)(155,363)(156,362)(157,361)(158,360)(159,359)
(160,358)(161,357)(162,356)(163,355)(164,354)(165,353)(166,352)(167,351)
(168,350)(169,349)(170,348)(171,347)(172,346)(173,345)(174,344)(175,343)
(176,342)(177,341)(178,340)(179,339)(180,338)(181,337)(182,336)(183,335)
(184,334)(185,333)(186,332)(187,331)(188,330)(189,329)(190,328)(191,327)
(192,326)(193,325)(194,324)(195,323)(196,322)(197,321)(198,320)(199,319)
(200,318)(201,317)(202,316)(203,315)(204,314)(205,313)(206,312)(413,620)
(414,619)(415,721)(416,720)(417,719)(418,718)(419,717)(420,716)(421,715)
(422,714)(423,713)(424,712)(425,711)(426,710)(427,709)(428,708)(429,707)
(430,706)(431,705)(432,704)(433,703)(434,702)(435,701)(436,700)(437,699)
(438,698)(439,697)(440,696)(441,695)(442,694)(443,693)(444,692)(445,691)
(446,690)(447,689)(448,688)(449,687)(450,686)(451,685)(452,684)(453,683)
(454,682)(455,681)(456,680)(457,679)(458,678)(459,677)(460,676)(461,675)
(462,674)(463,673)(464,672)(465,671)(466,670)(467,669)(468,668)(469,667)
(470,666)(471,665)(472,664)(473,663)(474,662)(475,661)(476,660)(477,659)
(478,658)(479,657)(480,656)(481,655)(482,654)(483,653)(484,652)(485,651)
(486,650)(487,649)(488,648)(489,647)(490,646)(491,645)(492,644)(493,643)
(494,642)(495,641)(496,640)(497,639)(498,638)(499,637)(500,636)(501,635)
(502,634)(503,633)(504,632)(505,631)(506,630)(507,629)(508,628)(509,627)
(510,626)(511,625)(512,624)(513,623)(514,622)(515,621)(516,723)(517,722)
(518,824)(519,823)(520,822)(521,821)(522,820)(523,819)(524,818)(525,817)
(526,816)(527,815)(528,814)(529,813)(530,812)(531,811)(532,810)(533,809)
(534,808)(535,807)(536,806)(537,805)(538,804)(539,803)(540,802)(541,801)
(542,800)(543,799)(544,798)(545,797)(546,796)(547,795)(548,794)(549,793)
(550,792)(551,791)(552,790)(553,789)(554,788)(555,787)(556,786)(557,785)
(558,784)(559,783)(560,782)(561,781)(562,780)(563,779)(564,778)(565,777)
(566,776)(567,775)(568,774)(569,773)(570,772)(571,771)(572,770)(573,769)
(574,768)(575,767)(576,766)(577,765)(578,764)(579,763)(580,762)(581,761)
(582,760)(583,759)(584,758)(585,757)(586,756)(587,755)(588,754)(589,753)
(590,752)(591,751)(592,750)(593,749)(594,748)(595,747)(596,746)(597,745)
(598,744)(599,743)(600,742)(601,741)(602,740)(603,739)(604,738)(605,737)
(606,736)(607,735)(608,734)(609,733)(610,732)(611,731)(612,730)(613,729)
(614,728)(615,727)(616,726)(617,725)(618,724);
poly := sub<Sym(824)|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*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope