Polytope of Type {54,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {54,8}*1728b
if this polytope has a name.
Group : SmallGroup(1728,11367)
Rank : 3
Schlafli Type : {54,8}
Number of vertices, edges, etc : 108, 432, 16
Order of s0s1s2 : 108
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {27,8}*864, {54,4}*864
3-fold quotients : {18,8}*576b
4-fold quotients : {27,4}*432, {54,4}*432b, {54,4}*432c
6-fold quotients : {9,8}*288, {18,4}*288
8-fold quotients : {27,4}*216, {54,2}*216
9-fold quotients : {6,8}*192b
12-fold quotients : {9,4}*144, {18,4}*144b, {18,4}*144c
16-fold quotients : {27,2}*108
18-fold quotients : {3,8}*96, {6,4}*96
24-fold quotients : {9,4}*72, {18,2}*72
36-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
48-fold quotients : {9,2}*36
72-fold quotients : {3,4}*24, {6,2}*24
144-fold quotients : {3,2}*12
216-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 7)( 6, 8)( 9, 17)( 10, 18)( 11, 20)( 12, 19)( 13, 23)
( 14, 24)( 15, 21)( 16, 22)( 25, 65)( 26, 66)( 27, 68)( 28, 67)( 29, 71)
( 30, 72)( 31, 69)( 32, 70)( 33, 57)( 34, 58)( 35, 60)( 36, 59)( 37, 63)
( 38, 64)( 39, 61)( 40, 62)( 41, 49)( 42, 50)( 43, 52)( 44, 51)( 45, 55)
( 46, 56)( 47, 53)( 48, 54)( 73,209)( 74,210)( 75,212)( 76,211)( 77,215)
( 78,216)( 79,213)( 80,214)( 81,201)( 82,202)( 83,204)( 84,203)( 85,207)
( 86,208)( 87,205)( 88,206)( 89,193)( 90,194)( 91,196)( 92,195)( 93,199)
( 94,200)( 95,197)( 96,198)( 97,185)( 98,186)( 99,188)(100,187)(101,191)
(102,192)(103,189)(104,190)(105,177)(106,178)(107,180)(108,179)(109,183)
(110,184)(111,181)(112,182)(113,169)(114,170)(115,172)(116,171)(117,175)
(118,176)(119,173)(120,174)(121,161)(122,162)(123,164)(124,163)(125,167)
(126,168)(127,165)(128,166)(129,153)(130,154)(131,156)(132,155)(133,159)
(134,160)(135,157)(136,158)(137,145)(138,146)(139,148)(140,147)(141,151)
(142,152)(143,149)(144,150)(217,218)(221,224)(222,223)(225,234)(226,233)
(227,235)(228,236)(229,240)(230,239)(231,238)(232,237)(241,282)(242,281)
(243,283)(244,284)(245,288)(246,287)(247,286)(248,285)(249,274)(250,273)
(251,275)(252,276)(253,280)(254,279)(255,278)(256,277)(257,266)(258,265)
(259,267)(260,268)(261,272)(262,271)(263,270)(264,269)(289,426)(290,425)
(291,427)(292,428)(293,432)(294,431)(295,430)(296,429)(297,418)(298,417)
(299,419)(300,420)(301,424)(302,423)(303,422)(304,421)(305,410)(306,409)
(307,411)(308,412)(309,416)(310,415)(311,414)(312,413)(313,402)(314,401)
(315,403)(316,404)(317,408)(318,407)(319,406)(320,405)(321,394)(322,393)
(323,395)(324,396)(325,400)(326,399)(327,398)(328,397)(329,386)(330,385)
(331,387)(332,388)(333,392)(334,391)(335,390)(336,389)(337,378)(338,377)
(339,379)(340,380)(341,384)(342,383)(343,382)(344,381)(345,370)(346,369)
(347,371)(348,372)(349,376)(350,375)(351,374)(352,373)(353,362)(354,361)
(355,363)(356,364)(357,368)(358,367)(359,366)(360,365)(435,436)(437,439)
(438,440)(441,449)(442,450)(443,452)(444,451)(445,455)(446,456)(447,453)
(448,454)(457,497)(458,498)(459,500)(460,499)(461,503)(462,504)(463,501)
(464,502)(465,489)(466,490)(467,492)(468,491)(469,495)(470,496)(471,493)
(472,494)(473,481)(474,482)(475,484)(476,483)(477,487)(478,488)(479,485)
(480,486)(505,641)(506,642)(507,644)(508,643)(509,647)(510,648)(511,645)
(512,646)(513,633)(514,634)(515,636)(516,635)(517,639)(518,640)(519,637)
(520,638)(521,625)(522,626)(523,628)(524,627)(525,631)(526,632)(527,629)
(528,630)(529,617)(530,618)(531,620)(532,619)(533,623)(534,624)(535,621)
(536,622)(537,609)(538,610)(539,612)(540,611)(541,615)(542,616)(543,613)
(544,614)(545,601)(546,602)(547,604)(548,603)(549,607)(550,608)(551,605)
(552,606)(553,593)(554,594)(555,596)(556,595)(557,599)(558,600)(559,597)
(560,598)(561,585)(562,586)(563,588)(564,587)(565,591)(566,592)(567,589)
(568,590)(569,577)(570,578)(571,580)(572,579)(573,583)(574,584)(575,581)
(576,582)(649,650)(653,656)(654,655)(657,666)(658,665)(659,667)(660,668)
(661,672)(662,671)(663,670)(664,669)(673,714)(674,713)(675,715)(676,716)
(677,720)(678,719)(679,718)(680,717)(681,706)(682,705)(683,707)(684,708)
(685,712)(686,711)(687,710)(688,709)(689,698)(690,697)(691,699)(692,700)
(693,704)(694,703)(695,702)(696,701)(721,858)(722,857)(723,859)(724,860)
(725,864)(726,863)(727,862)(728,861)(729,850)(730,849)(731,851)(732,852)
(733,856)(734,855)(735,854)(736,853)(737,842)(738,841)(739,843)(740,844)
(741,848)(742,847)(743,846)(744,845)(745,834)(746,833)(747,835)(748,836)
(749,840)(750,839)(751,838)(752,837)(753,826)(754,825)(755,827)(756,828)
(757,832)(758,831)(759,830)(760,829)(761,818)(762,817)(763,819)(764,820)
(765,824)(766,823)(767,822)(768,821)(769,810)(770,809)(771,811)(772,812)
(773,816)(774,815)(775,814)(776,813)(777,802)(778,801)(779,803)(780,804)
(781,808)(782,807)(783,806)(784,805)(785,794)(786,793)(787,795)(788,796)
(789,800)(790,799)(791,798)(792,797);;
s1 := ( 1,505)( 2,506)( 3,511)( 4,512)( 5,510)( 6,509)( 7,507)( 8,508)
( 9,521)( 10,522)( 11,527)( 12,528)( 13,526)( 14,525)( 15,523)( 16,524)
( 17,513)( 18,514)( 19,519)( 20,520)( 21,518)( 22,517)( 23,515)( 24,516)
( 25,569)( 26,570)( 27,575)( 28,576)( 29,574)( 30,573)( 31,571)( 32,572)
( 33,561)( 34,562)( 35,567)( 36,568)( 37,566)( 38,565)( 39,563)( 40,564)
( 41,553)( 42,554)( 43,559)( 44,560)( 45,558)( 46,557)( 47,555)( 48,556)
( 49,545)( 50,546)( 51,551)( 52,552)( 53,550)( 54,549)( 55,547)( 56,548)
( 57,537)( 58,538)( 59,543)( 60,544)( 61,542)( 62,541)( 63,539)( 64,540)
( 65,529)( 66,530)( 67,535)( 68,536)( 69,534)( 70,533)( 71,531)( 72,532)
( 73,433)( 74,434)( 75,439)( 76,440)( 77,438)( 78,437)( 79,435)( 80,436)
( 81,449)( 82,450)( 83,455)( 84,456)( 85,454)( 86,453)( 87,451)( 88,452)
( 89,441)( 90,442)( 91,447)( 92,448)( 93,446)( 94,445)( 95,443)( 96,444)
( 97,497)( 98,498)( 99,503)(100,504)(101,502)(102,501)(103,499)(104,500)
(105,489)(106,490)(107,495)(108,496)(109,494)(110,493)(111,491)(112,492)
(113,481)(114,482)(115,487)(116,488)(117,486)(118,485)(119,483)(120,484)
(121,473)(122,474)(123,479)(124,480)(125,478)(126,477)(127,475)(128,476)
(129,465)(130,466)(131,471)(132,472)(133,470)(134,469)(135,467)(136,468)
(137,457)(138,458)(139,463)(140,464)(141,462)(142,461)(143,459)(144,460)
(145,641)(146,642)(147,647)(148,648)(149,646)(150,645)(151,643)(152,644)
(153,633)(154,634)(155,639)(156,640)(157,638)(158,637)(159,635)(160,636)
(161,625)(162,626)(163,631)(164,632)(165,630)(166,629)(167,627)(168,628)
(169,617)(170,618)(171,623)(172,624)(173,622)(174,621)(175,619)(176,620)
(177,609)(178,610)(179,615)(180,616)(181,614)(182,613)(183,611)(184,612)
(185,601)(186,602)(187,607)(188,608)(189,606)(190,605)(191,603)(192,604)
(193,593)(194,594)(195,599)(196,600)(197,598)(198,597)(199,595)(200,596)
(201,585)(202,586)(203,591)(204,592)(205,590)(206,589)(207,587)(208,588)
(209,577)(210,578)(211,583)(212,584)(213,582)(214,581)(215,579)(216,580)
(217,722)(218,721)(219,728)(220,727)(221,725)(222,726)(223,724)(224,723)
(225,738)(226,737)(227,744)(228,743)(229,741)(230,742)(231,740)(232,739)
(233,730)(234,729)(235,736)(236,735)(237,733)(238,734)(239,732)(240,731)
(241,786)(242,785)(243,792)(244,791)(245,789)(246,790)(247,788)(248,787)
(249,778)(250,777)(251,784)(252,783)(253,781)(254,782)(255,780)(256,779)
(257,770)(258,769)(259,776)(260,775)(261,773)(262,774)(263,772)(264,771)
(265,762)(266,761)(267,768)(268,767)(269,765)(270,766)(271,764)(272,763)
(273,754)(274,753)(275,760)(276,759)(277,757)(278,758)(279,756)(280,755)
(281,746)(282,745)(283,752)(284,751)(285,749)(286,750)(287,748)(288,747)
(289,650)(290,649)(291,656)(292,655)(293,653)(294,654)(295,652)(296,651)
(297,666)(298,665)(299,672)(300,671)(301,669)(302,670)(303,668)(304,667)
(305,658)(306,657)(307,664)(308,663)(309,661)(310,662)(311,660)(312,659)
(313,714)(314,713)(315,720)(316,719)(317,717)(318,718)(319,716)(320,715)
(321,706)(322,705)(323,712)(324,711)(325,709)(326,710)(327,708)(328,707)
(329,698)(330,697)(331,704)(332,703)(333,701)(334,702)(335,700)(336,699)
(337,690)(338,689)(339,696)(340,695)(341,693)(342,694)(343,692)(344,691)
(345,682)(346,681)(347,688)(348,687)(349,685)(350,686)(351,684)(352,683)
(353,674)(354,673)(355,680)(356,679)(357,677)(358,678)(359,676)(360,675)
(361,858)(362,857)(363,864)(364,863)(365,861)(366,862)(367,860)(368,859)
(369,850)(370,849)(371,856)(372,855)(373,853)(374,854)(375,852)(376,851)
(377,842)(378,841)(379,848)(380,847)(381,845)(382,846)(383,844)(384,843)
(385,834)(386,833)(387,840)(388,839)(389,837)(390,838)(391,836)(392,835)
(393,826)(394,825)(395,832)(396,831)(397,829)(398,830)(399,828)(400,827)
(401,818)(402,817)(403,824)(404,823)(405,821)(406,822)(407,820)(408,819)
(409,810)(410,809)(411,816)(412,815)(413,813)(414,814)(415,812)(416,811)
(417,802)(418,801)(419,808)(420,807)(421,805)(422,806)(423,804)(424,803)
(425,794)(426,793)(427,800)(428,799)(429,797)(430,798)(431,796)(432,795);;
s2 := ( 1,219)( 2,220)( 3,218)( 4,217)( 5,223)( 6,224)( 7,222)( 8,221)
( 9,227)( 10,228)( 11,226)( 12,225)( 13,231)( 14,232)( 15,230)( 16,229)
( 17,235)( 18,236)( 19,234)( 20,233)( 21,239)( 22,240)( 23,238)( 24,237)
( 25,243)( 26,244)( 27,242)( 28,241)( 29,247)( 30,248)( 31,246)( 32,245)
( 33,251)( 34,252)( 35,250)( 36,249)( 37,255)( 38,256)( 39,254)( 40,253)
( 41,259)( 42,260)( 43,258)( 44,257)( 45,263)( 46,264)( 47,262)( 48,261)
( 49,267)( 50,268)( 51,266)( 52,265)( 53,271)( 54,272)( 55,270)( 56,269)
( 57,275)( 58,276)( 59,274)( 60,273)( 61,279)( 62,280)( 63,278)( 64,277)
( 65,283)( 66,284)( 67,282)( 68,281)( 69,287)( 70,288)( 71,286)( 72,285)
( 73,291)( 74,292)( 75,290)( 76,289)( 77,295)( 78,296)( 79,294)( 80,293)
( 81,299)( 82,300)( 83,298)( 84,297)( 85,303)( 86,304)( 87,302)( 88,301)
( 89,307)( 90,308)( 91,306)( 92,305)( 93,311)( 94,312)( 95,310)( 96,309)
( 97,315)( 98,316)( 99,314)(100,313)(101,319)(102,320)(103,318)(104,317)
(105,323)(106,324)(107,322)(108,321)(109,327)(110,328)(111,326)(112,325)
(113,331)(114,332)(115,330)(116,329)(117,335)(118,336)(119,334)(120,333)
(121,339)(122,340)(123,338)(124,337)(125,343)(126,344)(127,342)(128,341)
(129,347)(130,348)(131,346)(132,345)(133,351)(134,352)(135,350)(136,349)
(137,355)(138,356)(139,354)(140,353)(141,359)(142,360)(143,358)(144,357)
(145,363)(146,364)(147,362)(148,361)(149,367)(150,368)(151,366)(152,365)
(153,371)(154,372)(155,370)(156,369)(157,375)(158,376)(159,374)(160,373)
(161,379)(162,380)(163,378)(164,377)(165,383)(166,384)(167,382)(168,381)
(169,387)(170,388)(171,386)(172,385)(173,391)(174,392)(175,390)(176,389)
(177,395)(178,396)(179,394)(180,393)(181,399)(182,400)(183,398)(184,397)
(185,403)(186,404)(187,402)(188,401)(189,407)(190,408)(191,406)(192,405)
(193,411)(194,412)(195,410)(196,409)(197,415)(198,416)(199,414)(200,413)
(201,419)(202,420)(203,418)(204,417)(205,423)(206,424)(207,422)(208,421)
(209,427)(210,428)(211,426)(212,425)(213,431)(214,432)(215,430)(216,429)
(433,651)(434,652)(435,650)(436,649)(437,655)(438,656)(439,654)(440,653)
(441,659)(442,660)(443,658)(444,657)(445,663)(446,664)(447,662)(448,661)
(449,667)(450,668)(451,666)(452,665)(453,671)(454,672)(455,670)(456,669)
(457,675)(458,676)(459,674)(460,673)(461,679)(462,680)(463,678)(464,677)
(465,683)(466,684)(467,682)(468,681)(469,687)(470,688)(471,686)(472,685)
(473,691)(474,692)(475,690)(476,689)(477,695)(478,696)(479,694)(480,693)
(481,699)(482,700)(483,698)(484,697)(485,703)(486,704)(487,702)(488,701)
(489,707)(490,708)(491,706)(492,705)(493,711)(494,712)(495,710)(496,709)
(497,715)(498,716)(499,714)(500,713)(501,719)(502,720)(503,718)(504,717)
(505,723)(506,724)(507,722)(508,721)(509,727)(510,728)(511,726)(512,725)
(513,731)(514,732)(515,730)(516,729)(517,735)(518,736)(519,734)(520,733)
(521,739)(522,740)(523,738)(524,737)(525,743)(526,744)(527,742)(528,741)
(529,747)(530,748)(531,746)(532,745)(533,751)(534,752)(535,750)(536,749)
(537,755)(538,756)(539,754)(540,753)(541,759)(542,760)(543,758)(544,757)
(545,763)(546,764)(547,762)(548,761)(549,767)(550,768)(551,766)(552,765)
(553,771)(554,772)(555,770)(556,769)(557,775)(558,776)(559,774)(560,773)
(561,779)(562,780)(563,778)(564,777)(565,783)(566,784)(567,782)(568,781)
(569,787)(570,788)(571,786)(572,785)(573,791)(574,792)(575,790)(576,789)
(577,795)(578,796)(579,794)(580,793)(581,799)(582,800)(583,798)(584,797)
(585,803)(586,804)(587,802)(588,801)(589,807)(590,808)(591,806)(592,805)
(593,811)(594,812)(595,810)(596,809)(597,815)(598,816)(599,814)(600,813)
(601,819)(602,820)(603,818)(604,817)(605,823)(606,824)(607,822)(608,821)
(609,827)(610,828)(611,826)(612,825)(613,831)(614,832)(615,830)(616,829)
(617,835)(618,836)(619,834)(620,833)(621,839)(622,840)(623,838)(624,837)
(625,843)(626,844)(627,842)(628,841)(629,847)(630,848)(631,846)(632,845)
(633,851)(634,852)(635,850)(636,849)(637,855)(638,856)(639,854)(640,853)
(641,859)(642,860)(643,858)(644,857)(645,863)(646,864)(647,862)(648,861);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*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(864)!( 3, 4)( 5, 7)( 6, 8)( 9, 17)( 10, 18)( 11, 20)( 12, 19)
( 13, 23)( 14, 24)( 15, 21)( 16, 22)( 25, 65)( 26, 66)( 27, 68)( 28, 67)
( 29, 71)( 30, 72)( 31, 69)( 32, 70)( 33, 57)( 34, 58)( 35, 60)( 36, 59)
( 37, 63)( 38, 64)( 39, 61)( 40, 62)( 41, 49)( 42, 50)( 43, 52)( 44, 51)
( 45, 55)( 46, 56)( 47, 53)( 48, 54)( 73,209)( 74,210)( 75,212)( 76,211)
( 77,215)( 78,216)( 79,213)( 80,214)( 81,201)( 82,202)( 83,204)( 84,203)
( 85,207)( 86,208)( 87,205)( 88,206)( 89,193)( 90,194)( 91,196)( 92,195)
( 93,199)( 94,200)( 95,197)( 96,198)( 97,185)( 98,186)( 99,188)(100,187)
(101,191)(102,192)(103,189)(104,190)(105,177)(106,178)(107,180)(108,179)
(109,183)(110,184)(111,181)(112,182)(113,169)(114,170)(115,172)(116,171)
(117,175)(118,176)(119,173)(120,174)(121,161)(122,162)(123,164)(124,163)
(125,167)(126,168)(127,165)(128,166)(129,153)(130,154)(131,156)(132,155)
(133,159)(134,160)(135,157)(136,158)(137,145)(138,146)(139,148)(140,147)
(141,151)(142,152)(143,149)(144,150)(217,218)(221,224)(222,223)(225,234)
(226,233)(227,235)(228,236)(229,240)(230,239)(231,238)(232,237)(241,282)
(242,281)(243,283)(244,284)(245,288)(246,287)(247,286)(248,285)(249,274)
(250,273)(251,275)(252,276)(253,280)(254,279)(255,278)(256,277)(257,266)
(258,265)(259,267)(260,268)(261,272)(262,271)(263,270)(264,269)(289,426)
(290,425)(291,427)(292,428)(293,432)(294,431)(295,430)(296,429)(297,418)
(298,417)(299,419)(300,420)(301,424)(302,423)(303,422)(304,421)(305,410)
(306,409)(307,411)(308,412)(309,416)(310,415)(311,414)(312,413)(313,402)
(314,401)(315,403)(316,404)(317,408)(318,407)(319,406)(320,405)(321,394)
(322,393)(323,395)(324,396)(325,400)(326,399)(327,398)(328,397)(329,386)
(330,385)(331,387)(332,388)(333,392)(334,391)(335,390)(336,389)(337,378)
(338,377)(339,379)(340,380)(341,384)(342,383)(343,382)(344,381)(345,370)
(346,369)(347,371)(348,372)(349,376)(350,375)(351,374)(352,373)(353,362)
(354,361)(355,363)(356,364)(357,368)(358,367)(359,366)(360,365)(435,436)
(437,439)(438,440)(441,449)(442,450)(443,452)(444,451)(445,455)(446,456)
(447,453)(448,454)(457,497)(458,498)(459,500)(460,499)(461,503)(462,504)
(463,501)(464,502)(465,489)(466,490)(467,492)(468,491)(469,495)(470,496)
(471,493)(472,494)(473,481)(474,482)(475,484)(476,483)(477,487)(478,488)
(479,485)(480,486)(505,641)(506,642)(507,644)(508,643)(509,647)(510,648)
(511,645)(512,646)(513,633)(514,634)(515,636)(516,635)(517,639)(518,640)
(519,637)(520,638)(521,625)(522,626)(523,628)(524,627)(525,631)(526,632)
(527,629)(528,630)(529,617)(530,618)(531,620)(532,619)(533,623)(534,624)
(535,621)(536,622)(537,609)(538,610)(539,612)(540,611)(541,615)(542,616)
(543,613)(544,614)(545,601)(546,602)(547,604)(548,603)(549,607)(550,608)
(551,605)(552,606)(553,593)(554,594)(555,596)(556,595)(557,599)(558,600)
(559,597)(560,598)(561,585)(562,586)(563,588)(564,587)(565,591)(566,592)
(567,589)(568,590)(569,577)(570,578)(571,580)(572,579)(573,583)(574,584)
(575,581)(576,582)(649,650)(653,656)(654,655)(657,666)(658,665)(659,667)
(660,668)(661,672)(662,671)(663,670)(664,669)(673,714)(674,713)(675,715)
(676,716)(677,720)(678,719)(679,718)(680,717)(681,706)(682,705)(683,707)
(684,708)(685,712)(686,711)(687,710)(688,709)(689,698)(690,697)(691,699)
(692,700)(693,704)(694,703)(695,702)(696,701)(721,858)(722,857)(723,859)
(724,860)(725,864)(726,863)(727,862)(728,861)(729,850)(730,849)(731,851)
(732,852)(733,856)(734,855)(735,854)(736,853)(737,842)(738,841)(739,843)
(740,844)(741,848)(742,847)(743,846)(744,845)(745,834)(746,833)(747,835)
(748,836)(749,840)(750,839)(751,838)(752,837)(753,826)(754,825)(755,827)
(756,828)(757,832)(758,831)(759,830)(760,829)(761,818)(762,817)(763,819)
(764,820)(765,824)(766,823)(767,822)(768,821)(769,810)(770,809)(771,811)
(772,812)(773,816)(774,815)(775,814)(776,813)(777,802)(778,801)(779,803)
(780,804)(781,808)(782,807)(783,806)(784,805)(785,794)(786,793)(787,795)
(788,796)(789,800)(790,799)(791,798)(792,797);
s1 := Sym(864)!( 1,505)( 2,506)( 3,511)( 4,512)( 5,510)( 6,509)( 7,507)
( 8,508)( 9,521)( 10,522)( 11,527)( 12,528)( 13,526)( 14,525)( 15,523)
( 16,524)( 17,513)( 18,514)( 19,519)( 20,520)( 21,518)( 22,517)( 23,515)
( 24,516)( 25,569)( 26,570)( 27,575)( 28,576)( 29,574)( 30,573)( 31,571)
( 32,572)( 33,561)( 34,562)( 35,567)( 36,568)( 37,566)( 38,565)( 39,563)
( 40,564)( 41,553)( 42,554)( 43,559)( 44,560)( 45,558)( 46,557)( 47,555)
( 48,556)( 49,545)( 50,546)( 51,551)( 52,552)( 53,550)( 54,549)( 55,547)
( 56,548)( 57,537)( 58,538)( 59,543)( 60,544)( 61,542)( 62,541)( 63,539)
( 64,540)( 65,529)( 66,530)( 67,535)( 68,536)( 69,534)( 70,533)( 71,531)
( 72,532)( 73,433)( 74,434)( 75,439)( 76,440)( 77,438)( 78,437)( 79,435)
( 80,436)( 81,449)( 82,450)( 83,455)( 84,456)( 85,454)( 86,453)( 87,451)
( 88,452)( 89,441)( 90,442)( 91,447)( 92,448)( 93,446)( 94,445)( 95,443)
( 96,444)( 97,497)( 98,498)( 99,503)(100,504)(101,502)(102,501)(103,499)
(104,500)(105,489)(106,490)(107,495)(108,496)(109,494)(110,493)(111,491)
(112,492)(113,481)(114,482)(115,487)(116,488)(117,486)(118,485)(119,483)
(120,484)(121,473)(122,474)(123,479)(124,480)(125,478)(126,477)(127,475)
(128,476)(129,465)(130,466)(131,471)(132,472)(133,470)(134,469)(135,467)
(136,468)(137,457)(138,458)(139,463)(140,464)(141,462)(142,461)(143,459)
(144,460)(145,641)(146,642)(147,647)(148,648)(149,646)(150,645)(151,643)
(152,644)(153,633)(154,634)(155,639)(156,640)(157,638)(158,637)(159,635)
(160,636)(161,625)(162,626)(163,631)(164,632)(165,630)(166,629)(167,627)
(168,628)(169,617)(170,618)(171,623)(172,624)(173,622)(174,621)(175,619)
(176,620)(177,609)(178,610)(179,615)(180,616)(181,614)(182,613)(183,611)
(184,612)(185,601)(186,602)(187,607)(188,608)(189,606)(190,605)(191,603)
(192,604)(193,593)(194,594)(195,599)(196,600)(197,598)(198,597)(199,595)
(200,596)(201,585)(202,586)(203,591)(204,592)(205,590)(206,589)(207,587)
(208,588)(209,577)(210,578)(211,583)(212,584)(213,582)(214,581)(215,579)
(216,580)(217,722)(218,721)(219,728)(220,727)(221,725)(222,726)(223,724)
(224,723)(225,738)(226,737)(227,744)(228,743)(229,741)(230,742)(231,740)
(232,739)(233,730)(234,729)(235,736)(236,735)(237,733)(238,734)(239,732)
(240,731)(241,786)(242,785)(243,792)(244,791)(245,789)(246,790)(247,788)
(248,787)(249,778)(250,777)(251,784)(252,783)(253,781)(254,782)(255,780)
(256,779)(257,770)(258,769)(259,776)(260,775)(261,773)(262,774)(263,772)
(264,771)(265,762)(266,761)(267,768)(268,767)(269,765)(270,766)(271,764)
(272,763)(273,754)(274,753)(275,760)(276,759)(277,757)(278,758)(279,756)
(280,755)(281,746)(282,745)(283,752)(284,751)(285,749)(286,750)(287,748)
(288,747)(289,650)(290,649)(291,656)(292,655)(293,653)(294,654)(295,652)
(296,651)(297,666)(298,665)(299,672)(300,671)(301,669)(302,670)(303,668)
(304,667)(305,658)(306,657)(307,664)(308,663)(309,661)(310,662)(311,660)
(312,659)(313,714)(314,713)(315,720)(316,719)(317,717)(318,718)(319,716)
(320,715)(321,706)(322,705)(323,712)(324,711)(325,709)(326,710)(327,708)
(328,707)(329,698)(330,697)(331,704)(332,703)(333,701)(334,702)(335,700)
(336,699)(337,690)(338,689)(339,696)(340,695)(341,693)(342,694)(343,692)
(344,691)(345,682)(346,681)(347,688)(348,687)(349,685)(350,686)(351,684)
(352,683)(353,674)(354,673)(355,680)(356,679)(357,677)(358,678)(359,676)
(360,675)(361,858)(362,857)(363,864)(364,863)(365,861)(366,862)(367,860)
(368,859)(369,850)(370,849)(371,856)(372,855)(373,853)(374,854)(375,852)
(376,851)(377,842)(378,841)(379,848)(380,847)(381,845)(382,846)(383,844)
(384,843)(385,834)(386,833)(387,840)(388,839)(389,837)(390,838)(391,836)
(392,835)(393,826)(394,825)(395,832)(396,831)(397,829)(398,830)(399,828)
(400,827)(401,818)(402,817)(403,824)(404,823)(405,821)(406,822)(407,820)
(408,819)(409,810)(410,809)(411,816)(412,815)(413,813)(414,814)(415,812)
(416,811)(417,802)(418,801)(419,808)(420,807)(421,805)(422,806)(423,804)
(424,803)(425,794)(426,793)(427,800)(428,799)(429,797)(430,798)(431,796)
(432,795);
s2 := Sym(864)!( 1,219)( 2,220)( 3,218)( 4,217)( 5,223)( 6,224)( 7,222)
( 8,221)( 9,227)( 10,228)( 11,226)( 12,225)( 13,231)( 14,232)( 15,230)
( 16,229)( 17,235)( 18,236)( 19,234)( 20,233)( 21,239)( 22,240)( 23,238)
( 24,237)( 25,243)( 26,244)( 27,242)( 28,241)( 29,247)( 30,248)( 31,246)
( 32,245)( 33,251)( 34,252)( 35,250)( 36,249)( 37,255)( 38,256)( 39,254)
( 40,253)( 41,259)( 42,260)( 43,258)( 44,257)( 45,263)( 46,264)( 47,262)
( 48,261)( 49,267)( 50,268)( 51,266)( 52,265)( 53,271)( 54,272)( 55,270)
( 56,269)( 57,275)( 58,276)( 59,274)( 60,273)( 61,279)( 62,280)( 63,278)
( 64,277)( 65,283)( 66,284)( 67,282)( 68,281)( 69,287)( 70,288)( 71,286)
( 72,285)( 73,291)( 74,292)( 75,290)( 76,289)( 77,295)( 78,296)( 79,294)
( 80,293)( 81,299)( 82,300)( 83,298)( 84,297)( 85,303)( 86,304)( 87,302)
( 88,301)( 89,307)( 90,308)( 91,306)( 92,305)( 93,311)( 94,312)( 95,310)
( 96,309)( 97,315)( 98,316)( 99,314)(100,313)(101,319)(102,320)(103,318)
(104,317)(105,323)(106,324)(107,322)(108,321)(109,327)(110,328)(111,326)
(112,325)(113,331)(114,332)(115,330)(116,329)(117,335)(118,336)(119,334)
(120,333)(121,339)(122,340)(123,338)(124,337)(125,343)(126,344)(127,342)
(128,341)(129,347)(130,348)(131,346)(132,345)(133,351)(134,352)(135,350)
(136,349)(137,355)(138,356)(139,354)(140,353)(141,359)(142,360)(143,358)
(144,357)(145,363)(146,364)(147,362)(148,361)(149,367)(150,368)(151,366)
(152,365)(153,371)(154,372)(155,370)(156,369)(157,375)(158,376)(159,374)
(160,373)(161,379)(162,380)(163,378)(164,377)(165,383)(166,384)(167,382)
(168,381)(169,387)(170,388)(171,386)(172,385)(173,391)(174,392)(175,390)
(176,389)(177,395)(178,396)(179,394)(180,393)(181,399)(182,400)(183,398)
(184,397)(185,403)(186,404)(187,402)(188,401)(189,407)(190,408)(191,406)
(192,405)(193,411)(194,412)(195,410)(196,409)(197,415)(198,416)(199,414)
(200,413)(201,419)(202,420)(203,418)(204,417)(205,423)(206,424)(207,422)
(208,421)(209,427)(210,428)(211,426)(212,425)(213,431)(214,432)(215,430)
(216,429)(433,651)(434,652)(435,650)(436,649)(437,655)(438,656)(439,654)
(440,653)(441,659)(442,660)(443,658)(444,657)(445,663)(446,664)(447,662)
(448,661)(449,667)(450,668)(451,666)(452,665)(453,671)(454,672)(455,670)
(456,669)(457,675)(458,676)(459,674)(460,673)(461,679)(462,680)(463,678)
(464,677)(465,683)(466,684)(467,682)(468,681)(469,687)(470,688)(471,686)
(472,685)(473,691)(474,692)(475,690)(476,689)(477,695)(478,696)(479,694)
(480,693)(481,699)(482,700)(483,698)(484,697)(485,703)(486,704)(487,702)
(488,701)(489,707)(490,708)(491,706)(492,705)(493,711)(494,712)(495,710)
(496,709)(497,715)(498,716)(499,714)(500,713)(501,719)(502,720)(503,718)
(504,717)(505,723)(506,724)(507,722)(508,721)(509,727)(510,728)(511,726)
(512,725)(513,731)(514,732)(515,730)(516,729)(517,735)(518,736)(519,734)
(520,733)(521,739)(522,740)(523,738)(524,737)(525,743)(526,744)(527,742)
(528,741)(529,747)(530,748)(531,746)(532,745)(533,751)(534,752)(535,750)
(536,749)(537,755)(538,756)(539,754)(540,753)(541,759)(542,760)(543,758)
(544,757)(545,763)(546,764)(547,762)(548,761)(549,767)(550,768)(551,766)
(552,765)(553,771)(554,772)(555,770)(556,769)(557,775)(558,776)(559,774)
(560,773)(561,779)(562,780)(563,778)(564,777)(565,783)(566,784)(567,782)
(568,781)(569,787)(570,788)(571,786)(572,785)(573,791)(574,792)(575,790)
(576,789)(577,795)(578,796)(579,794)(580,793)(581,799)(582,800)(583,798)
(584,797)(585,803)(586,804)(587,802)(588,801)(589,807)(590,808)(591,806)
(592,805)(593,811)(594,812)(595,810)(596,809)(597,815)(598,816)(599,814)
(600,813)(601,819)(602,820)(603,818)(604,817)(605,823)(606,824)(607,822)
(608,821)(609,827)(610,828)(611,826)(612,825)(613,831)(614,832)(615,830)
(616,829)(617,835)(618,836)(619,834)(620,833)(621,839)(622,840)(623,838)
(624,837)(625,843)(626,844)(627,842)(628,841)(629,847)(630,848)(631,846)
(632,845)(633,851)(634,852)(635,850)(636,849)(637,855)(638,856)(639,854)
(640,853)(641,859)(642,860)(643,858)(644,857)(645,863)(646,864)(647,862)
(648,861);
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, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*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