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Polytope of Type {2,8,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,6}*1728b
if this polytope has a name.
Group : SmallGroup(1728,46634)
Rank : 4
Schlafli Type : {2,8,6}
Number of vertices, edges, etc : 2, 72, 216, 54
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   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 : {2,4,6}*864b
   3-fold quotients : {2,8,6}*576
   6-fold quotients : {2,4,6}*288
   9-fold quotients : {2,8,6}*192
   12-fold quotients : {2,4,6}*144
   18-fold quotients : {2,4,6}*96a
   27-fold quotients : {2,8,2}*64
   36-fold quotients : {2,2,6}*48
   54-fold quotients : {2,4,2}*32
   72-fold quotients : {2,2,3}*24
   108-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  3,219)(  4,220)(  5,221)(  6,240)(  7,241)(  8,242)(  9,234)( 10,235)
( 11,236)( 12,237)( 13,238)( 14,239)( 15,231)( 16,232)( 17,233)( 18,225)
( 19,226)( 20,227)( 21,228)( 22,229)( 23,230)( 24,222)( 25,223)( 26,224)
( 27,243)( 28,244)( 29,245)( 30,246)( 31,247)( 32,248)( 33,267)( 34,268)
( 35,269)( 36,261)( 37,262)( 38,263)( 39,264)( 40,265)( 41,266)( 42,258)
( 43,259)( 44,260)( 45,252)( 46,253)( 47,254)( 48,255)( 49,256)( 50,257)
( 51,249)( 52,250)( 53,251)( 54,270)( 55,271)( 56,272)( 57,300)( 58,301)
( 59,302)( 60,321)( 61,322)( 62,323)( 63,315)( 64,316)( 65,317)( 66,318)
( 67,319)( 68,320)( 69,312)( 70,313)( 71,314)( 72,306)( 73,307)( 74,308)
( 75,309)( 76,310)( 77,311)( 78,303)( 79,304)( 80,305)( 81,324)( 82,325)
( 83,326)( 84,273)( 85,274)( 86,275)( 87,294)( 88,295)( 89,296)( 90,288)
( 91,289)( 92,290)( 93,291)( 94,292)( 95,293)( 96,285)( 97,286)( 98,287)
( 99,279)(100,280)(101,281)(102,282)(103,283)(104,284)(105,276)(106,277)
(107,278)(108,297)(109,298)(110,299)(111,381)(112,382)(113,383)(114,402)
(115,403)(116,404)(117,396)(118,397)(119,398)(120,399)(121,400)(122,401)
(123,393)(124,394)(125,395)(126,387)(127,388)(128,389)(129,390)(130,391)
(131,392)(132,384)(133,385)(134,386)(135,405)(136,406)(137,407)(138,408)
(139,409)(140,410)(141,429)(142,430)(143,431)(144,423)(145,424)(146,425)
(147,426)(148,427)(149,428)(150,420)(151,421)(152,422)(153,414)(154,415)
(155,416)(156,417)(157,418)(158,419)(159,411)(160,412)(161,413)(162,432)
(163,433)(164,434)(165,327)(166,328)(167,329)(168,348)(169,349)(170,350)
(171,342)(172,343)(173,344)(174,345)(175,346)(176,347)(177,339)(178,340)
(179,341)(180,333)(181,334)(182,335)(183,336)(184,337)(185,338)(186,330)
(187,331)(188,332)(189,351)(190,352)(191,353)(192,354)(193,355)(194,356)
(195,375)(196,376)(197,377)(198,369)(199,370)(200,371)(201,372)(202,373)
(203,374)(204,366)(205,367)(206,368)(207,360)(208,361)(209,362)(210,363)
(211,364)(212,365)(213,357)(214,358)(215,359)(216,378)(217,379)(218,380)
(435,651)(436,652)(437,653)(438,672)(439,673)(440,674)(441,666)(442,667)
(443,668)(444,669)(445,670)(446,671)(447,663)(448,664)(449,665)(450,657)
(451,658)(452,659)(453,660)(454,661)(455,662)(456,654)(457,655)(458,656)
(459,675)(460,676)(461,677)(462,678)(463,679)(464,680)(465,699)(466,700)
(467,701)(468,693)(469,694)(470,695)(471,696)(472,697)(473,698)(474,690)
(475,691)(476,692)(477,684)(478,685)(479,686)(480,687)(481,688)(482,689)
(483,681)(484,682)(485,683)(486,702)(487,703)(488,704)(489,732)(490,733)
(491,734)(492,753)(493,754)(494,755)(495,747)(496,748)(497,749)(498,750)
(499,751)(500,752)(501,744)(502,745)(503,746)(504,738)(505,739)(506,740)
(507,741)(508,742)(509,743)(510,735)(511,736)(512,737)(513,756)(514,757)
(515,758)(516,705)(517,706)(518,707)(519,726)(520,727)(521,728)(522,720)
(523,721)(524,722)(525,723)(526,724)(527,725)(528,717)(529,718)(530,719)
(531,711)(532,712)(533,713)(534,714)(535,715)(536,716)(537,708)(538,709)
(539,710)(540,729)(541,730)(542,731)(543,813)(544,814)(545,815)(546,834)
(547,835)(548,836)(549,828)(550,829)(551,830)(552,831)(553,832)(554,833)
(555,825)(556,826)(557,827)(558,819)(559,820)(560,821)(561,822)(562,823)
(563,824)(564,816)(565,817)(566,818)(567,837)(568,838)(569,839)(570,840)
(571,841)(572,842)(573,861)(574,862)(575,863)(576,855)(577,856)(578,857)
(579,858)(580,859)(581,860)(582,852)(583,853)(584,854)(585,846)(586,847)
(587,848)(588,849)(589,850)(590,851)(591,843)(592,844)(593,845)(594,864)
(595,865)(596,866)(597,759)(598,760)(599,761)(600,780)(601,781)(602,782)
(603,774)(604,775)(605,776)(606,777)(607,778)(608,779)(609,771)(610,772)
(611,773)(612,765)(613,766)(614,767)(615,768)(616,769)(617,770)(618,762)
(619,763)(620,764)(621,783)(622,784)(623,785)(624,786)(625,787)(626,788)
(627,807)(628,808)(629,809)(630,801)(631,802)(632,803)(633,804)(634,805)
(635,806)(636,798)(637,799)(638,800)(639,792)(640,793)(641,794)(642,795)
(643,796)(644,797)(645,789)(646,790)(647,791)(648,810)(649,811)(650,812);;
s2 := (  3,543)(  4,545)(  5,544)(  6,546)(  7,548)(  8,547)(  9,549)( 10,551)
( 11,550)( 12,567)( 13,569)( 14,568)( 15,561)( 16,563)( 17,562)( 18,564)
( 19,566)( 20,565)( 21,555)( 22,557)( 23,556)( 24,558)( 25,560)( 26,559)
( 27,552)( 28,554)( 29,553)( 30,570)( 31,572)( 32,571)( 33,573)( 34,575)
( 35,574)( 36,576)( 37,578)( 38,577)( 39,594)( 40,596)( 41,595)( 42,588)
( 43,590)( 44,589)( 45,591)( 46,593)( 47,592)( 48,582)( 49,584)( 50,583)
( 51,585)( 52,587)( 53,586)( 54,579)( 55,581)( 56,580)( 57,624)( 58,626)
( 59,625)( 60,627)( 61,629)( 62,628)( 63,630)( 64,632)( 65,631)( 66,648)
( 67,650)( 68,649)( 69,642)( 70,644)( 71,643)( 72,645)( 73,647)( 74,646)
( 75,636)( 76,638)( 77,637)( 78,639)( 79,641)( 80,640)( 81,633)( 82,635)
( 83,634)( 84,597)( 85,599)( 86,598)( 87,600)( 88,602)( 89,601)( 90,603)
( 91,605)( 92,604)( 93,621)( 94,623)( 95,622)( 96,615)( 97,617)( 98,616)
( 99,618)(100,620)(101,619)(102,609)(103,611)(104,610)(105,612)(106,614)
(107,613)(108,606)(109,608)(110,607)(111,462)(112,464)(113,463)(114,465)
(115,467)(116,466)(117,468)(118,470)(119,469)(120,486)(121,488)(122,487)
(123,480)(124,482)(125,481)(126,483)(127,485)(128,484)(129,474)(130,476)
(131,475)(132,477)(133,479)(134,478)(135,471)(136,473)(137,472)(138,435)
(139,437)(140,436)(141,438)(142,440)(143,439)(144,441)(145,443)(146,442)
(147,459)(148,461)(149,460)(150,453)(151,455)(152,454)(153,456)(154,458)
(155,457)(156,447)(157,449)(158,448)(159,450)(160,452)(161,451)(162,444)
(163,446)(164,445)(165,489)(166,491)(167,490)(168,492)(169,494)(170,493)
(171,495)(172,497)(173,496)(174,513)(175,515)(176,514)(177,507)(178,509)
(179,508)(180,510)(181,512)(182,511)(183,501)(184,503)(185,502)(186,504)
(187,506)(188,505)(189,498)(190,500)(191,499)(192,516)(193,518)(194,517)
(195,519)(196,521)(197,520)(198,522)(199,524)(200,523)(201,540)(202,542)
(203,541)(204,534)(205,536)(206,535)(207,537)(208,539)(209,538)(210,528)
(211,530)(212,529)(213,531)(214,533)(215,532)(216,525)(217,527)(218,526)
(219,786)(220,788)(221,787)(222,789)(223,791)(224,790)(225,792)(226,794)
(227,793)(228,810)(229,812)(230,811)(231,804)(232,806)(233,805)(234,807)
(235,809)(236,808)(237,798)(238,800)(239,799)(240,801)(241,803)(242,802)
(243,795)(244,797)(245,796)(246,759)(247,761)(248,760)(249,762)(250,764)
(251,763)(252,765)(253,767)(254,766)(255,783)(256,785)(257,784)(258,777)
(259,779)(260,778)(261,780)(262,782)(263,781)(264,771)(265,773)(266,772)
(267,774)(268,776)(269,775)(270,768)(271,770)(272,769)(273,813)(274,815)
(275,814)(276,816)(277,818)(278,817)(279,819)(280,821)(281,820)(282,837)
(283,839)(284,838)(285,831)(286,833)(287,832)(288,834)(289,836)(290,835)
(291,825)(292,827)(293,826)(294,828)(295,830)(296,829)(297,822)(298,824)
(299,823)(300,840)(301,842)(302,841)(303,843)(304,845)(305,844)(306,846)
(307,848)(308,847)(309,864)(310,866)(311,865)(312,858)(313,860)(314,859)
(315,861)(316,863)(317,862)(318,852)(319,854)(320,853)(321,855)(322,857)
(323,856)(324,849)(325,851)(326,850)(327,651)(328,653)(329,652)(330,654)
(331,656)(332,655)(333,657)(334,659)(335,658)(336,675)(337,677)(338,676)
(339,669)(340,671)(341,670)(342,672)(343,674)(344,673)(345,663)(346,665)
(347,664)(348,666)(349,668)(350,667)(351,660)(352,662)(353,661)(354,678)
(355,680)(356,679)(357,681)(358,683)(359,682)(360,684)(361,686)(362,685)
(363,702)(364,704)(365,703)(366,696)(367,698)(368,697)(369,699)(370,701)
(371,700)(372,690)(373,692)(374,691)(375,693)(376,695)(377,694)(378,687)
(379,689)(380,688)(381,732)(382,734)(383,733)(384,735)(385,737)(386,736)
(387,738)(388,740)(389,739)(390,756)(391,758)(392,757)(393,750)(394,752)
(395,751)(396,753)(397,755)(398,754)(399,744)(400,746)(401,745)(402,747)
(403,749)(404,748)(405,741)(406,743)(407,742)(408,705)(409,707)(410,706)
(411,708)(412,710)(413,709)(414,711)(415,713)(416,712)(417,729)(418,731)
(419,730)(420,723)(421,725)(422,724)(423,726)(424,728)(425,727)(426,717)
(427,719)(428,718)(429,720)(430,722)(431,721)(432,714)(433,716)(434,715);;
s3 := (  3,502)(  4,501)(  5,503)(  6,499)(  7,498)(  8,500)(  9,505)( 10,504)
( 11,506)( 12,493)( 13,492)( 14,494)( 15,490)( 16,489)( 17,491)( 18,496)
( 19,495)( 20,497)( 21,511)( 22,510)( 23,512)( 24,508)( 25,507)( 26,509)
( 27,514)( 28,513)( 29,515)( 30,529)( 31,528)( 32,530)( 33,526)( 34,525)
( 35,527)( 36,532)( 37,531)( 38,533)( 39,520)( 40,519)( 41,521)( 42,517)
( 43,516)( 44,518)( 45,523)( 46,522)( 47,524)( 48,538)( 49,537)( 50,539)
( 51,535)( 52,534)( 53,536)( 54,541)( 55,540)( 56,542)( 57,475)( 58,474)
( 59,476)( 60,472)( 61,471)( 62,473)( 63,478)( 64,477)( 65,479)( 66,466)
( 67,465)( 68,467)( 69,463)( 70,462)( 71,464)( 72,469)( 73,468)( 74,470)
( 75,484)( 76,483)( 77,485)( 78,481)( 79,480)( 80,482)( 81,487)( 82,486)
( 83,488)( 84,448)( 85,447)( 86,449)( 87,445)( 88,444)( 89,446)( 90,451)
( 91,450)( 92,452)( 93,439)( 94,438)( 95,440)( 96,436)( 97,435)( 98,437)
( 99,442)(100,441)(101,443)(102,457)(103,456)(104,458)(105,454)(106,453)
(107,455)(108,460)(109,459)(110,461)(111,637)(112,636)(113,638)(114,634)
(115,633)(116,635)(117,640)(118,639)(119,641)(120,628)(121,627)(122,629)
(123,625)(124,624)(125,626)(126,631)(127,630)(128,632)(129,646)(130,645)
(131,647)(132,643)(133,642)(134,644)(135,649)(136,648)(137,650)(138,610)
(139,609)(140,611)(141,607)(142,606)(143,608)(144,613)(145,612)(146,614)
(147,601)(148,600)(149,602)(150,598)(151,597)(152,599)(153,604)(154,603)
(155,605)(156,619)(157,618)(158,620)(159,616)(160,615)(161,617)(162,622)
(163,621)(164,623)(165,556)(166,555)(167,557)(168,553)(169,552)(170,554)
(171,559)(172,558)(173,560)(174,547)(175,546)(176,548)(177,544)(178,543)
(179,545)(180,550)(181,549)(182,551)(183,565)(184,564)(185,566)(186,562)
(187,561)(188,563)(189,568)(190,567)(191,569)(192,583)(193,582)(194,584)
(195,580)(196,579)(197,581)(198,586)(199,585)(200,587)(201,574)(202,573)
(203,575)(204,571)(205,570)(206,572)(207,577)(208,576)(209,578)(210,592)
(211,591)(212,593)(213,589)(214,588)(215,590)(216,595)(217,594)(218,596)
(219,745)(220,744)(221,746)(222,742)(223,741)(224,743)(225,748)(226,747)
(227,749)(228,736)(229,735)(230,737)(231,733)(232,732)(233,734)(234,739)
(235,738)(236,740)(237,754)(238,753)(239,755)(240,751)(241,750)(242,752)
(243,757)(244,756)(245,758)(246,718)(247,717)(248,719)(249,715)(250,714)
(251,716)(252,721)(253,720)(254,722)(255,709)(256,708)(257,710)(258,706)
(259,705)(260,707)(261,712)(262,711)(263,713)(264,727)(265,726)(266,728)
(267,724)(268,723)(269,725)(270,730)(271,729)(272,731)(273,664)(274,663)
(275,665)(276,661)(277,660)(278,662)(279,667)(280,666)(281,668)(282,655)
(283,654)(284,656)(285,652)(286,651)(287,653)(288,658)(289,657)(290,659)
(291,673)(292,672)(293,674)(294,670)(295,669)(296,671)(297,676)(298,675)
(299,677)(300,691)(301,690)(302,692)(303,688)(304,687)(305,689)(306,694)
(307,693)(308,695)(309,682)(310,681)(311,683)(312,679)(313,678)(314,680)
(315,685)(316,684)(317,686)(318,700)(319,699)(320,701)(321,697)(322,696)
(323,698)(324,703)(325,702)(326,704)(327,826)(328,825)(329,827)(330,823)
(331,822)(332,824)(333,829)(334,828)(335,830)(336,817)(337,816)(338,818)
(339,814)(340,813)(341,815)(342,820)(343,819)(344,821)(345,835)(346,834)
(347,836)(348,832)(349,831)(350,833)(351,838)(352,837)(353,839)(354,853)
(355,852)(356,854)(357,850)(358,849)(359,851)(360,856)(361,855)(362,857)
(363,844)(364,843)(365,845)(366,841)(367,840)(368,842)(369,847)(370,846)
(371,848)(372,862)(373,861)(374,863)(375,859)(376,858)(377,860)(378,865)
(379,864)(380,866)(381,799)(382,798)(383,800)(384,796)(385,795)(386,797)
(387,802)(388,801)(389,803)(390,790)(391,789)(392,791)(393,787)(394,786)
(395,788)(396,793)(397,792)(398,794)(399,808)(400,807)(401,809)(402,805)
(403,804)(404,806)(405,811)(406,810)(407,812)(408,772)(409,771)(410,773)
(411,769)(412,768)(413,770)(414,775)(415,774)(416,776)(417,763)(418,762)
(419,764)(420,760)(421,759)(422,761)(423,766)(424,765)(425,767)(426,781)
(427,780)(428,782)(429,778)(430,777)(431,779)(432,784)(433,783)(434,785);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s2*s3*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(866)!(1,2);
s1 := Sym(866)!(  3,219)(  4,220)(  5,221)(  6,240)(  7,241)(  8,242)(  9,234)
( 10,235)( 11,236)( 12,237)( 13,238)( 14,239)( 15,231)( 16,232)( 17,233)
( 18,225)( 19,226)( 20,227)( 21,228)( 22,229)( 23,230)( 24,222)( 25,223)
( 26,224)( 27,243)( 28,244)( 29,245)( 30,246)( 31,247)( 32,248)( 33,267)
( 34,268)( 35,269)( 36,261)( 37,262)( 38,263)( 39,264)( 40,265)( 41,266)
( 42,258)( 43,259)( 44,260)( 45,252)( 46,253)( 47,254)( 48,255)( 49,256)
( 50,257)( 51,249)( 52,250)( 53,251)( 54,270)( 55,271)( 56,272)( 57,300)
( 58,301)( 59,302)( 60,321)( 61,322)( 62,323)( 63,315)( 64,316)( 65,317)
( 66,318)( 67,319)( 68,320)( 69,312)( 70,313)( 71,314)( 72,306)( 73,307)
( 74,308)( 75,309)( 76,310)( 77,311)( 78,303)( 79,304)( 80,305)( 81,324)
( 82,325)( 83,326)( 84,273)( 85,274)( 86,275)( 87,294)( 88,295)( 89,296)
( 90,288)( 91,289)( 92,290)( 93,291)( 94,292)( 95,293)( 96,285)( 97,286)
( 98,287)( 99,279)(100,280)(101,281)(102,282)(103,283)(104,284)(105,276)
(106,277)(107,278)(108,297)(109,298)(110,299)(111,381)(112,382)(113,383)
(114,402)(115,403)(116,404)(117,396)(118,397)(119,398)(120,399)(121,400)
(122,401)(123,393)(124,394)(125,395)(126,387)(127,388)(128,389)(129,390)
(130,391)(131,392)(132,384)(133,385)(134,386)(135,405)(136,406)(137,407)
(138,408)(139,409)(140,410)(141,429)(142,430)(143,431)(144,423)(145,424)
(146,425)(147,426)(148,427)(149,428)(150,420)(151,421)(152,422)(153,414)
(154,415)(155,416)(156,417)(157,418)(158,419)(159,411)(160,412)(161,413)
(162,432)(163,433)(164,434)(165,327)(166,328)(167,329)(168,348)(169,349)
(170,350)(171,342)(172,343)(173,344)(174,345)(175,346)(176,347)(177,339)
(178,340)(179,341)(180,333)(181,334)(182,335)(183,336)(184,337)(185,338)
(186,330)(187,331)(188,332)(189,351)(190,352)(191,353)(192,354)(193,355)
(194,356)(195,375)(196,376)(197,377)(198,369)(199,370)(200,371)(201,372)
(202,373)(203,374)(204,366)(205,367)(206,368)(207,360)(208,361)(209,362)
(210,363)(211,364)(212,365)(213,357)(214,358)(215,359)(216,378)(217,379)
(218,380)(435,651)(436,652)(437,653)(438,672)(439,673)(440,674)(441,666)
(442,667)(443,668)(444,669)(445,670)(446,671)(447,663)(448,664)(449,665)
(450,657)(451,658)(452,659)(453,660)(454,661)(455,662)(456,654)(457,655)
(458,656)(459,675)(460,676)(461,677)(462,678)(463,679)(464,680)(465,699)
(466,700)(467,701)(468,693)(469,694)(470,695)(471,696)(472,697)(473,698)
(474,690)(475,691)(476,692)(477,684)(478,685)(479,686)(480,687)(481,688)
(482,689)(483,681)(484,682)(485,683)(486,702)(487,703)(488,704)(489,732)
(490,733)(491,734)(492,753)(493,754)(494,755)(495,747)(496,748)(497,749)
(498,750)(499,751)(500,752)(501,744)(502,745)(503,746)(504,738)(505,739)
(506,740)(507,741)(508,742)(509,743)(510,735)(511,736)(512,737)(513,756)
(514,757)(515,758)(516,705)(517,706)(518,707)(519,726)(520,727)(521,728)
(522,720)(523,721)(524,722)(525,723)(526,724)(527,725)(528,717)(529,718)
(530,719)(531,711)(532,712)(533,713)(534,714)(535,715)(536,716)(537,708)
(538,709)(539,710)(540,729)(541,730)(542,731)(543,813)(544,814)(545,815)
(546,834)(547,835)(548,836)(549,828)(550,829)(551,830)(552,831)(553,832)
(554,833)(555,825)(556,826)(557,827)(558,819)(559,820)(560,821)(561,822)
(562,823)(563,824)(564,816)(565,817)(566,818)(567,837)(568,838)(569,839)
(570,840)(571,841)(572,842)(573,861)(574,862)(575,863)(576,855)(577,856)
(578,857)(579,858)(580,859)(581,860)(582,852)(583,853)(584,854)(585,846)
(586,847)(587,848)(588,849)(589,850)(590,851)(591,843)(592,844)(593,845)
(594,864)(595,865)(596,866)(597,759)(598,760)(599,761)(600,780)(601,781)
(602,782)(603,774)(604,775)(605,776)(606,777)(607,778)(608,779)(609,771)
(610,772)(611,773)(612,765)(613,766)(614,767)(615,768)(616,769)(617,770)
(618,762)(619,763)(620,764)(621,783)(622,784)(623,785)(624,786)(625,787)
(626,788)(627,807)(628,808)(629,809)(630,801)(631,802)(632,803)(633,804)
(634,805)(635,806)(636,798)(637,799)(638,800)(639,792)(640,793)(641,794)
(642,795)(643,796)(644,797)(645,789)(646,790)(647,791)(648,810)(649,811)
(650,812);
s2 := Sym(866)!(  3,543)(  4,545)(  5,544)(  6,546)(  7,548)(  8,547)(  9,549)
( 10,551)( 11,550)( 12,567)( 13,569)( 14,568)( 15,561)( 16,563)( 17,562)
( 18,564)( 19,566)( 20,565)( 21,555)( 22,557)( 23,556)( 24,558)( 25,560)
( 26,559)( 27,552)( 28,554)( 29,553)( 30,570)( 31,572)( 32,571)( 33,573)
( 34,575)( 35,574)( 36,576)( 37,578)( 38,577)( 39,594)( 40,596)( 41,595)
( 42,588)( 43,590)( 44,589)( 45,591)( 46,593)( 47,592)( 48,582)( 49,584)
( 50,583)( 51,585)( 52,587)( 53,586)( 54,579)( 55,581)( 56,580)( 57,624)
( 58,626)( 59,625)( 60,627)( 61,629)( 62,628)( 63,630)( 64,632)( 65,631)
( 66,648)( 67,650)( 68,649)( 69,642)( 70,644)( 71,643)( 72,645)( 73,647)
( 74,646)( 75,636)( 76,638)( 77,637)( 78,639)( 79,641)( 80,640)( 81,633)
( 82,635)( 83,634)( 84,597)( 85,599)( 86,598)( 87,600)( 88,602)( 89,601)
( 90,603)( 91,605)( 92,604)( 93,621)( 94,623)( 95,622)( 96,615)( 97,617)
( 98,616)( 99,618)(100,620)(101,619)(102,609)(103,611)(104,610)(105,612)
(106,614)(107,613)(108,606)(109,608)(110,607)(111,462)(112,464)(113,463)
(114,465)(115,467)(116,466)(117,468)(118,470)(119,469)(120,486)(121,488)
(122,487)(123,480)(124,482)(125,481)(126,483)(127,485)(128,484)(129,474)
(130,476)(131,475)(132,477)(133,479)(134,478)(135,471)(136,473)(137,472)
(138,435)(139,437)(140,436)(141,438)(142,440)(143,439)(144,441)(145,443)
(146,442)(147,459)(148,461)(149,460)(150,453)(151,455)(152,454)(153,456)
(154,458)(155,457)(156,447)(157,449)(158,448)(159,450)(160,452)(161,451)
(162,444)(163,446)(164,445)(165,489)(166,491)(167,490)(168,492)(169,494)
(170,493)(171,495)(172,497)(173,496)(174,513)(175,515)(176,514)(177,507)
(178,509)(179,508)(180,510)(181,512)(182,511)(183,501)(184,503)(185,502)
(186,504)(187,506)(188,505)(189,498)(190,500)(191,499)(192,516)(193,518)
(194,517)(195,519)(196,521)(197,520)(198,522)(199,524)(200,523)(201,540)
(202,542)(203,541)(204,534)(205,536)(206,535)(207,537)(208,539)(209,538)
(210,528)(211,530)(212,529)(213,531)(214,533)(215,532)(216,525)(217,527)
(218,526)(219,786)(220,788)(221,787)(222,789)(223,791)(224,790)(225,792)
(226,794)(227,793)(228,810)(229,812)(230,811)(231,804)(232,806)(233,805)
(234,807)(235,809)(236,808)(237,798)(238,800)(239,799)(240,801)(241,803)
(242,802)(243,795)(244,797)(245,796)(246,759)(247,761)(248,760)(249,762)
(250,764)(251,763)(252,765)(253,767)(254,766)(255,783)(256,785)(257,784)
(258,777)(259,779)(260,778)(261,780)(262,782)(263,781)(264,771)(265,773)
(266,772)(267,774)(268,776)(269,775)(270,768)(271,770)(272,769)(273,813)
(274,815)(275,814)(276,816)(277,818)(278,817)(279,819)(280,821)(281,820)
(282,837)(283,839)(284,838)(285,831)(286,833)(287,832)(288,834)(289,836)
(290,835)(291,825)(292,827)(293,826)(294,828)(295,830)(296,829)(297,822)
(298,824)(299,823)(300,840)(301,842)(302,841)(303,843)(304,845)(305,844)
(306,846)(307,848)(308,847)(309,864)(310,866)(311,865)(312,858)(313,860)
(314,859)(315,861)(316,863)(317,862)(318,852)(319,854)(320,853)(321,855)
(322,857)(323,856)(324,849)(325,851)(326,850)(327,651)(328,653)(329,652)
(330,654)(331,656)(332,655)(333,657)(334,659)(335,658)(336,675)(337,677)
(338,676)(339,669)(340,671)(341,670)(342,672)(343,674)(344,673)(345,663)
(346,665)(347,664)(348,666)(349,668)(350,667)(351,660)(352,662)(353,661)
(354,678)(355,680)(356,679)(357,681)(358,683)(359,682)(360,684)(361,686)
(362,685)(363,702)(364,704)(365,703)(366,696)(367,698)(368,697)(369,699)
(370,701)(371,700)(372,690)(373,692)(374,691)(375,693)(376,695)(377,694)
(378,687)(379,689)(380,688)(381,732)(382,734)(383,733)(384,735)(385,737)
(386,736)(387,738)(388,740)(389,739)(390,756)(391,758)(392,757)(393,750)
(394,752)(395,751)(396,753)(397,755)(398,754)(399,744)(400,746)(401,745)
(402,747)(403,749)(404,748)(405,741)(406,743)(407,742)(408,705)(409,707)
(410,706)(411,708)(412,710)(413,709)(414,711)(415,713)(416,712)(417,729)
(418,731)(419,730)(420,723)(421,725)(422,724)(423,726)(424,728)(425,727)
(426,717)(427,719)(428,718)(429,720)(430,722)(431,721)(432,714)(433,716)
(434,715);
s3 := Sym(866)!(  3,502)(  4,501)(  5,503)(  6,499)(  7,498)(  8,500)(  9,505)
( 10,504)( 11,506)( 12,493)( 13,492)( 14,494)( 15,490)( 16,489)( 17,491)
( 18,496)( 19,495)( 20,497)( 21,511)( 22,510)( 23,512)( 24,508)( 25,507)
( 26,509)( 27,514)( 28,513)( 29,515)( 30,529)( 31,528)( 32,530)( 33,526)
( 34,525)( 35,527)( 36,532)( 37,531)( 38,533)( 39,520)( 40,519)( 41,521)
( 42,517)( 43,516)( 44,518)( 45,523)( 46,522)( 47,524)( 48,538)( 49,537)
( 50,539)( 51,535)( 52,534)( 53,536)( 54,541)( 55,540)( 56,542)( 57,475)
( 58,474)( 59,476)( 60,472)( 61,471)( 62,473)( 63,478)( 64,477)( 65,479)
( 66,466)( 67,465)( 68,467)( 69,463)( 70,462)( 71,464)( 72,469)( 73,468)
( 74,470)( 75,484)( 76,483)( 77,485)( 78,481)( 79,480)( 80,482)( 81,487)
( 82,486)( 83,488)( 84,448)( 85,447)( 86,449)( 87,445)( 88,444)( 89,446)
( 90,451)( 91,450)( 92,452)( 93,439)( 94,438)( 95,440)( 96,436)( 97,435)
( 98,437)( 99,442)(100,441)(101,443)(102,457)(103,456)(104,458)(105,454)
(106,453)(107,455)(108,460)(109,459)(110,461)(111,637)(112,636)(113,638)
(114,634)(115,633)(116,635)(117,640)(118,639)(119,641)(120,628)(121,627)
(122,629)(123,625)(124,624)(125,626)(126,631)(127,630)(128,632)(129,646)
(130,645)(131,647)(132,643)(133,642)(134,644)(135,649)(136,648)(137,650)
(138,610)(139,609)(140,611)(141,607)(142,606)(143,608)(144,613)(145,612)
(146,614)(147,601)(148,600)(149,602)(150,598)(151,597)(152,599)(153,604)
(154,603)(155,605)(156,619)(157,618)(158,620)(159,616)(160,615)(161,617)
(162,622)(163,621)(164,623)(165,556)(166,555)(167,557)(168,553)(169,552)
(170,554)(171,559)(172,558)(173,560)(174,547)(175,546)(176,548)(177,544)
(178,543)(179,545)(180,550)(181,549)(182,551)(183,565)(184,564)(185,566)
(186,562)(187,561)(188,563)(189,568)(190,567)(191,569)(192,583)(193,582)
(194,584)(195,580)(196,579)(197,581)(198,586)(199,585)(200,587)(201,574)
(202,573)(203,575)(204,571)(205,570)(206,572)(207,577)(208,576)(209,578)
(210,592)(211,591)(212,593)(213,589)(214,588)(215,590)(216,595)(217,594)
(218,596)(219,745)(220,744)(221,746)(222,742)(223,741)(224,743)(225,748)
(226,747)(227,749)(228,736)(229,735)(230,737)(231,733)(232,732)(233,734)
(234,739)(235,738)(236,740)(237,754)(238,753)(239,755)(240,751)(241,750)
(242,752)(243,757)(244,756)(245,758)(246,718)(247,717)(248,719)(249,715)
(250,714)(251,716)(252,721)(253,720)(254,722)(255,709)(256,708)(257,710)
(258,706)(259,705)(260,707)(261,712)(262,711)(263,713)(264,727)(265,726)
(266,728)(267,724)(268,723)(269,725)(270,730)(271,729)(272,731)(273,664)
(274,663)(275,665)(276,661)(277,660)(278,662)(279,667)(280,666)(281,668)
(282,655)(283,654)(284,656)(285,652)(286,651)(287,653)(288,658)(289,657)
(290,659)(291,673)(292,672)(293,674)(294,670)(295,669)(296,671)(297,676)
(298,675)(299,677)(300,691)(301,690)(302,692)(303,688)(304,687)(305,689)
(306,694)(307,693)(308,695)(309,682)(310,681)(311,683)(312,679)(313,678)
(314,680)(315,685)(316,684)(317,686)(318,700)(319,699)(320,701)(321,697)
(322,696)(323,698)(324,703)(325,702)(326,704)(327,826)(328,825)(329,827)
(330,823)(331,822)(332,824)(333,829)(334,828)(335,830)(336,817)(337,816)
(338,818)(339,814)(340,813)(341,815)(342,820)(343,819)(344,821)(345,835)
(346,834)(347,836)(348,832)(349,831)(350,833)(351,838)(352,837)(353,839)
(354,853)(355,852)(356,854)(357,850)(358,849)(359,851)(360,856)(361,855)
(362,857)(363,844)(364,843)(365,845)(366,841)(367,840)(368,842)(369,847)
(370,846)(371,848)(372,862)(373,861)(374,863)(375,859)(376,858)(377,860)
(378,865)(379,864)(380,866)(381,799)(382,798)(383,800)(384,796)(385,795)
(386,797)(387,802)(388,801)(389,803)(390,790)(391,789)(392,791)(393,787)
(394,786)(395,788)(396,793)(397,792)(398,794)(399,808)(400,807)(401,809)
(402,805)(403,804)(404,806)(405,811)(406,810)(407,812)(408,772)(409,771)
(410,773)(411,769)(412,768)(413,770)(414,775)(415,774)(416,776)(417,763)
(418,762)(419,764)(420,760)(421,759)(422,761)(423,766)(424,765)(425,767)
(426,781)(427,780)(428,782)(429,778)(430,777)(431,779)(432,784)(433,783)
(434,785);
poly := sub<Sym(866)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s2*s3*s2 >; 
 

to this polytope