Polytope of Type {48,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {48,6}*1728g
if this polytope has a name.
Group : SmallGroup(1728,31412)
Rank : 3
Schlafli Type : {48,6}
Number of vertices, edges, etc : 144, 432, 18
Order of s₀s₁s₂ : 16
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {24,6}*864g
   3-fold quotients : {16,6}*576
   4-fold quotients : {12,6}*432h
   6-fold quotients : {8,6}*288
   12-fold quotients : {4,6}*144
   24-fold quotients : {4,6}*72
   27-fold quotients : {16,2}*64
   54-fold quotients : {8,2}*32
   108-fold quotients : {4,2}*16
   216-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope