Polytope of Type {102,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {102,4}*1632
if this polytope has a name.
Group : SmallGroup(1632,1200)
Rank : 3
Schlafli Type : {102,4}
Number of vertices, edges, etc : 204, 408, 8
Order of s0s1s2 : 102
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {51,4}*816, {102,4}*816b, {102,4}*816c
4-fold quotients : {51,4}*408, {102,2}*408
8-fold quotients : {51,2}*204
12-fold quotients : {34,2}*136
17-fold quotients : {6,4}*96
24-fold quotients : {17,2}*68
34-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
68-fold quotients : {3,4}*24, {6,2}*24
136-fold quotients : {3,2}*12
204-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 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);;
s1 := ( 1,481)( 2,484)( 3,483)( 4,482)( 5,477)( 6,480)( 7,479)( 8,478)
( 9,541)( 10,544)( 11,543)( 12,542)( 13,537)( 14,540)( 15,539)( 16,538)
( 17,533)( 18,536)( 19,535)( 20,534)( 21,529)( 22,532)( 23,531)( 24,530)
( 25,525)( 26,528)( 27,527)( 28,526)( 29,521)( 30,524)( 31,523)( 32,522)
( 33,517)( 34,520)( 35,519)( 36,518)( 37,513)( 38,516)( 39,515)( 40,514)
( 41,509)( 42,512)( 43,511)( 44,510)( 45,505)( 46,508)( 47,507)( 48,506)
( 49,501)( 50,504)( 51,503)( 52,502)( 53,497)( 54,500)( 55,499)( 56,498)
( 57,493)( 58,496)( 59,495)( 60,494)( 61,489)( 62,492)( 63,491)( 64,490)
( 65,485)( 66,488)( 67,487)( 68,486)( 69,413)( 70,416)( 71,415)( 72,414)
( 73,409)( 74,412)( 75,411)( 76,410)( 77,473)( 78,476)( 79,475)( 80,474)
( 81,469)( 82,472)( 83,471)( 84,470)( 85,465)( 86,468)( 87,467)( 88,466)
( 89,461)( 90,464)( 91,463)( 92,462)( 93,457)( 94,460)( 95,459)( 96,458)
( 97,453)( 98,456)( 99,455)(100,454)(101,449)(102,452)(103,451)(104,450)
(105,445)(106,448)(107,447)(108,446)(109,441)(110,444)(111,443)(112,442)
(113,437)(114,440)(115,439)(116,438)(117,433)(118,436)(119,435)(120,434)
(121,429)(122,432)(123,431)(124,430)(125,425)(126,428)(127,427)(128,426)
(129,421)(130,424)(131,423)(132,422)(133,417)(134,420)(135,419)(136,418)
(137,549)(138,552)(139,551)(140,550)(141,545)(142,548)(143,547)(144,546)
(145,609)(146,612)(147,611)(148,610)(149,605)(150,608)(151,607)(152,606)
(153,601)(154,604)(155,603)(156,602)(157,597)(158,600)(159,599)(160,598)
(161,593)(162,596)(163,595)(164,594)(165,589)(166,592)(167,591)(168,590)
(169,585)(170,588)(171,587)(172,586)(173,581)(174,584)(175,583)(176,582)
(177,577)(178,580)(179,579)(180,578)(181,573)(182,576)(183,575)(184,574)
(185,569)(186,572)(187,571)(188,570)(189,565)(190,568)(191,567)(192,566)
(193,561)(194,564)(195,563)(196,562)(197,557)(198,560)(199,559)(200,558)
(201,553)(202,556)(203,555)(204,554)(205,685)(206,688)(207,687)(208,686)
(209,681)(210,684)(211,683)(212,682)(213,745)(214,748)(215,747)(216,746)
(217,741)(218,744)(219,743)(220,742)(221,737)(222,740)(223,739)(224,738)
(225,733)(226,736)(227,735)(228,734)(229,729)(230,732)(231,731)(232,730)
(233,725)(234,728)(235,727)(236,726)(237,721)(238,724)(239,723)(240,722)
(241,717)(242,720)(243,719)(244,718)(245,713)(246,716)(247,715)(248,714)
(249,709)(250,712)(251,711)(252,710)(253,705)(254,708)(255,707)(256,706)
(257,701)(258,704)(259,703)(260,702)(261,697)(262,700)(263,699)(264,698)
(265,693)(266,696)(267,695)(268,694)(269,689)(270,692)(271,691)(272,690)
(273,617)(274,620)(275,619)(276,618)(277,613)(278,616)(279,615)(280,614)
(281,677)(282,680)(283,679)(284,678)(285,673)(286,676)(287,675)(288,674)
(289,669)(290,672)(291,671)(292,670)(293,665)(294,668)(295,667)(296,666)
(297,661)(298,664)(299,663)(300,662)(301,657)(302,660)(303,659)(304,658)
(305,653)(306,656)(307,655)(308,654)(309,649)(310,652)(311,651)(312,650)
(313,645)(314,648)(315,647)(316,646)(317,641)(318,644)(319,643)(320,642)
(321,637)(322,640)(323,639)(324,638)(325,633)(326,636)(327,635)(328,634)
(329,629)(330,632)(331,631)(332,630)(333,625)(334,628)(335,627)(336,626)
(337,621)(338,624)(339,623)(340,622)(341,753)(342,756)(343,755)(344,754)
(345,749)(346,752)(347,751)(348,750)(349,813)(350,816)(351,815)(352,814)
(353,809)(354,812)(355,811)(356,810)(357,805)(358,808)(359,807)(360,806)
(361,801)(362,804)(363,803)(364,802)(365,797)(366,800)(367,799)(368,798)
(369,793)(370,796)(371,795)(372,794)(373,789)(374,792)(375,791)(376,790)
(377,785)(378,788)(379,787)(380,786)(381,781)(382,784)(383,783)(384,782)
(385,777)(386,780)(387,779)(388,778)(389,773)(390,776)(391,775)(392,774)
(393,769)(394,772)(395,771)(396,770)(397,765)(398,768)(399,767)(400,766)
(401,761)(402,764)(403,763)(404,762)(405,757)(406,760)(407,759)(408,758);;
s2 := ( 1,206)( 2,205)( 3,208)( 4,207)( 5,210)( 6,209)( 7,212)( 8,211)
( 9,214)( 10,213)( 11,216)( 12,215)( 13,218)( 14,217)( 15,220)( 16,219)
( 17,222)( 18,221)( 19,224)( 20,223)( 21,226)( 22,225)( 23,228)( 24,227)
( 25,230)( 26,229)( 27,232)( 28,231)( 29,234)( 30,233)( 31,236)( 32,235)
( 33,238)( 34,237)( 35,240)( 36,239)( 37,242)( 38,241)( 39,244)( 40,243)
( 41,246)( 42,245)( 43,248)( 44,247)( 45,250)( 46,249)( 47,252)( 48,251)
( 49,254)( 50,253)( 51,256)( 52,255)( 53,258)( 54,257)( 55,260)( 56,259)
( 57,262)( 58,261)( 59,264)( 60,263)( 61,266)( 62,265)( 63,268)( 64,267)
( 65,270)( 66,269)( 67,272)( 68,271)( 69,274)( 70,273)( 71,276)( 72,275)
( 73,278)( 74,277)( 75,280)( 76,279)( 77,282)( 78,281)( 79,284)( 80,283)
( 81,286)( 82,285)( 83,288)( 84,287)( 85,290)( 86,289)( 87,292)( 88,291)
( 89,294)( 90,293)( 91,296)( 92,295)( 93,298)( 94,297)( 95,300)( 96,299)
( 97,302)( 98,301)( 99,304)(100,303)(101,306)(102,305)(103,308)(104,307)
(105,310)(106,309)(107,312)(108,311)(109,314)(110,313)(111,316)(112,315)
(113,318)(114,317)(115,320)(116,319)(117,322)(118,321)(119,324)(120,323)
(121,326)(122,325)(123,328)(124,327)(125,330)(126,329)(127,332)(128,331)
(129,334)(130,333)(131,336)(132,335)(133,338)(134,337)(135,340)(136,339)
(137,342)(138,341)(139,344)(140,343)(141,346)(142,345)(143,348)(144,347)
(145,350)(146,349)(147,352)(148,351)(149,354)(150,353)(151,356)(152,355)
(153,358)(154,357)(155,360)(156,359)(157,362)(158,361)(159,364)(160,363)
(161,366)(162,365)(163,368)(164,367)(165,370)(166,369)(167,372)(168,371)
(169,374)(170,373)(171,376)(172,375)(173,378)(174,377)(175,380)(176,379)
(177,382)(178,381)(179,384)(180,383)(181,386)(182,385)(183,388)(184,387)
(185,390)(186,389)(187,392)(188,391)(189,394)(190,393)(191,396)(192,395)
(193,398)(194,397)(195,400)(196,399)(197,402)(198,401)(199,404)(200,403)
(201,406)(202,405)(203,408)(204,407)(409,614)(410,613)(411,616)(412,615)
(413,618)(414,617)(415,620)(416,619)(417,622)(418,621)(419,624)(420,623)
(421,626)(422,625)(423,628)(424,627)(425,630)(426,629)(427,632)(428,631)
(429,634)(430,633)(431,636)(432,635)(433,638)(434,637)(435,640)(436,639)
(437,642)(438,641)(439,644)(440,643)(441,646)(442,645)(443,648)(444,647)
(445,650)(446,649)(447,652)(448,651)(449,654)(450,653)(451,656)(452,655)
(453,658)(454,657)(455,660)(456,659)(457,662)(458,661)(459,664)(460,663)
(461,666)(462,665)(463,668)(464,667)(465,670)(466,669)(467,672)(468,671)
(469,674)(470,673)(471,676)(472,675)(473,678)(474,677)(475,680)(476,679)
(477,682)(478,681)(479,684)(480,683)(481,686)(482,685)(483,688)(484,687)
(485,690)(486,689)(487,692)(488,691)(489,694)(490,693)(491,696)(492,695)
(493,698)(494,697)(495,700)(496,699)(497,702)(498,701)(499,704)(500,703)
(501,706)(502,705)(503,708)(504,707)(505,710)(506,709)(507,712)(508,711)
(509,714)(510,713)(511,716)(512,715)(513,718)(514,717)(515,720)(516,719)
(517,722)(518,721)(519,724)(520,723)(521,726)(522,725)(523,728)(524,727)
(525,730)(526,729)(527,732)(528,731)(529,734)(530,733)(531,736)(532,735)
(533,738)(534,737)(535,740)(536,739)(537,742)(538,741)(539,744)(540,743)
(541,746)(542,745)(543,748)(544,747)(545,750)(546,749)(547,752)(548,751)
(549,754)(550,753)(551,756)(552,755)(553,758)(554,757)(555,760)(556,759)
(557,762)(558,761)(559,764)(560,763)(561,766)(562,765)(563,768)(564,767)
(565,770)(566,769)(567,772)(568,771)(569,774)(570,773)(571,776)(572,775)
(573,778)(574,777)(575,780)(576,779)(577,782)(578,781)(579,784)(580,783)
(581,786)(582,785)(583,788)(584,787)(585,790)(586,789)(587,792)(588,791)
(589,794)(590,793)(591,796)(592,795)(593,798)(594,797)(595,800)(596,799)
(597,802)(598,801)(599,804)(600,803)(601,806)(602,805)(603,808)(604,807)
(605,810)(606,809)(607,812)(608,811)(609,814)(610,813)(611,816)(612,815);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(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);
s1 := Sym(816)!( 1,481)( 2,484)( 3,483)( 4,482)( 5,477)( 6,480)( 7,479)
( 8,478)( 9,541)( 10,544)( 11,543)( 12,542)( 13,537)( 14,540)( 15,539)
( 16,538)( 17,533)( 18,536)( 19,535)( 20,534)( 21,529)( 22,532)( 23,531)
( 24,530)( 25,525)( 26,528)( 27,527)( 28,526)( 29,521)( 30,524)( 31,523)
( 32,522)( 33,517)( 34,520)( 35,519)( 36,518)( 37,513)( 38,516)( 39,515)
( 40,514)( 41,509)( 42,512)( 43,511)( 44,510)( 45,505)( 46,508)( 47,507)
( 48,506)( 49,501)( 50,504)( 51,503)( 52,502)( 53,497)( 54,500)( 55,499)
( 56,498)( 57,493)( 58,496)( 59,495)( 60,494)( 61,489)( 62,492)( 63,491)
( 64,490)( 65,485)( 66,488)( 67,487)( 68,486)( 69,413)( 70,416)( 71,415)
( 72,414)( 73,409)( 74,412)( 75,411)( 76,410)( 77,473)( 78,476)( 79,475)
( 80,474)( 81,469)( 82,472)( 83,471)( 84,470)( 85,465)( 86,468)( 87,467)
( 88,466)( 89,461)( 90,464)( 91,463)( 92,462)( 93,457)( 94,460)( 95,459)
( 96,458)( 97,453)( 98,456)( 99,455)(100,454)(101,449)(102,452)(103,451)
(104,450)(105,445)(106,448)(107,447)(108,446)(109,441)(110,444)(111,443)
(112,442)(113,437)(114,440)(115,439)(116,438)(117,433)(118,436)(119,435)
(120,434)(121,429)(122,432)(123,431)(124,430)(125,425)(126,428)(127,427)
(128,426)(129,421)(130,424)(131,423)(132,422)(133,417)(134,420)(135,419)
(136,418)(137,549)(138,552)(139,551)(140,550)(141,545)(142,548)(143,547)
(144,546)(145,609)(146,612)(147,611)(148,610)(149,605)(150,608)(151,607)
(152,606)(153,601)(154,604)(155,603)(156,602)(157,597)(158,600)(159,599)
(160,598)(161,593)(162,596)(163,595)(164,594)(165,589)(166,592)(167,591)
(168,590)(169,585)(170,588)(171,587)(172,586)(173,581)(174,584)(175,583)
(176,582)(177,577)(178,580)(179,579)(180,578)(181,573)(182,576)(183,575)
(184,574)(185,569)(186,572)(187,571)(188,570)(189,565)(190,568)(191,567)
(192,566)(193,561)(194,564)(195,563)(196,562)(197,557)(198,560)(199,559)
(200,558)(201,553)(202,556)(203,555)(204,554)(205,685)(206,688)(207,687)
(208,686)(209,681)(210,684)(211,683)(212,682)(213,745)(214,748)(215,747)
(216,746)(217,741)(218,744)(219,743)(220,742)(221,737)(222,740)(223,739)
(224,738)(225,733)(226,736)(227,735)(228,734)(229,729)(230,732)(231,731)
(232,730)(233,725)(234,728)(235,727)(236,726)(237,721)(238,724)(239,723)
(240,722)(241,717)(242,720)(243,719)(244,718)(245,713)(246,716)(247,715)
(248,714)(249,709)(250,712)(251,711)(252,710)(253,705)(254,708)(255,707)
(256,706)(257,701)(258,704)(259,703)(260,702)(261,697)(262,700)(263,699)
(264,698)(265,693)(266,696)(267,695)(268,694)(269,689)(270,692)(271,691)
(272,690)(273,617)(274,620)(275,619)(276,618)(277,613)(278,616)(279,615)
(280,614)(281,677)(282,680)(283,679)(284,678)(285,673)(286,676)(287,675)
(288,674)(289,669)(290,672)(291,671)(292,670)(293,665)(294,668)(295,667)
(296,666)(297,661)(298,664)(299,663)(300,662)(301,657)(302,660)(303,659)
(304,658)(305,653)(306,656)(307,655)(308,654)(309,649)(310,652)(311,651)
(312,650)(313,645)(314,648)(315,647)(316,646)(317,641)(318,644)(319,643)
(320,642)(321,637)(322,640)(323,639)(324,638)(325,633)(326,636)(327,635)
(328,634)(329,629)(330,632)(331,631)(332,630)(333,625)(334,628)(335,627)
(336,626)(337,621)(338,624)(339,623)(340,622)(341,753)(342,756)(343,755)
(344,754)(345,749)(346,752)(347,751)(348,750)(349,813)(350,816)(351,815)
(352,814)(353,809)(354,812)(355,811)(356,810)(357,805)(358,808)(359,807)
(360,806)(361,801)(362,804)(363,803)(364,802)(365,797)(366,800)(367,799)
(368,798)(369,793)(370,796)(371,795)(372,794)(373,789)(374,792)(375,791)
(376,790)(377,785)(378,788)(379,787)(380,786)(381,781)(382,784)(383,783)
(384,782)(385,777)(386,780)(387,779)(388,778)(389,773)(390,776)(391,775)
(392,774)(393,769)(394,772)(395,771)(396,770)(397,765)(398,768)(399,767)
(400,766)(401,761)(402,764)(403,763)(404,762)(405,757)(406,760)(407,759)
(408,758);
s2 := Sym(816)!( 1,206)( 2,205)( 3,208)( 4,207)( 5,210)( 6,209)( 7,212)
( 8,211)( 9,214)( 10,213)( 11,216)( 12,215)( 13,218)( 14,217)( 15,220)
( 16,219)( 17,222)( 18,221)( 19,224)( 20,223)( 21,226)( 22,225)( 23,228)
( 24,227)( 25,230)( 26,229)( 27,232)( 28,231)( 29,234)( 30,233)( 31,236)
( 32,235)( 33,238)( 34,237)( 35,240)( 36,239)( 37,242)( 38,241)( 39,244)
( 40,243)( 41,246)( 42,245)( 43,248)( 44,247)( 45,250)( 46,249)( 47,252)
( 48,251)( 49,254)( 50,253)( 51,256)( 52,255)( 53,258)( 54,257)( 55,260)
( 56,259)( 57,262)( 58,261)( 59,264)( 60,263)( 61,266)( 62,265)( 63,268)
( 64,267)( 65,270)( 66,269)( 67,272)( 68,271)( 69,274)( 70,273)( 71,276)
( 72,275)( 73,278)( 74,277)( 75,280)( 76,279)( 77,282)( 78,281)( 79,284)
( 80,283)( 81,286)( 82,285)( 83,288)( 84,287)( 85,290)( 86,289)( 87,292)
( 88,291)( 89,294)( 90,293)( 91,296)( 92,295)( 93,298)( 94,297)( 95,300)
( 96,299)( 97,302)( 98,301)( 99,304)(100,303)(101,306)(102,305)(103,308)
(104,307)(105,310)(106,309)(107,312)(108,311)(109,314)(110,313)(111,316)
(112,315)(113,318)(114,317)(115,320)(116,319)(117,322)(118,321)(119,324)
(120,323)(121,326)(122,325)(123,328)(124,327)(125,330)(126,329)(127,332)
(128,331)(129,334)(130,333)(131,336)(132,335)(133,338)(134,337)(135,340)
(136,339)(137,342)(138,341)(139,344)(140,343)(141,346)(142,345)(143,348)
(144,347)(145,350)(146,349)(147,352)(148,351)(149,354)(150,353)(151,356)
(152,355)(153,358)(154,357)(155,360)(156,359)(157,362)(158,361)(159,364)
(160,363)(161,366)(162,365)(163,368)(164,367)(165,370)(166,369)(167,372)
(168,371)(169,374)(170,373)(171,376)(172,375)(173,378)(174,377)(175,380)
(176,379)(177,382)(178,381)(179,384)(180,383)(181,386)(182,385)(183,388)
(184,387)(185,390)(186,389)(187,392)(188,391)(189,394)(190,393)(191,396)
(192,395)(193,398)(194,397)(195,400)(196,399)(197,402)(198,401)(199,404)
(200,403)(201,406)(202,405)(203,408)(204,407)(409,614)(410,613)(411,616)
(412,615)(413,618)(414,617)(415,620)(416,619)(417,622)(418,621)(419,624)
(420,623)(421,626)(422,625)(423,628)(424,627)(425,630)(426,629)(427,632)
(428,631)(429,634)(430,633)(431,636)(432,635)(433,638)(434,637)(435,640)
(436,639)(437,642)(438,641)(439,644)(440,643)(441,646)(442,645)(443,648)
(444,647)(445,650)(446,649)(447,652)(448,651)(449,654)(450,653)(451,656)
(452,655)(453,658)(454,657)(455,660)(456,659)(457,662)(458,661)(459,664)
(460,663)(461,666)(462,665)(463,668)(464,667)(465,670)(466,669)(467,672)
(468,671)(469,674)(470,673)(471,676)(472,675)(473,678)(474,677)(475,680)
(476,679)(477,682)(478,681)(479,684)(480,683)(481,686)(482,685)(483,688)
(484,687)(485,690)(486,689)(487,692)(488,691)(489,694)(490,693)(491,696)
(492,695)(493,698)(494,697)(495,700)(496,699)(497,702)(498,701)(499,704)
(500,703)(501,706)(502,705)(503,708)(504,707)(505,710)(506,709)(507,712)
(508,711)(509,714)(510,713)(511,716)(512,715)(513,718)(514,717)(515,720)
(516,719)(517,722)(518,721)(519,724)(520,723)(521,726)(522,725)(523,728)
(524,727)(525,730)(526,729)(527,732)(528,731)(529,734)(530,733)(531,736)
(532,735)(533,738)(534,737)(535,740)(536,739)(537,742)(538,741)(539,744)
(540,743)(541,746)(542,745)(543,748)(544,747)(545,750)(546,749)(547,752)
(548,751)(549,754)(550,753)(551,756)(552,755)(553,758)(554,757)(555,760)
(556,759)(557,762)(558,761)(559,764)(560,763)(561,766)(562,765)(563,768)
(564,767)(565,770)(566,769)(567,772)(568,771)(569,774)(570,773)(571,776)
(572,775)(573,778)(574,777)(575,780)(576,779)(577,782)(578,781)(579,784)
(580,783)(581,786)(582,785)(583,788)(584,787)(585,790)(586,789)(587,792)
(588,791)(589,794)(590,793)(591,796)(592,795)(593,798)(594,797)(595,800)
(596,799)(597,802)(598,801)(599,804)(600,803)(601,806)(602,805)(603,808)
(604,807)(605,810)(606,809)(607,812)(608,811)(609,814)(610,813)(611,816)
(612,815);
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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