Polytope of Type {4,208}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,208}*1664a
Also Known As : {4,208|2}. if this polytope has another name.
Group : SmallGroup(1664,6424)
Rank : 3
Schlafli Type : {4,208}
Number of vertices, edges, etc : 4, 416, 208
Order of s₀s₁s₂ : 208
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 : {4,104}*832a, {2,208}*832
   4-fold quotients : {4,52}*416, {2,104}*416
   8-fold quotients : {2,52}*208, {4,26}*208
   13-fold quotients : {4,16}*128a
   16-fold quotients : {2,26}*104
   26-fold quotients : {4,8}*64a, {2,16}*64
   32-fold quotients : {2,13}*52
   52-fold quotients : {4,4}*32, {2,8}*32
   104-fold quotients : {2,4}*16, {4,2}*16
   208-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  1,209)(  2,210)(  3,211)(  4,212)(  5,213)(  6,214)(  7,215)(  8,216)
(  9,217)( 10,218)( 11,219)( 12,220)( 13,221)( 14,222)( 15,223)( 16,224)
( 17,225)( 18,226)( 19,227)( 20,228)( 21,229)( 22,230)( 23,231)( 24,232)
( 25,233)( 26,234)( 27,235)( 28,236)( 29,237)( 30,238)( 31,239)( 32,240)
( 33,241)( 34,242)( 35,243)( 36,244)( 37,245)( 38,246)( 39,247)( 40,248)
( 41,249)( 42,250)( 43,251)( 44,252)( 45,253)( 46,254)( 47,255)( 48,256)
( 49,257)( 50,258)( 51,259)( 52,260)( 53,261)( 54,262)( 55,263)( 56,264)
( 57,265)( 58,266)( 59,267)( 60,268)( 61,269)( 62,270)( 63,271)( 64,272)
( 65,273)( 66,274)( 67,275)( 68,276)( 69,277)( 70,278)( 71,279)( 72,280)
( 73,281)( 74,282)( 75,283)( 76,284)( 77,285)( 78,286)( 79,287)( 80,288)
( 81,289)( 82,290)( 83,291)( 84,292)( 85,293)( 86,294)( 87,295)( 88,296)
( 89,297)( 90,298)( 91,299)( 92,300)( 93,301)( 94,302)( 95,303)( 96,304)
( 97,305)( 98,306)( 99,307)(100,308)(101,309)(102,310)(103,311)(104,312)
(105,313)(106,314)(107,315)(108,316)(109,317)(110,318)(111,319)(112,320)
(113,321)(114,322)(115,323)(116,324)(117,325)(118,326)(119,327)(120,328)
(121,329)(122,330)(123,331)(124,332)(125,333)(126,334)(127,335)(128,336)
(129,337)(130,338)(131,339)(132,340)(133,341)(134,342)(135,343)(136,344)
(137,345)(138,346)(139,347)(140,348)(141,349)(142,350)(143,351)(144,352)
(145,353)(146,354)(147,355)(148,356)(149,357)(150,358)(151,359)(152,360)
(153,361)(154,362)(155,363)(156,364)(157,365)(158,366)(159,367)(160,368)
(161,369)(162,370)(163,371)(164,372)(165,373)(166,374)(167,375)(168,376)
(169,377)(170,378)(171,379)(172,380)(173,381)(174,382)(175,383)(176,384)
(177,385)(178,386)(179,387)(180,388)(181,389)(182,390)(183,391)(184,392)
(185,393)(186,394)(187,395)(188,396)(189,397)(190,398)(191,399)(192,400)
(193,401)(194,402)(195,403)(196,404)(197,405)(198,406)(199,407)(200,408)
(201,409)(202,410)(203,411)(204,412)(205,413)(206,414)(207,415)(208,416)
(417,625)(418,626)(419,627)(420,628)(421,629)(422,630)(423,631)(424,632)
(425,633)(426,634)(427,635)(428,636)(429,637)(430,638)(431,639)(432,640)
(433,641)(434,642)(435,643)(436,644)(437,645)(438,646)(439,647)(440,648)
(441,649)(442,650)(443,651)(444,652)(445,653)(446,654)(447,655)(448,656)
(449,657)(450,658)(451,659)(452,660)(453,661)(454,662)(455,663)(456,664)
(457,665)(458,666)(459,667)(460,668)(461,669)(462,670)(463,671)(464,672)
(465,673)(466,674)(467,675)(468,676)(469,677)(470,678)(471,679)(472,680)
(473,681)(474,682)(475,683)(476,684)(477,685)(478,686)(479,687)(480,688)
(481,689)(482,690)(483,691)(484,692)(485,693)(486,694)(487,695)(488,696)
(489,697)(490,698)(491,699)(492,700)(493,701)(494,702)(495,703)(496,704)
(497,705)(498,706)(499,707)(500,708)(501,709)(502,710)(503,711)(504,712)
(505,713)(506,714)(507,715)(508,716)(509,717)(510,718)(511,719)(512,720)
(513,721)(514,722)(515,723)(516,724)(517,725)(518,726)(519,727)(520,728)
(521,729)(522,730)(523,731)(524,732)(525,733)(526,734)(527,735)(528,736)
(529,737)(530,738)(531,739)(532,740)(533,741)(534,742)(535,743)(536,744)
(537,745)(538,746)(539,747)(540,748)(541,749)(542,750)(543,751)(544,752)
(545,753)(546,754)(547,755)(548,756)(549,757)(550,758)(551,759)(552,760)
(553,761)(554,762)(555,763)(556,764)(557,765)(558,766)(559,767)(560,768)
(561,769)(562,770)(563,771)(564,772)(565,773)(566,774)(567,775)(568,776)
(569,777)(570,778)(571,779)(572,780)(573,781)(574,782)(575,783)(576,784)
(577,785)(578,786)(579,787)(580,788)(581,789)(582,790)(583,791)(584,792)
(585,793)(586,794)(587,795)(588,796)(589,797)(590,798)(591,799)(592,800)
(593,801)(594,802)(595,803)(596,804)(597,805)(598,806)(599,807)(600,808)
(601,809)(602,810)(603,811)(604,812)(605,813)(606,814)(607,815)(608,816)
(609,817)(610,818)(611,819)(612,820)(613,821)(614,822)(615,823)(616,824)
(617,825)(618,826)(619,827)(620,828)(621,829)(622,830)(623,831)(624,832);;
s1 := (  2, 13)(  3, 12)(  4, 11)(  5, 10)(  6,  9)(  7,  8)( 15, 26)( 16, 25)
( 17, 24)( 18, 23)( 19, 22)( 20, 21)( 27, 40)( 28, 52)( 29, 51)( 30, 50)
( 31, 49)( 32, 48)( 33, 47)( 34, 46)( 35, 45)( 36, 44)( 37, 43)( 38, 42)
( 39, 41)( 54, 65)( 55, 64)( 56, 63)( 57, 62)( 58, 61)( 59, 60)( 67, 78)
( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79, 92)( 80,104)( 81,103)
( 82,102)( 83,101)( 84,100)( 85, 99)( 86, 98)( 87, 97)( 88, 96)( 89, 95)
( 90, 94)( 91, 93)(105,131)(106,143)(107,142)(108,141)(109,140)(110,139)
(111,138)(112,137)(113,136)(114,135)(115,134)(116,133)(117,132)(118,144)
(119,156)(120,155)(121,154)(122,153)(123,152)(124,151)(125,150)(126,149)
(127,148)(128,147)(129,146)(130,145)(157,183)(158,195)(159,194)(160,193)
(161,192)(162,191)(163,190)(164,189)(165,188)(166,187)(167,186)(168,185)
(169,184)(170,196)(171,208)(172,207)(173,206)(174,205)(175,204)(176,203)
(177,202)(178,201)(179,200)(180,199)(181,198)(182,197)(209,261)(210,273)
(211,272)(212,271)(213,270)(214,269)(215,268)(216,267)(217,266)(218,265)
(219,264)(220,263)(221,262)(222,274)(223,286)(224,285)(225,284)(226,283)
(227,282)(228,281)(229,280)(230,279)(231,278)(232,277)(233,276)(234,275)
(235,300)(236,312)(237,311)(238,310)(239,309)(240,308)(241,307)(242,306)
(243,305)(244,304)(245,303)(246,302)(247,301)(248,287)(249,299)(250,298)
(251,297)(252,296)(253,295)(254,294)(255,293)(256,292)(257,291)(258,290)
(259,289)(260,288)(313,391)(314,403)(315,402)(316,401)(317,400)(318,399)
(319,398)(320,397)(321,396)(322,395)(323,394)(324,393)(325,392)(326,404)
(327,416)(328,415)(329,414)(330,413)(331,412)(332,411)(333,410)(334,409)
(335,408)(336,407)(337,406)(338,405)(339,365)(340,377)(341,376)(342,375)
(343,374)(344,373)(345,372)(346,371)(347,370)(348,369)(349,368)(350,367)
(351,366)(352,378)(353,390)(354,389)(355,388)(356,387)(357,386)(358,385)
(359,384)(360,383)(361,382)(362,381)(363,380)(364,379)(417,521)(418,533)
(419,532)(420,531)(421,530)(422,529)(423,528)(424,527)(425,526)(426,525)
(427,524)(428,523)(429,522)(430,534)(431,546)(432,545)(433,544)(434,543)
(435,542)(436,541)(437,540)(438,539)(439,538)(440,537)(441,536)(442,535)
(443,560)(444,572)(445,571)(446,570)(447,569)(448,568)(449,567)(450,566)
(451,565)(452,564)(453,563)(454,562)(455,561)(456,547)(457,559)(458,558)
(459,557)(460,556)(461,555)(462,554)(463,553)(464,552)(465,551)(466,550)
(467,549)(468,548)(469,573)(470,585)(471,584)(472,583)(473,582)(474,581)
(475,580)(476,579)(477,578)(478,577)(479,576)(480,575)(481,574)(482,586)
(483,598)(484,597)(485,596)(486,595)(487,594)(488,593)(489,592)(490,591)
(491,590)(492,589)(493,588)(494,587)(495,612)(496,624)(497,623)(498,622)
(499,621)(500,620)(501,619)(502,618)(503,617)(504,616)(505,615)(506,614)
(507,613)(508,599)(509,611)(510,610)(511,609)(512,608)(513,607)(514,606)
(515,605)(516,604)(517,603)(518,602)(519,601)(520,600)(625,781)(626,793)
(627,792)(628,791)(629,790)(630,789)(631,788)(632,787)(633,786)(634,785)
(635,784)(636,783)(637,782)(638,794)(639,806)(640,805)(641,804)(642,803)
(643,802)(644,801)(645,800)(646,799)(647,798)(648,797)(649,796)(650,795)
(651,820)(652,832)(653,831)(654,830)(655,829)(656,828)(657,827)(658,826)
(659,825)(660,824)(661,823)(662,822)(663,821)(664,807)(665,819)(666,818)
(667,817)(668,816)(669,815)(670,814)(671,813)(672,812)(673,811)(674,810)
(675,809)(676,808)(677,729)(678,741)(679,740)(680,739)(681,738)(682,737)
(683,736)(684,735)(685,734)(686,733)(687,732)(688,731)(689,730)(690,742)
(691,754)(692,753)(693,752)(694,751)(695,750)(696,749)(697,748)(698,747)
(699,746)(700,745)(701,744)(702,743)(703,768)(704,780)(705,779)(706,778)
(707,777)(708,776)(709,775)(710,774)(711,773)(712,772)(713,771)(714,770)
(715,769)(716,755)(717,767)(718,766)(719,765)(720,764)(721,763)(722,762)
(723,761)(724,760)(725,759)(726,758)(727,757)(728,756);;
s2 := (  1,418)(  2,417)(  3,429)(  4,428)(  5,427)(  6,426)(  7,425)(  8,424)
(  9,423)( 10,422)( 11,421)( 12,420)( 13,419)( 14,431)( 15,430)( 16,442)
( 17,441)( 18,440)( 19,439)( 20,438)( 21,437)( 22,436)( 23,435)( 24,434)
( 25,433)( 26,432)( 27,457)( 28,456)( 29,468)( 30,467)( 31,466)( 32,465)
( 33,464)( 34,463)( 35,462)( 36,461)( 37,460)( 38,459)( 39,458)( 40,444)
( 41,443)( 42,455)( 43,454)( 44,453)( 45,452)( 46,451)( 47,450)( 48,449)
( 49,448)( 50,447)( 51,446)( 52,445)( 53,470)( 54,469)( 55,481)( 56,480)
( 57,479)( 58,478)( 59,477)( 60,476)( 61,475)( 62,474)( 63,473)( 64,472)
( 65,471)( 66,483)( 67,482)( 68,494)( 69,493)( 70,492)( 71,491)( 72,490)
( 73,489)( 74,488)( 75,487)( 76,486)( 77,485)( 78,484)( 79,509)( 80,508)
( 81,520)( 82,519)( 83,518)( 84,517)( 85,516)( 86,515)( 87,514)( 88,513)
( 89,512)( 90,511)( 91,510)( 92,496)( 93,495)( 94,507)( 95,506)( 96,505)
( 97,504)( 98,503)( 99,502)(100,501)(101,500)(102,499)(103,498)(104,497)
(105,548)(106,547)(107,559)(108,558)(109,557)(110,556)(111,555)(112,554)
(113,553)(114,552)(115,551)(116,550)(117,549)(118,561)(119,560)(120,572)
(121,571)(122,570)(123,569)(124,568)(125,567)(126,566)(127,565)(128,564)
(129,563)(130,562)(131,522)(132,521)(133,533)(134,532)(135,531)(136,530)
(137,529)(138,528)(139,527)(140,526)(141,525)(142,524)(143,523)(144,535)
(145,534)(146,546)(147,545)(148,544)(149,543)(150,542)(151,541)(152,540)
(153,539)(154,538)(155,537)(156,536)(157,600)(158,599)(159,611)(160,610)
(161,609)(162,608)(163,607)(164,606)(165,605)(166,604)(167,603)(168,602)
(169,601)(170,613)(171,612)(172,624)(173,623)(174,622)(175,621)(176,620)
(177,619)(178,618)(179,617)(180,616)(181,615)(182,614)(183,574)(184,573)
(185,585)(186,584)(187,583)(188,582)(189,581)(190,580)(191,579)(192,578)
(193,577)(194,576)(195,575)(196,587)(197,586)(198,598)(199,597)(200,596)
(201,595)(202,594)(203,593)(204,592)(205,591)(206,590)(207,589)(208,588)
(209,626)(210,625)(211,637)(212,636)(213,635)(214,634)(215,633)(216,632)
(217,631)(218,630)(219,629)(220,628)(221,627)(222,639)(223,638)(224,650)
(225,649)(226,648)(227,647)(228,646)(229,645)(230,644)(231,643)(232,642)
(233,641)(234,640)(235,665)(236,664)(237,676)(238,675)(239,674)(240,673)
(241,672)(242,671)(243,670)(244,669)(245,668)(246,667)(247,666)(248,652)
(249,651)(250,663)(251,662)(252,661)(253,660)(254,659)(255,658)(256,657)
(257,656)(258,655)(259,654)(260,653)(261,678)(262,677)(263,689)(264,688)
(265,687)(266,686)(267,685)(268,684)(269,683)(270,682)(271,681)(272,680)
(273,679)(274,691)(275,690)(276,702)(277,701)(278,700)(279,699)(280,698)
(281,697)(282,696)(283,695)(284,694)(285,693)(286,692)(287,717)(288,716)
(289,728)(290,727)(291,726)(292,725)(293,724)(294,723)(295,722)(296,721)
(297,720)(298,719)(299,718)(300,704)(301,703)(302,715)(303,714)(304,713)
(305,712)(306,711)(307,710)(308,709)(309,708)(310,707)(311,706)(312,705)
(313,756)(314,755)(315,767)(316,766)(317,765)(318,764)(319,763)(320,762)
(321,761)(322,760)(323,759)(324,758)(325,757)(326,769)(327,768)(328,780)
(329,779)(330,778)(331,777)(332,776)(333,775)(334,774)(335,773)(336,772)
(337,771)(338,770)(339,730)(340,729)(341,741)(342,740)(343,739)(344,738)
(345,737)(346,736)(347,735)(348,734)(349,733)(350,732)(351,731)(352,743)
(353,742)(354,754)(355,753)(356,752)(357,751)(358,750)(359,749)(360,748)
(361,747)(362,746)(363,745)(364,744)(365,808)(366,807)(367,819)(368,818)
(369,817)(370,816)(371,815)(372,814)(373,813)(374,812)(375,811)(376,810)
(377,809)(378,821)(379,820)(380,832)(381,831)(382,830)(383,829)(384,828)
(385,827)(386,826)(387,825)(388,824)(389,823)(390,822)(391,782)(392,781)
(393,793)(394,792)(395,791)(396,790)(397,789)(398,788)(399,787)(400,786)
(401,785)(402,784)(403,783)(404,795)(405,794)(406,806)(407,805)(408,804)
(409,803)(410,802)(411,801)(412,800)(413,799)(414,798)(415,797)(416,796);;
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*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(832)!(  1,209)(  2,210)(  3,211)(  4,212)(  5,213)(  6,214)(  7,215)
(  8,216)(  9,217)( 10,218)( 11,219)( 12,220)( 13,221)( 14,222)( 15,223)
( 16,224)( 17,225)( 18,226)( 19,227)( 20,228)( 21,229)( 22,230)( 23,231)
( 24,232)( 25,233)( 26,234)( 27,235)( 28,236)( 29,237)( 30,238)( 31,239)
( 32,240)( 33,241)( 34,242)( 35,243)( 36,244)( 37,245)( 38,246)( 39,247)
( 40,248)( 41,249)( 42,250)( 43,251)( 44,252)( 45,253)( 46,254)( 47,255)
( 48,256)( 49,257)( 50,258)( 51,259)( 52,260)( 53,261)( 54,262)( 55,263)
( 56,264)( 57,265)( 58,266)( 59,267)( 60,268)( 61,269)( 62,270)( 63,271)
( 64,272)( 65,273)( 66,274)( 67,275)( 68,276)( 69,277)( 70,278)( 71,279)
( 72,280)( 73,281)( 74,282)( 75,283)( 76,284)( 77,285)( 78,286)( 79,287)
( 80,288)( 81,289)( 82,290)( 83,291)( 84,292)( 85,293)( 86,294)( 87,295)
( 88,296)( 89,297)( 90,298)( 91,299)( 92,300)( 93,301)( 94,302)( 95,303)
( 96,304)( 97,305)( 98,306)( 99,307)(100,308)(101,309)(102,310)(103,311)
(104,312)(105,313)(106,314)(107,315)(108,316)(109,317)(110,318)(111,319)
(112,320)(113,321)(114,322)(115,323)(116,324)(117,325)(118,326)(119,327)
(120,328)(121,329)(122,330)(123,331)(124,332)(125,333)(126,334)(127,335)
(128,336)(129,337)(130,338)(131,339)(132,340)(133,341)(134,342)(135,343)
(136,344)(137,345)(138,346)(139,347)(140,348)(141,349)(142,350)(143,351)
(144,352)(145,353)(146,354)(147,355)(148,356)(149,357)(150,358)(151,359)
(152,360)(153,361)(154,362)(155,363)(156,364)(157,365)(158,366)(159,367)
(160,368)(161,369)(162,370)(163,371)(164,372)(165,373)(166,374)(167,375)
(168,376)(169,377)(170,378)(171,379)(172,380)(173,381)(174,382)(175,383)
(176,384)(177,385)(178,386)(179,387)(180,388)(181,389)(182,390)(183,391)
(184,392)(185,393)(186,394)(187,395)(188,396)(189,397)(190,398)(191,399)
(192,400)(193,401)(194,402)(195,403)(196,404)(197,405)(198,406)(199,407)
(200,408)(201,409)(202,410)(203,411)(204,412)(205,413)(206,414)(207,415)
(208,416)(417,625)(418,626)(419,627)(420,628)(421,629)(422,630)(423,631)
(424,632)(425,633)(426,634)(427,635)(428,636)(429,637)(430,638)(431,639)
(432,640)(433,641)(434,642)(435,643)(436,644)(437,645)(438,646)(439,647)
(440,648)(441,649)(442,650)(443,651)(444,652)(445,653)(446,654)(447,655)
(448,656)(449,657)(450,658)(451,659)(452,660)(453,661)(454,662)(455,663)
(456,664)(457,665)(458,666)(459,667)(460,668)(461,669)(462,670)(463,671)
(464,672)(465,673)(466,674)(467,675)(468,676)(469,677)(470,678)(471,679)
(472,680)(473,681)(474,682)(475,683)(476,684)(477,685)(478,686)(479,687)
(480,688)(481,689)(482,690)(483,691)(484,692)(485,693)(486,694)(487,695)
(488,696)(489,697)(490,698)(491,699)(492,700)(493,701)(494,702)(495,703)
(496,704)(497,705)(498,706)(499,707)(500,708)(501,709)(502,710)(503,711)
(504,712)(505,713)(506,714)(507,715)(508,716)(509,717)(510,718)(511,719)
(512,720)(513,721)(514,722)(515,723)(516,724)(517,725)(518,726)(519,727)
(520,728)(521,729)(522,730)(523,731)(524,732)(525,733)(526,734)(527,735)
(528,736)(529,737)(530,738)(531,739)(532,740)(533,741)(534,742)(535,743)
(536,744)(537,745)(538,746)(539,747)(540,748)(541,749)(542,750)(543,751)
(544,752)(545,753)(546,754)(547,755)(548,756)(549,757)(550,758)(551,759)
(552,760)(553,761)(554,762)(555,763)(556,764)(557,765)(558,766)(559,767)
(560,768)(561,769)(562,770)(563,771)(564,772)(565,773)(566,774)(567,775)
(568,776)(569,777)(570,778)(571,779)(572,780)(573,781)(574,782)(575,783)
(576,784)(577,785)(578,786)(579,787)(580,788)(581,789)(582,790)(583,791)
(584,792)(585,793)(586,794)(587,795)(588,796)(589,797)(590,798)(591,799)
(592,800)(593,801)(594,802)(595,803)(596,804)(597,805)(598,806)(599,807)
(600,808)(601,809)(602,810)(603,811)(604,812)(605,813)(606,814)(607,815)
(608,816)(609,817)(610,818)(611,819)(612,820)(613,821)(614,822)(615,823)
(616,824)(617,825)(618,826)(619,827)(620,828)(621,829)(622,830)(623,831)
(624,832);
s1 := Sym(832)!(  2, 13)(  3, 12)(  4, 11)(  5, 10)(  6,  9)(  7,  8)( 15, 26)
( 16, 25)( 17, 24)( 18, 23)( 19, 22)( 20, 21)( 27, 40)( 28, 52)( 29, 51)
( 30, 50)( 31, 49)( 32, 48)( 33, 47)( 34, 46)( 35, 45)( 36, 44)( 37, 43)
( 38, 42)( 39, 41)( 54, 65)( 55, 64)( 56, 63)( 57, 62)( 58, 61)( 59, 60)
( 67, 78)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79, 92)( 80,104)
( 81,103)( 82,102)( 83,101)( 84,100)( 85, 99)( 86, 98)( 87, 97)( 88, 96)
( 89, 95)( 90, 94)( 91, 93)(105,131)(106,143)(107,142)(108,141)(109,140)
(110,139)(111,138)(112,137)(113,136)(114,135)(115,134)(116,133)(117,132)
(118,144)(119,156)(120,155)(121,154)(122,153)(123,152)(124,151)(125,150)
(126,149)(127,148)(128,147)(129,146)(130,145)(157,183)(158,195)(159,194)
(160,193)(161,192)(162,191)(163,190)(164,189)(165,188)(166,187)(167,186)
(168,185)(169,184)(170,196)(171,208)(172,207)(173,206)(174,205)(175,204)
(176,203)(177,202)(178,201)(179,200)(180,199)(181,198)(182,197)(209,261)
(210,273)(211,272)(212,271)(213,270)(214,269)(215,268)(216,267)(217,266)
(218,265)(219,264)(220,263)(221,262)(222,274)(223,286)(224,285)(225,284)
(226,283)(227,282)(228,281)(229,280)(230,279)(231,278)(232,277)(233,276)
(234,275)(235,300)(236,312)(237,311)(238,310)(239,309)(240,308)(241,307)
(242,306)(243,305)(244,304)(245,303)(246,302)(247,301)(248,287)(249,299)
(250,298)(251,297)(252,296)(253,295)(254,294)(255,293)(256,292)(257,291)
(258,290)(259,289)(260,288)(313,391)(314,403)(315,402)(316,401)(317,400)
(318,399)(319,398)(320,397)(321,396)(322,395)(323,394)(324,393)(325,392)
(326,404)(327,416)(328,415)(329,414)(330,413)(331,412)(332,411)(333,410)
(334,409)(335,408)(336,407)(337,406)(338,405)(339,365)(340,377)(341,376)
(342,375)(343,374)(344,373)(345,372)(346,371)(347,370)(348,369)(349,368)
(350,367)(351,366)(352,378)(353,390)(354,389)(355,388)(356,387)(357,386)
(358,385)(359,384)(360,383)(361,382)(362,381)(363,380)(364,379)(417,521)
(418,533)(419,532)(420,531)(421,530)(422,529)(423,528)(424,527)(425,526)
(426,525)(427,524)(428,523)(429,522)(430,534)(431,546)(432,545)(433,544)
(434,543)(435,542)(436,541)(437,540)(438,539)(439,538)(440,537)(441,536)
(442,535)(443,560)(444,572)(445,571)(446,570)(447,569)(448,568)(449,567)
(450,566)(451,565)(452,564)(453,563)(454,562)(455,561)(456,547)(457,559)
(458,558)(459,557)(460,556)(461,555)(462,554)(463,553)(464,552)(465,551)
(466,550)(467,549)(468,548)(469,573)(470,585)(471,584)(472,583)(473,582)
(474,581)(475,580)(476,579)(477,578)(478,577)(479,576)(480,575)(481,574)
(482,586)(483,598)(484,597)(485,596)(486,595)(487,594)(488,593)(489,592)
(490,591)(491,590)(492,589)(493,588)(494,587)(495,612)(496,624)(497,623)
(498,622)(499,621)(500,620)(501,619)(502,618)(503,617)(504,616)(505,615)
(506,614)(507,613)(508,599)(509,611)(510,610)(511,609)(512,608)(513,607)
(514,606)(515,605)(516,604)(517,603)(518,602)(519,601)(520,600)(625,781)
(626,793)(627,792)(628,791)(629,790)(630,789)(631,788)(632,787)(633,786)
(634,785)(635,784)(636,783)(637,782)(638,794)(639,806)(640,805)(641,804)
(642,803)(643,802)(644,801)(645,800)(646,799)(647,798)(648,797)(649,796)
(650,795)(651,820)(652,832)(653,831)(654,830)(655,829)(656,828)(657,827)
(658,826)(659,825)(660,824)(661,823)(662,822)(663,821)(664,807)(665,819)
(666,818)(667,817)(668,816)(669,815)(670,814)(671,813)(672,812)(673,811)
(674,810)(675,809)(676,808)(677,729)(678,741)(679,740)(680,739)(681,738)
(682,737)(683,736)(684,735)(685,734)(686,733)(687,732)(688,731)(689,730)
(690,742)(691,754)(692,753)(693,752)(694,751)(695,750)(696,749)(697,748)
(698,747)(699,746)(700,745)(701,744)(702,743)(703,768)(704,780)(705,779)
(706,778)(707,777)(708,776)(709,775)(710,774)(711,773)(712,772)(713,771)
(714,770)(715,769)(716,755)(717,767)(718,766)(719,765)(720,764)(721,763)
(722,762)(723,761)(724,760)(725,759)(726,758)(727,757)(728,756);
s2 := Sym(832)!(  1,418)(  2,417)(  3,429)(  4,428)(  5,427)(  6,426)(  7,425)
(  8,424)(  9,423)( 10,422)( 11,421)( 12,420)( 13,419)( 14,431)( 15,430)
( 16,442)( 17,441)( 18,440)( 19,439)( 20,438)( 21,437)( 22,436)( 23,435)
( 24,434)( 25,433)( 26,432)( 27,457)( 28,456)( 29,468)( 30,467)( 31,466)
( 32,465)( 33,464)( 34,463)( 35,462)( 36,461)( 37,460)( 38,459)( 39,458)
( 40,444)( 41,443)( 42,455)( 43,454)( 44,453)( 45,452)( 46,451)( 47,450)
( 48,449)( 49,448)( 50,447)( 51,446)( 52,445)( 53,470)( 54,469)( 55,481)
( 56,480)( 57,479)( 58,478)( 59,477)( 60,476)( 61,475)( 62,474)( 63,473)
( 64,472)( 65,471)( 66,483)( 67,482)( 68,494)( 69,493)( 70,492)( 71,491)
( 72,490)( 73,489)( 74,488)( 75,487)( 76,486)( 77,485)( 78,484)( 79,509)
( 80,508)( 81,520)( 82,519)( 83,518)( 84,517)( 85,516)( 86,515)( 87,514)
( 88,513)( 89,512)( 90,511)( 91,510)( 92,496)( 93,495)( 94,507)( 95,506)
( 96,505)( 97,504)( 98,503)( 99,502)(100,501)(101,500)(102,499)(103,498)
(104,497)(105,548)(106,547)(107,559)(108,558)(109,557)(110,556)(111,555)
(112,554)(113,553)(114,552)(115,551)(116,550)(117,549)(118,561)(119,560)
(120,572)(121,571)(122,570)(123,569)(124,568)(125,567)(126,566)(127,565)
(128,564)(129,563)(130,562)(131,522)(132,521)(133,533)(134,532)(135,531)
(136,530)(137,529)(138,528)(139,527)(140,526)(141,525)(142,524)(143,523)
(144,535)(145,534)(146,546)(147,545)(148,544)(149,543)(150,542)(151,541)
(152,540)(153,539)(154,538)(155,537)(156,536)(157,600)(158,599)(159,611)
(160,610)(161,609)(162,608)(163,607)(164,606)(165,605)(166,604)(167,603)
(168,602)(169,601)(170,613)(171,612)(172,624)(173,623)(174,622)(175,621)
(176,620)(177,619)(178,618)(179,617)(180,616)(181,615)(182,614)(183,574)
(184,573)(185,585)(186,584)(187,583)(188,582)(189,581)(190,580)(191,579)
(192,578)(193,577)(194,576)(195,575)(196,587)(197,586)(198,598)(199,597)
(200,596)(201,595)(202,594)(203,593)(204,592)(205,591)(206,590)(207,589)
(208,588)(209,626)(210,625)(211,637)(212,636)(213,635)(214,634)(215,633)
(216,632)(217,631)(218,630)(219,629)(220,628)(221,627)(222,639)(223,638)
(224,650)(225,649)(226,648)(227,647)(228,646)(229,645)(230,644)(231,643)
(232,642)(233,641)(234,640)(235,665)(236,664)(237,676)(238,675)(239,674)
(240,673)(241,672)(242,671)(243,670)(244,669)(245,668)(246,667)(247,666)
(248,652)(249,651)(250,663)(251,662)(252,661)(253,660)(254,659)(255,658)
(256,657)(257,656)(258,655)(259,654)(260,653)(261,678)(262,677)(263,689)
(264,688)(265,687)(266,686)(267,685)(268,684)(269,683)(270,682)(271,681)
(272,680)(273,679)(274,691)(275,690)(276,702)(277,701)(278,700)(279,699)
(280,698)(281,697)(282,696)(283,695)(284,694)(285,693)(286,692)(287,717)
(288,716)(289,728)(290,727)(291,726)(292,725)(293,724)(294,723)(295,722)
(296,721)(297,720)(298,719)(299,718)(300,704)(301,703)(302,715)(303,714)
(304,713)(305,712)(306,711)(307,710)(308,709)(309,708)(310,707)(311,706)
(312,705)(313,756)(314,755)(315,767)(316,766)(317,765)(318,764)(319,763)
(320,762)(321,761)(322,760)(323,759)(324,758)(325,757)(326,769)(327,768)
(328,780)(329,779)(330,778)(331,777)(332,776)(333,775)(334,774)(335,773)
(336,772)(337,771)(338,770)(339,730)(340,729)(341,741)(342,740)(343,739)
(344,738)(345,737)(346,736)(347,735)(348,734)(349,733)(350,732)(351,731)
(352,743)(353,742)(354,754)(355,753)(356,752)(357,751)(358,750)(359,749)
(360,748)(361,747)(362,746)(363,745)(364,744)(365,808)(366,807)(367,819)
(368,818)(369,817)(370,816)(371,815)(372,814)(373,813)(374,812)(375,811)
(376,810)(377,809)(378,821)(379,820)(380,832)(381,831)(382,830)(383,829)
(384,828)(385,827)(386,826)(387,825)(388,824)(389,823)(390,822)(391,782)
(392,781)(393,793)(394,792)(395,791)(396,790)(397,789)(398,788)(399,787)
(400,786)(401,785)(402,784)(403,783)(404,795)(405,794)(406,806)(407,805)
(408,804)(409,803)(410,802)(411,801)(412,800)(413,799)(414,798)(415,797)
(416,796);
poly := sub<Sym(832)|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*s1*s2*s1*s2 >;

References : None.
to this polytope