Polytope of Type {4,102}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,102}*1632
if this polytope has a name.
Group : SmallGroup(1632,1200)
Rank : 3
Schlafli Type : {4,102}
Number of vertices, edges, etc : 8, 408, 204
Order of s₀s₁s₂ : 102
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,51}*816, {4,102}*816b, {4,102}*816c
   4-fold quotients : {4,51}*408, {2,102}*408
   8-fold quotients : {2,51}*204
   12-fold quotients : {2,34}*136
   17-fold quotients : {4,6}*96
   24-fold quotients : {2,17}*68
   34-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   68-fold quotients : {4,3}*24, {2,6}*24
   136-fold quotients : {2,3}*12
   204-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope