Polytope of Type {228,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {228,4}*1824c
if this polytope has a name.
Group : SmallGroup(1824,1071)
Rank : 3
Schlafli Type : {228,4}
Number of vertices, edges, etc : 228, 456, 4
Order of s₀s₁s₂ : 228
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
   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 : {114,4}*912b
   4-fold quotients : {57,4}*456
   19-fold quotients : {12,4}*96c
   38-fold quotients : {6,4}*48c
   76-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  3,  4)(  5, 73)(  6, 74)(  7, 76)(  8, 75)(  9, 69)( 10, 70)( 11, 72)
( 12, 71)( 13, 65)( 14, 66)( 15, 68)( 16, 67)( 17, 61)( 18, 62)( 19, 64)
( 20, 63)( 21, 57)( 22, 58)( 23, 60)( 24, 59)( 25, 53)( 26, 54)( 27, 56)
( 28, 55)( 29, 49)( 30, 50)( 31, 52)( 32, 51)( 33, 45)( 34, 46)( 35, 48)
( 36, 47)( 37, 41)( 38, 42)( 39, 44)( 40, 43)( 77,153)( 78,154)( 79,156)
( 80,155)( 81,225)( 82,226)( 83,228)( 84,227)( 85,221)( 86,222)( 87,224)
( 88,223)( 89,217)( 90,218)( 91,220)( 92,219)( 93,213)( 94,214)( 95,216)
( 96,215)( 97,209)( 98,210)( 99,212)(100,211)(101,205)(102,206)(103,208)
(104,207)(105,201)(106,202)(107,204)(108,203)(109,197)(110,198)(111,200)
(112,199)(113,193)(114,194)(115,196)(116,195)(117,189)(118,190)(119,192)
(120,191)(121,185)(122,186)(123,188)(124,187)(125,181)(126,182)(127,184)
(128,183)(129,177)(130,178)(131,180)(132,179)(133,173)(134,174)(135,176)
(136,175)(137,169)(138,170)(139,172)(140,171)(141,165)(142,166)(143,168)
(144,167)(145,161)(146,162)(147,164)(148,163)(149,157)(150,158)(151,160)
(152,159)(231,232)(233,301)(234,302)(235,304)(236,303)(237,297)(238,298)
(239,300)(240,299)(241,293)(242,294)(243,296)(244,295)(245,289)(246,290)
(247,292)(248,291)(249,285)(250,286)(251,288)(252,287)(253,281)(254,282)
(255,284)(256,283)(257,277)(258,278)(259,280)(260,279)(261,273)(262,274)
(263,276)(264,275)(265,269)(266,270)(267,272)(268,271)(305,381)(306,382)
(307,384)(308,383)(309,453)(310,454)(311,456)(312,455)(313,449)(314,450)
(315,452)(316,451)(317,445)(318,446)(319,448)(320,447)(321,441)(322,442)
(323,444)(324,443)(325,437)(326,438)(327,440)(328,439)(329,433)(330,434)
(331,436)(332,435)(333,429)(334,430)(335,432)(336,431)(337,425)(338,426)
(339,428)(340,427)(341,421)(342,422)(343,424)(344,423)(345,417)(346,418)
(347,420)(348,419)(349,413)(350,414)(351,416)(352,415)(353,409)(354,410)
(355,412)(356,411)(357,405)(358,406)(359,408)(360,407)(361,401)(362,402)
(363,404)(364,403)(365,397)(366,398)(367,400)(368,399)(369,393)(370,394)
(371,396)(372,395)(373,389)(374,390)(375,392)(376,391)(377,385)(378,386)
(379,388)(380,387)(457,685)(458,686)(459,688)(460,687)(461,757)(462,758)
(463,760)(464,759)(465,753)(466,754)(467,756)(468,755)(469,749)(470,750)
(471,752)(472,751)(473,745)(474,746)(475,748)(476,747)(477,741)(478,742)
(479,744)(480,743)(481,737)(482,738)(483,740)(484,739)(485,733)(486,734)
(487,736)(488,735)(489,729)(490,730)(491,732)(492,731)(493,725)(494,726)
(495,728)(496,727)(497,721)(498,722)(499,724)(500,723)(501,717)(502,718)
(503,720)(504,719)(505,713)(506,714)(507,716)(508,715)(509,709)(510,710)
(511,712)(512,711)(513,705)(514,706)(515,708)(516,707)(517,701)(518,702)
(519,704)(520,703)(521,697)(522,698)(523,700)(524,699)(525,693)(526,694)
(527,696)(528,695)(529,689)(530,690)(531,692)(532,691)(533,837)(534,838)
(535,840)(536,839)(537,909)(538,910)(539,912)(540,911)(541,905)(542,906)
(543,908)(544,907)(545,901)(546,902)(547,904)(548,903)(549,897)(550,898)
(551,900)(552,899)(553,893)(554,894)(555,896)(556,895)(557,889)(558,890)
(559,892)(560,891)(561,885)(562,886)(563,888)(564,887)(565,881)(566,882)
(567,884)(568,883)(569,877)(570,878)(571,880)(572,879)(573,873)(574,874)
(575,876)(576,875)(577,869)(578,870)(579,872)(580,871)(581,865)(582,866)
(583,868)(584,867)(585,861)(586,862)(587,864)(588,863)(589,857)(590,858)
(591,860)(592,859)(593,853)(594,854)(595,856)(596,855)(597,849)(598,850)
(599,852)(600,851)(601,845)(602,846)(603,848)(604,847)(605,841)(606,842)
(607,844)(608,843)(609,761)(610,762)(611,764)(612,763)(613,833)(614,834)
(615,836)(616,835)(617,829)(618,830)(619,832)(620,831)(621,825)(622,826)
(623,828)(624,827)(625,821)(626,822)(627,824)(628,823)(629,817)(630,818)
(631,820)(632,819)(633,813)(634,814)(635,816)(636,815)(637,809)(638,810)
(639,812)(640,811)(641,805)(642,806)(643,808)(644,807)(645,801)(646,802)
(647,804)(648,803)(649,797)(650,798)(651,800)(652,799)(653,793)(654,794)
(655,796)(656,795)(657,789)(658,790)(659,792)(660,791)(661,785)(662,786)
(663,788)(664,787)(665,781)(666,782)(667,784)(668,783)(669,777)(670,778)
(671,780)(672,779)(673,773)(674,774)(675,776)(676,775)(677,769)(678,770)
(679,772)(680,771)(681,765)(682,766)(683,768)(684,767);;
s1 := (  1,537)(  2,540)(  3,539)(  4,538)(  5,533)(  6,536)(  7,535)(  8,534)
(  9,605)( 10,608)( 11,607)( 12,606)( 13,601)( 14,604)( 15,603)( 16,602)
( 17,597)( 18,600)( 19,599)( 20,598)( 21,593)( 22,596)( 23,595)( 24,594)
( 25,589)( 26,592)( 27,591)( 28,590)( 29,585)( 30,588)( 31,587)( 32,586)
( 33,581)( 34,584)( 35,583)( 36,582)( 37,577)( 38,580)( 39,579)( 40,578)
( 41,573)( 42,576)( 43,575)( 44,574)( 45,569)( 46,572)( 47,571)( 48,570)
( 49,565)( 50,568)( 51,567)( 52,566)( 53,561)( 54,564)( 55,563)( 56,562)
( 57,557)( 58,560)( 59,559)( 60,558)( 61,553)( 62,556)( 63,555)( 64,554)
( 65,549)( 66,552)( 67,551)( 68,550)( 69,545)( 70,548)( 71,547)( 72,546)
( 73,541)( 74,544)( 75,543)( 76,542)( 77,461)( 78,464)( 79,463)( 80,462)
( 81,457)( 82,460)( 83,459)( 84,458)( 85,529)( 86,532)( 87,531)( 88,530)
( 89,525)( 90,528)( 91,527)( 92,526)( 93,521)( 94,524)( 95,523)( 96,522)
( 97,517)( 98,520)( 99,519)(100,518)(101,513)(102,516)(103,515)(104,514)
(105,509)(106,512)(107,511)(108,510)(109,505)(110,508)(111,507)(112,506)
(113,501)(114,504)(115,503)(116,502)(117,497)(118,500)(119,499)(120,498)
(121,493)(122,496)(123,495)(124,494)(125,489)(126,492)(127,491)(128,490)
(129,485)(130,488)(131,487)(132,486)(133,481)(134,484)(135,483)(136,482)
(137,477)(138,480)(139,479)(140,478)(141,473)(142,476)(143,475)(144,474)
(145,469)(146,472)(147,471)(148,470)(149,465)(150,468)(151,467)(152,466)
(153,613)(154,616)(155,615)(156,614)(157,609)(158,612)(159,611)(160,610)
(161,681)(162,684)(163,683)(164,682)(165,677)(166,680)(167,679)(168,678)
(169,673)(170,676)(171,675)(172,674)(173,669)(174,672)(175,671)(176,670)
(177,665)(178,668)(179,667)(180,666)(181,661)(182,664)(183,663)(184,662)
(185,657)(186,660)(187,659)(188,658)(189,653)(190,656)(191,655)(192,654)
(193,649)(194,652)(195,651)(196,650)(197,645)(198,648)(199,647)(200,646)
(201,641)(202,644)(203,643)(204,642)(205,637)(206,640)(207,639)(208,638)
(209,633)(210,636)(211,635)(212,634)(213,629)(214,632)(215,631)(216,630)
(217,625)(218,628)(219,627)(220,626)(221,621)(222,624)(223,623)(224,622)
(225,617)(226,620)(227,619)(228,618)(229,765)(230,768)(231,767)(232,766)
(233,761)(234,764)(235,763)(236,762)(237,833)(238,836)(239,835)(240,834)
(241,829)(242,832)(243,831)(244,830)(245,825)(246,828)(247,827)(248,826)
(249,821)(250,824)(251,823)(252,822)(253,817)(254,820)(255,819)(256,818)
(257,813)(258,816)(259,815)(260,814)(261,809)(262,812)(263,811)(264,810)
(265,805)(266,808)(267,807)(268,806)(269,801)(270,804)(271,803)(272,802)
(273,797)(274,800)(275,799)(276,798)(277,793)(278,796)(279,795)(280,794)
(281,789)(282,792)(283,791)(284,790)(285,785)(286,788)(287,787)(288,786)
(289,781)(290,784)(291,783)(292,782)(293,777)(294,780)(295,779)(296,778)
(297,773)(298,776)(299,775)(300,774)(301,769)(302,772)(303,771)(304,770)
(305,689)(306,692)(307,691)(308,690)(309,685)(310,688)(311,687)(312,686)
(313,757)(314,760)(315,759)(316,758)(317,753)(318,756)(319,755)(320,754)
(321,749)(322,752)(323,751)(324,750)(325,745)(326,748)(327,747)(328,746)
(329,741)(330,744)(331,743)(332,742)(333,737)(334,740)(335,739)(336,738)
(337,733)(338,736)(339,735)(340,734)(341,729)(342,732)(343,731)(344,730)
(345,725)(346,728)(347,727)(348,726)(349,721)(350,724)(351,723)(352,722)
(353,717)(354,720)(355,719)(356,718)(357,713)(358,716)(359,715)(360,714)
(361,709)(362,712)(363,711)(364,710)(365,705)(366,708)(367,707)(368,706)
(369,701)(370,704)(371,703)(372,702)(373,697)(374,700)(375,699)(376,698)
(377,693)(378,696)(379,695)(380,694)(381,841)(382,844)(383,843)(384,842)
(385,837)(386,840)(387,839)(388,838)(389,909)(390,912)(391,911)(392,910)
(393,905)(394,908)(395,907)(396,906)(397,901)(398,904)(399,903)(400,902)
(401,897)(402,900)(403,899)(404,898)(405,893)(406,896)(407,895)(408,894)
(409,889)(410,892)(411,891)(412,890)(413,885)(414,888)(415,887)(416,886)
(417,881)(418,884)(419,883)(420,882)(421,877)(422,880)(423,879)(424,878)
(425,873)(426,876)(427,875)(428,874)(429,869)(430,872)(431,871)(432,870)
(433,865)(434,868)(435,867)(436,866)(437,861)(438,864)(439,863)(440,862)
(441,857)(442,860)(443,859)(444,858)(445,853)(446,856)(447,855)(448,854)
(449,849)(450,852)(451,851)(452,850)(453,845)(454,848)(455,847)(456,846);;
s2 := (  1,230)(  2,229)(  3,232)(  4,231)(  5,234)(  6,233)(  7,236)(  8,235)
(  9,238)( 10,237)( 11,240)( 12,239)( 13,242)( 14,241)( 15,244)( 16,243)
( 17,246)( 18,245)( 19,248)( 20,247)( 21,250)( 22,249)( 23,252)( 24,251)
( 25,254)( 26,253)( 27,256)( 28,255)( 29,258)( 30,257)( 31,260)( 32,259)
( 33,262)( 34,261)( 35,264)( 36,263)( 37,266)( 38,265)( 39,268)( 40,267)
( 41,270)( 42,269)( 43,272)( 44,271)( 45,274)( 46,273)( 47,276)( 48,275)
( 49,278)( 50,277)( 51,280)( 52,279)( 53,282)( 54,281)( 55,284)( 56,283)
( 57,286)( 58,285)( 59,288)( 60,287)( 61,290)( 62,289)( 63,292)( 64,291)
( 65,294)( 66,293)( 67,296)( 68,295)( 69,298)( 70,297)( 71,300)( 72,299)
( 73,302)( 74,301)( 75,304)( 76,303)( 77,306)( 78,305)( 79,308)( 80,307)
( 81,310)( 82,309)( 83,312)( 84,311)( 85,314)( 86,313)( 87,316)( 88,315)
( 89,318)( 90,317)( 91,320)( 92,319)( 93,322)( 94,321)( 95,324)( 96,323)
( 97,326)( 98,325)( 99,328)(100,327)(101,330)(102,329)(103,332)(104,331)
(105,334)(106,333)(107,336)(108,335)(109,338)(110,337)(111,340)(112,339)
(113,342)(114,341)(115,344)(116,343)(117,346)(118,345)(119,348)(120,347)
(121,350)(122,349)(123,352)(124,351)(125,354)(126,353)(127,356)(128,355)
(129,358)(130,357)(131,360)(132,359)(133,362)(134,361)(135,364)(136,363)
(137,366)(138,365)(139,368)(140,367)(141,370)(142,369)(143,372)(144,371)
(145,374)(146,373)(147,376)(148,375)(149,378)(150,377)(151,380)(152,379)
(153,382)(154,381)(155,384)(156,383)(157,386)(158,385)(159,388)(160,387)
(161,390)(162,389)(163,392)(164,391)(165,394)(166,393)(167,396)(168,395)
(169,398)(170,397)(171,400)(172,399)(173,402)(174,401)(175,404)(176,403)
(177,406)(178,405)(179,408)(180,407)(181,410)(182,409)(183,412)(184,411)
(185,414)(186,413)(187,416)(188,415)(189,418)(190,417)(191,420)(192,419)
(193,422)(194,421)(195,424)(196,423)(197,426)(198,425)(199,428)(200,427)
(201,430)(202,429)(203,432)(204,431)(205,434)(206,433)(207,436)(208,435)
(209,438)(210,437)(211,440)(212,439)(213,442)(214,441)(215,444)(216,443)
(217,446)(218,445)(219,448)(220,447)(221,450)(222,449)(223,452)(224,451)
(225,454)(226,453)(227,456)(228,455)(457,686)(458,685)(459,688)(460,687)
(461,690)(462,689)(463,692)(464,691)(465,694)(466,693)(467,696)(468,695)
(469,698)(470,697)(471,700)(472,699)(473,702)(474,701)(475,704)(476,703)
(477,706)(478,705)(479,708)(480,707)(481,710)(482,709)(483,712)(484,711)
(485,714)(486,713)(487,716)(488,715)(489,718)(490,717)(491,720)(492,719)
(493,722)(494,721)(495,724)(496,723)(497,726)(498,725)(499,728)(500,727)
(501,730)(502,729)(503,732)(504,731)(505,734)(506,733)(507,736)(508,735)
(509,738)(510,737)(511,740)(512,739)(513,742)(514,741)(515,744)(516,743)
(517,746)(518,745)(519,748)(520,747)(521,750)(522,749)(523,752)(524,751)
(525,754)(526,753)(527,756)(528,755)(529,758)(530,757)(531,760)(532,759)
(533,762)(534,761)(535,764)(536,763)(537,766)(538,765)(539,768)(540,767)
(541,770)(542,769)(543,772)(544,771)(545,774)(546,773)(547,776)(548,775)
(549,778)(550,777)(551,780)(552,779)(553,782)(554,781)(555,784)(556,783)
(557,786)(558,785)(559,788)(560,787)(561,790)(562,789)(563,792)(564,791)
(565,794)(566,793)(567,796)(568,795)(569,798)(570,797)(571,800)(572,799)
(573,802)(574,801)(575,804)(576,803)(577,806)(578,805)(579,808)(580,807)
(581,810)(582,809)(583,812)(584,811)(585,814)(586,813)(587,816)(588,815)
(589,818)(590,817)(591,820)(592,819)(593,822)(594,821)(595,824)(596,823)
(597,826)(598,825)(599,828)(600,827)(601,830)(602,829)(603,832)(604,831)
(605,834)(606,833)(607,836)(608,835)(609,838)(610,837)(611,840)(612,839)
(613,842)(614,841)(615,844)(616,843)(617,846)(618,845)(619,848)(620,847)
(621,850)(622,849)(623,852)(624,851)(625,854)(626,853)(627,856)(628,855)
(629,858)(630,857)(631,860)(632,859)(633,862)(634,861)(635,864)(636,863)
(637,866)(638,865)(639,868)(640,867)(641,870)(642,869)(643,872)(644,871)
(645,874)(646,873)(647,876)(648,875)(649,878)(650,877)(651,880)(652,879)
(653,882)(654,881)(655,884)(656,883)(657,886)(658,885)(659,888)(660,887)
(661,890)(662,889)(663,892)(664,891)(665,894)(666,893)(667,896)(668,895)
(669,898)(670,897)(671,900)(672,899)(673,902)(674,901)(675,904)(676,903)
(677,906)(678,905)(679,908)(680,907)(681,910)(682,909)(683,912)(684,911);;
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*s2*s0*s1*s2*s0*s1*s2*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(912)!(  3,  4)(  5, 73)(  6, 74)(  7, 76)(  8, 75)(  9, 69)( 10, 70)
( 11, 72)( 12, 71)( 13, 65)( 14, 66)( 15, 68)( 16, 67)( 17, 61)( 18, 62)
( 19, 64)( 20, 63)( 21, 57)( 22, 58)( 23, 60)( 24, 59)( 25, 53)( 26, 54)
( 27, 56)( 28, 55)( 29, 49)( 30, 50)( 31, 52)( 32, 51)( 33, 45)( 34, 46)
( 35, 48)( 36, 47)( 37, 41)( 38, 42)( 39, 44)( 40, 43)( 77,153)( 78,154)
( 79,156)( 80,155)( 81,225)( 82,226)( 83,228)( 84,227)( 85,221)( 86,222)
( 87,224)( 88,223)( 89,217)( 90,218)( 91,220)( 92,219)( 93,213)( 94,214)
( 95,216)( 96,215)( 97,209)( 98,210)( 99,212)(100,211)(101,205)(102,206)
(103,208)(104,207)(105,201)(106,202)(107,204)(108,203)(109,197)(110,198)
(111,200)(112,199)(113,193)(114,194)(115,196)(116,195)(117,189)(118,190)
(119,192)(120,191)(121,185)(122,186)(123,188)(124,187)(125,181)(126,182)
(127,184)(128,183)(129,177)(130,178)(131,180)(132,179)(133,173)(134,174)
(135,176)(136,175)(137,169)(138,170)(139,172)(140,171)(141,165)(142,166)
(143,168)(144,167)(145,161)(146,162)(147,164)(148,163)(149,157)(150,158)
(151,160)(152,159)(231,232)(233,301)(234,302)(235,304)(236,303)(237,297)
(238,298)(239,300)(240,299)(241,293)(242,294)(243,296)(244,295)(245,289)
(246,290)(247,292)(248,291)(249,285)(250,286)(251,288)(252,287)(253,281)
(254,282)(255,284)(256,283)(257,277)(258,278)(259,280)(260,279)(261,273)
(262,274)(263,276)(264,275)(265,269)(266,270)(267,272)(268,271)(305,381)
(306,382)(307,384)(308,383)(309,453)(310,454)(311,456)(312,455)(313,449)
(314,450)(315,452)(316,451)(317,445)(318,446)(319,448)(320,447)(321,441)
(322,442)(323,444)(324,443)(325,437)(326,438)(327,440)(328,439)(329,433)
(330,434)(331,436)(332,435)(333,429)(334,430)(335,432)(336,431)(337,425)
(338,426)(339,428)(340,427)(341,421)(342,422)(343,424)(344,423)(345,417)
(346,418)(347,420)(348,419)(349,413)(350,414)(351,416)(352,415)(353,409)
(354,410)(355,412)(356,411)(357,405)(358,406)(359,408)(360,407)(361,401)
(362,402)(363,404)(364,403)(365,397)(366,398)(367,400)(368,399)(369,393)
(370,394)(371,396)(372,395)(373,389)(374,390)(375,392)(376,391)(377,385)
(378,386)(379,388)(380,387)(457,685)(458,686)(459,688)(460,687)(461,757)
(462,758)(463,760)(464,759)(465,753)(466,754)(467,756)(468,755)(469,749)
(470,750)(471,752)(472,751)(473,745)(474,746)(475,748)(476,747)(477,741)
(478,742)(479,744)(480,743)(481,737)(482,738)(483,740)(484,739)(485,733)
(486,734)(487,736)(488,735)(489,729)(490,730)(491,732)(492,731)(493,725)
(494,726)(495,728)(496,727)(497,721)(498,722)(499,724)(500,723)(501,717)
(502,718)(503,720)(504,719)(505,713)(506,714)(507,716)(508,715)(509,709)
(510,710)(511,712)(512,711)(513,705)(514,706)(515,708)(516,707)(517,701)
(518,702)(519,704)(520,703)(521,697)(522,698)(523,700)(524,699)(525,693)
(526,694)(527,696)(528,695)(529,689)(530,690)(531,692)(532,691)(533,837)
(534,838)(535,840)(536,839)(537,909)(538,910)(539,912)(540,911)(541,905)
(542,906)(543,908)(544,907)(545,901)(546,902)(547,904)(548,903)(549,897)
(550,898)(551,900)(552,899)(553,893)(554,894)(555,896)(556,895)(557,889)
(558,890)(559,892)(560,891)(561,885)(562,886)(563,888)(564,887)(565,881)
(566,882)(567,884)(568,883)(569,877)(570,878)(571,880)(572,879)(573,873)
(574,874)(575,876)(576,875)(577,869)(578,870)(579,872)(580,871)(581,865)
(582,866)(583,868)(584,867)(585,861)(586,862)(587,864)(588,863)(589,857)
(590,858)(591,860)(592,859)(593,853)(594,854)(595,856)(596,855)(597,849)
(598,850)(599,852)(600,851)(601,845)(602,846)(603,848)(604,847)(605,841)
(606,842)(607,844)(608,843)(609,761)(610,762)(611,764)(612,763)(613,833)
(614,834)(615,836)(616,835)(617,829)(618,830)(619,832)(620,831)(621,825)
(622,826)(623,828)(624,827)(625,821)(626,822)(627,824)(628,823)(629,817)
(630,818)(631,820)(632,819)(633,813)(634,814)(635,816)(636,815)(637,809)
(638,810)(639,812)(640,811)(641,805)(642,806)(643,808)(644,807)(645,801)
(646,802)(647,804)(648,803)(649,797)(650,798)(651,800)(652,799)(653,793)
(654,794)(655,796)(656,795)(657,789)(658,790)(659,792)(660,791)(661,785)
(662,786)(663,788)(664,787)(665,781)(666,782)(667,784)(668,783)(669,777)
(670,778)(671,780)(672,779)(673,773)(674,774)(675,776)(676,775)(677,769)
(678,770)(679,772)(680,771)(681,765)(682,766)(683,768)(684,767);
s1 := Sym(912)!(  1,537)(  2,540)(  3,539)(  4,538)(  5,533)(  6,536)(  7,535)
(  8,534)(  9,605)( 10,608)( 11,607)( 12,606)( 13,601)( 14,604)( 15,603)
( 16,602)( 17,597)( 18,600)( 19,599)( 20,598)( 21,593)( 22,596)( 23,595)
( 24,594)( 25,589)( 26,592)( 27,591)( 28,590)( 29,585)( 30,588)( 31,587)
( 32,586)( 33,581)( 34,584)( 35,583)( 36,582)( 37,577)( 38,580)( 39,579)
( 40,578)( 41,573)( 42,576)( 43,575)( 44,574)( 45,569)( 46,572)( 47,571)
( 48,570)( 49,565)( 50,568)( 51,567)( 52,566)( 53,561)( 54,564)( 55,563)
( 56,562)( 57,557)( 58,560)( 59,559)( 60,558)( 61,553)( 62,556)( 63,555)
( 64,554)( 65,549)( 66,552)( 67,551)( 68,550)( 69,545)( 70,548)( 71,547)
( 72,546)( 73,541)( 74,544)( 75,543)( 76,542)( 77,461)( 78,464)( 79,463)
( 80,462)( 81,457)( 82,460)( 83,459)( 84,458)( 85,529)( 86,532)( 87,531)
( 88,530)( 89,525)( 90,528)( 91,527)( 92,526)( 93,521)( 94,524)( 95,523)
( 96,522)( 97,517)( 98,520)( 99,519)(100,518)(101,513)(102,516)(103,515)
(104,514)(105,509)(106,512)(107,511)(108,510)(109,505)(110,508)(111,507)
(112,506)(113,501)(114,504)(115,503)(116,502)(117,497)(118,500)(119,499)
(120,498)(121,493)(122,496)(123,495)(124,494)(125,489)(126,492)(127,491)
(128,490)(129,485)(130,488)(131,487)(132,486)(133,481)(134,484)(135,483)
(136,482)(137,477)(138,480)(139,479)(140,478)(141,473)(142,476)(143,475)
(144,474)(145,469)(146,472)(147,471)(148,470)(149,465)(150,468)(151,467)
(152,466)(153,613)(154,616)(155,615)(156,614)(157,609)(158,612)(159,611)
(160,610)(161,681)(162,684)(163,683)(164,682)(165,677)(166,680)(167,679)
(168,678)(169,673)(170,676)(171,675)(172,674)(173,669)(174,672)(175,671)
(176,670)(177,665)(178,668)(179,667)(180,666)(181,661)(182,664)(183,663)
(184,662)(185,657)(186,660)(187,659)(188,658)(189,653)(190,656)(191,655)
(192,654)(193,649)(194,652)(195,651)(196,650)(197,645)(198,648)(199,647)
(200,646)(201,641)(202,644)(203,643)(204,642)(205,637)(206,640)(207,639)
(208,638)(209,633)(210,636)(211,635)(212,634)(213,629)(214,632)(215,631)
(216,630)(217,625)(218,628)(219,627)(220,626)(221,621)(222,624)(223,623)
(224,622)(225,617)(226,620)(227,619)(228,618)(229,765)(230,768)(231,767)
(232,766)(233,761)(234,764)(235,763)(236,762)(237,833)(238,836)(239,835)
(240,834)(241,829)(242,832)(243,831)(244,830)(245,825)(246,828)(247,827)
(248,826)(249,821)(250,824)(251,823)(252,822)(253,817)(254,820)(255,819)
(256,818)(257,813)(258,816)(259,815)(260,814)(261,809)(262,812)(263,811)
(264,810)(265,805)(266,808)(267,807)(268,806)(269,801)(270,804)(271,803)
(272,802)(273,797)(274,800)(275,799)(276,798)(277,793)(278,796)(279,795)
(280,794)(281,789)(282,792)(283,791)(284,790)(285,785)(286,788)(287,787)
(288,786)(289,781)(290,784)(291,783)(292,782)(293,777)(294,780)(295,779)
(296,778)(297,773)(298,776)(299,775)(300,774)(301,769)(302,772)(303,771)
(304,770)(305,689)(306,692)(307,691)(308,690)(309,685)(310,688)(311,687)
(312,686)(313,757)(314,760)(315,759)(316,758)(317,753)(318,756)(319,755)
(320,754)(321,749)(322,752)(323,751)(324,750)(325,745)(326,748)(327,747)
(328,746)(329,741)(330,744)(331,743)(332,742)(333,737)(334,740)(335,739)
(336,738)(337,733)(338,736)(339,735)(340,734)(341,729)(342,732)(343,731)
(344,730)(345,725)(346,728)(347,727)(348,726)(349,721)(350,724)(351,723)
(352,722)(353,717)(354,720)(355,719)(356,718)(357,713)(358,716)(359,715)
(360,714)(361,709)(362,712)(363,711)(364,710)(365,705)(366,708)(367,707)
(368,706)(369,701)(370,704)(371,703)(372,702)(373,697)(374,700)(375,699)
(376,698)(377,693)(378,696)(379,695)(380,694)(381,841)(382,844)(383,843)
(384,842)(385,837)(386,840)(387,839)(388,838)(389,909)(390,912)(391,911)
(392,910)(393,905)(394,908)(395,907)(396,906)(397,901)(398,904)(399,903)
(400,902)(401,897)(402,900)(403,899)(404,898)(405,893)(406,896)(407,895)
(408,894)(409,889)(410,892)(411,891)(412,890)(413,885)(414,888)(415,887)
(416,886)(417,881)(418,884)(419,883)(420,882)(421,877)(422,880)(423,879)
(424,878)(425,873)(426,876)(427,875)(428,874)(429,869)(430,872)(431,871)
(432,870)(433,865)(434,868)(435,867)(436,866)(437,861)(438,864)(439,863)
(440,862)(441,857)(442,860)(443,859)(444,858)(445,853)(446,856)(447,855)
(448,854)(449,849)(450,852)(451,851)(452,850)(453,845)(454,848)(455,847)
(456,846);
s2 := Sym(912)!(  1,230)(  2,229)(  3,232)(  4,231)(  5,234)(  6,233)(  7,236)
(  8,235)(  9,238)( 10,237)( 11,240)( 12,239)( 13,242)( 14,241)( 15,244)
( 16,243)( 17,246)( 18,245)( 19,248)( 20,247)( 21,250)( 22,249)( 23,252)
( 24,251)( 25,254)( 26,253)( 27,256)( 28,255)( 29,258)( 30,257)( 31,260)
( 32,259)( 33,262)( 34,261)( 35,264)( 36,263)( 37,266)( 38,265)( 39,268)
( 40,267)( 41,270)( 42,269)( 43,272)( 44,271)( 45,274)( 46,273)( 47,276)
( 48,275)( 49,278)( 50,277)( 51,280)( 52,279)( 53,282)( 54,281)( 55,284)
( 56,283)( 57,286)( 58,285)( 59,288)( 60,287)( 61,290)( 62,289)( 63,292)
( 64,291)( 65,294)( 66,293)( 67,296)( 68,295)( 69,298)( 70,297)( 71,300)
( 72,299)( 73,302)( 74,301)( 75,304)( 76,303)( 77,306)( 78,305)( 79,308)
( 80,307)( 81,310)( 82,309)( 83,312)( 84,311)( 85,314)( 86,313)( 87,316)
( 88,315)( 89,318)( 90,317)( 91,320)( 92,319)( 93,322)( 94,321)( 95,324)
( 96,323)( 97,326)( 98,325)( 99,328)(100,327)(101,330)(102,329)(103,332)
(104,331)(105,334)(106,333)(107,336)(108,335)(109,338)(110,337)(111,340)
(112,339)(113,342)(114,341)(115,344)(116,343)(117,346)(118,345)(119,348)
(120,347)(121,350)(122,349)(123,352)(124,351)(125,354)(126,353)(127,356)
(128,355)(129,358)(130,357)(131,360)(132,359)(133,362)(134,361)(135,364)
(136,363)(137,366)(138,365)(139,368)(140,367)(141,370)(142,369)(143,372)
(144,371)(145,374)(146,373)(147,376)(148,375)(149,378)(150,377)(151,380)
(152,379)(153,382)(154,381)(155,384)(156,383)(157,386)(158,385)(159,388)
(160,387)(161,390)(162,389)(163,392)(164,391)(165,394)(166,393)(167,396)
(168,395)(169,398)(170,397)(171,400)(172,399)(173,402)(174,401)(175,404)
(176,403)(177,406)(178,405)(179,408)(180,407)(181,410)(182,409)(183,412)
(184,411)(185,414)(186,413)(187,416)(188,415)(189,418)(190,417)(191,420)
(192,419)(193,422)(194,421)(195,424)(196,423)(197,426)(198,425)(199,428)
(200,427)(201,430)(202,429)(203,432)(204,431)(205,434)(206,433)(207,436)
(208,435)(209,438)(210,437)(211,440)(212,439)(213,442)(214,441)(215,444)
(216,443)(217,446)(218,445)(219,448)(220,447)(221,450)(222,449)(223,452)
(224,451)(225,454)(226,453)(227,456)(228,455)(457,686)(458,685)(459,688)
(460,687)(461,690)(462,689)(463,692)(464,691)(465,694)(466,693)(467,696)
(468,695)(469,698)(470,697)(471,700)(472,699)(473,702)(474,701)(475,704)
(476,703)(477,706)(478,705)(479,708)(480,707)(481,710)(482,709)(483,712)
(484,711)(485,714)(486,713)(487,716)(488,715)(489,718)(490,717)(491,720)
(492,719)(493,722)(494,721)(495,724)(496,723)(497,726)(498,725)(499,728)
(500,727)(501,730)(502,729)(503,732)(504,731)(505,734)(506,733)(507,736)
(508,735)(509,738)(510,737)(511,740)(512,739)(513,742)(514,741)(515,744)
(516,743)(517,746)(518,745)(519,748)(520,747)(521,750)(522,749)(523,752)
(524,751)(525,754)(526,753)(527,756)(528,755)(529,758)(530,757)(531,760)
(532,759)(533,762)(534,761)(535,764)(536,763)(537,766)(538,765)(539,768)
(540,767)(541,770)(542,769)(543,772)(544,771)(545,774)(546,773)(547,776)
(548,775)(549,778)(550,777)(551,780)(552,779)(553,782)(554,781)(555,784)
(556,783)(557,786)(558,785)(559,788)(560,787)(561,790)(562,789)(563,792)
(564,791)(565,794)(566,793)(567,796)(568,795)(569,798)(570,797)(571,800)
(572,799)(573,802)(574,801)(575,804)(576,803)(577,806)(578,805)(579,808)
(580,807)(581,810)(582,809)(583,812)(584,811)(585,814)(586,813)(587,816)
(588,815)(589,818)(590,817)(591,820)(592,819)(593,822)(594,821)(595,824)
(596,823)(597,826)(598,825)(599,828)(600,827)(601,830)(602,829)(603,832)
(604,831)(605,834)(606,833)(607,836)(608,835)(609,838)(610,837)(611,840)
(612,839)(613,842)(614,841)(615,844)(616,843)(617,846)(618,845)(619,848)
(620,847)(621,850)(622,849)(623,852)(624,851)(625,854)(626,853)(627,856)
(628,855)(629,858)(630,857)(631,860)(632,859)(633,862)(634,861)(635,864)
(636,863)(637,866)(638,865)(639,868)(640,867)(641,870)(642,869)(643,872)
(644,871)(645,874)(646,873)(647,876)(648,875)(649,878)(650,877)(651,880)
(652,879)(653,882)(654,881)(655,884)(656,883)(657,886)(658,885)(659,888)
(660,887)(661,890)(662,889)(663,892)(664,891)(665,894)(666,893)(667,896)
(668,895)(669,898)(670,897)(671,900)(672,899)(673,902)(674,901)(675,904)
(676,903)(677,906)(678,905)(679,908)(680,907)(681,910)(682,909)(683,912)
(684,911);
poly := sub<Sym(912)|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*s2*s0*s1*s2*s0*s1*s2*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