Polytope of Type {6,16}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,16}*1728b
if this polytope has a name.
Group : SmallGroup(1728,31412)
Rank : 3
Schlafli Type : {6,16}
Number of vertices, edges, etc : 54, 432, 144
Order of s0s1s2 : 48
Order of s0s1s2s1 : 6
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 : {6,8}*864b
3-fold quotients : {6,16}*576
4-fold quotients : {6,4}*432b
6-fold quotients : {6,8}*288
9-fold quotients : {6,16}*192
12-fold quotients : {6,4}*144
18-fold quotients : {6,8}*96
24-fold quotients : {6,4}*72
27-fold quotients : {2,16}*64
36-fold quotients : {6,4}*48a
54-fold quotients : {2,8}*32
72-fold quotients : {6,2}*24
108-fold quotients : {2,4}*16
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 := ( 1,325)( 2,327)( 3,326)( 4,331)( 5,333)( 6,332)( 7,328)( 8,330)
( 9,329)( 10,343)( 11,345)( 12,344)( 13,349)( 14,351)( 15,350)( 16,346)
( 17,348)( 18,347)( 19,334)( 20,336)( 21,335)( 22,340)( 23,342)( 24,341)
( 25,337)( 26,339)( 27,338)( 28,352)( 29,354)( 30,353)( 31,358)( 32,360)
( 33,359)( 34,355)( 35,357)( 36,356)( 37,370)( 38,372)( 39,371)( 40,376)
( 41,378)( 42,377)( 43,373)( 44,375)( 45,374)( 46,361)( 47,363)( 48,362)
( 49,367)( 50,369)( 51,368)( 52,364)( 53,366)( 54,365)( 55,379)( 56,381)
( 57,380)( 58,385)( 59,387)( 60,386)( 61,382)( 62,384)( 63,383)( 64,397)
( 65,399)( 66,398)( 67,403)( 68,405)( 69,404)( 70,400)( 71,402)( 72,401)
( 73,388)( 74,390)( 75,389)( 76,394)( 77,396)( 78,395)( 79,391)( 80,393)
( 81,392)( 82,406)( 83,408)( 84,407)( 85,412)( 86,414)( 87,413)( 88,409)
( 89,411)( 90,410)( 91,424)( 92,426)( 93,425)( 94,430)( 95,432)( 96,431)
( 97,427)( 98,429)( 99,428)(100,415)(101,417)(102,416)(103,421)(104,423)
(105,422)(106,418)(107,420)(108,419)(109,298)(110,300)(111,299)(112,304)
(113,306)(114,305)(115,301)(116,303)(117,302)(118,316)(119,318)(120,317)
(121,322)(122,324)(123,323)(124,319)(125,321)(126,320)(127,307)(128,309)
(129,308)(130,313)(131,315)(132,314)(133,310)(134,312)(135,311)(136,271)
(137,273)(138,272)(139,277)(140,279)(141,278)(142,274)(143,276)(144,275)
(145,289)(146,291)(147,290)(148,295)(149,297)(150,296)(151,292)(152,294)
(153,293)(154,280)(155,282)(156,281)(157,286)(158,288)(159,287)(160,283)
(161,285)(162,284)(163,217)(164,219)(165,218)(166,223)(167,225)(168,224)
(169,220)(170,222)(171,221)(172,235)(173,237)(174,236)(175,241)(176,243)
(177,242)(178,238)(179,240)(180,239)(181,226)(182,228)(183,227)(184,232)
(185,234)(186,233)(187,229)(188,231)(189,230)(190,244)(191,246)(192,245)
(193,250)(194,252)(195,251)(196,247)(197,249)(198,248)(199,262)(200,264)
(201,263)(202,268)(203,270)(204,269)(205,265)(206,267)(207,266)(208,253)
(209,255)(210,254)(211,259)(212,261)(213,260)(214,256)(215,258)(216,257)
(433,757)(434,759)(435,758)(436,763)(437,765)(438,764)(439,760)(440,762)
(441,761)(442,775)(443,777)(444,776)(445,781)(446,783)(447,782)(448,778)
(449,780)(450,779)(451,766)(452,768)(453,767)(454,772)(455,774)(456,773)
(457,769)(458,771)(459,770)(460,784)(461,786)(462,785)(463,790)(464,792)
(465,791)(466,787)(467,789)(468,788)(469,802)(470,804)(471,803)(472,808)
(473,810)(474,809)(475,805)(476,807)(477,806)(478,793)(479,795)(480,794)
(481,799)(482,801)(483,800)(484,796)(485,798)(486,797)(487,811)(488,813)
(489,812)(490,817)(491,819)(492,818)(493,814)(494,816)(495,815)(496,829)
(497,831)(498,830)(499,835)(500,837)(501,836)(502,832)(503,834)(504,833)
(505,820)(506,822)(507,821)(508,826)(509,828)(510,827)(511,823)(512,825)
(513,824)(514,838)(515,840)(516,839)(517,844)(518,846)(519,845)(520,841)
(521,843)(522,842)(523,856)(524,858)(525,857)(526,862)(527,864)(528,863)
(529,859)(530,861)(531,860)(532,847)(533,849)(534,848)(535,853)(536,855)
(537,854)(538,850)(539,852)(540,851)(541,730)(542,732)(543,731)(544,736)
(545,738)(546,737)(547,733)(548,735)(549,734)(550,748)(551,750)(552,749)
(553,754)(554,756)(555,755)(556,751)(557,753)(558,752)(559,739)(560,741)
(561,740)(562,745)(563,747)(564,746)(565,742)(566,744)(567,743)(568,703)
(569,705)(570,704)(571,709)(572,711)(573,710)(574,706)(575,708)(576,707)
(577,721)(578,723)(579,722)(580,727)(581,729)(582,728)(583,724)(584,726)
(585,725)(586,712)(587,714)(588,713)(589,718)(590,720)(591,719)(592,715)
(593,717)(594,716)(595,649)(596,651)(597,650)(598,655)(599,657)(600,656)
(601,652)(602,654)(603,653)(604,667)(605,669)(606,668)(607,673)(608,675)
(609,674)(610,670)(611,672)(612,671)(613,658)(614,660)(615,659)(616,664)
(617,666)(618,665)(619,661)(620,663)(621,662)(622,676)(623,678)(624,677)
(625,682)(626,684)(627,683)(628,679)(629,681)(630,680)(631,694)(632,696)
(633,695)(634,700)(635,702)(636,701)(637,697)(638,699)(639,698)(640,685)
(641,687)(642,686)(643,691)(644,693)(645,692)(646,688)(647,690)(648,689);;
s1 := ( 1,229)( 2,227)( 3,234)( 4,226)( 5,233)( 6,231)( 7,232)( 8,230)
( 9,228)( 10,220)( 11,218)( 12,225)( 13,217)( 14,224)( 15,222)( 16,223)
( 17,221)( 18,219)( 19,238)( 20,236)( 21,243)( 22,235)( 23,242)( 24,240)
( 25,241)( 26,239)( 27,237)( 28,256)( 29,254)( 30,261)( 31,253)( 32,260)
( 33,258)( 34,259)( 35,257)( 36,255)( 37,247)( 38,245)( 39,252)( 40,244)
( 41,251)( 42,249)( 43,250)( 44,248)( 45,246)( 46,265)( 47,263)( 48,270)
( 49,262)( 50,269)( 51,267)( 52,268)( 53,266)( 54,264)( 55,310)( 56,308)
( 57,315)( 58,307)( 59,314)( 60,312)( 61,313)( 62,311)( 63,309)( 64,301)
( 65,299)( 66,306)( 67,298)( 68,305)( 69,303)( 70,304)( 71,302)( 72,300)
( 73,319)( 74,317)( 75,324)( 76,316)( 77,323)( 78,321)( 79,322)( 80,320)
( 81,318)( 82,283)( 83,281)( 84,288)( 85,280)( 86,287)( 87,285)( 88,286)
( 89,284)( 90,282)( 91,274)( 92,272)( 93,279)( 94,271)( 95,278)( 96,276)
( 97,277)( 98,275)( 99,273)(100,292)(101,290)(102,297)(103,289)(104,296)
(105,294)(106,295)(107,293)(108,291)(109,391)(110,389)(111,396)(112,388)
(113,395)(114,393)(115,394)(116,392)(117,390)(118,382)(119,380)(120,387)
(121,379)(122,386)(123,384)(124,385)(125,383)(126,381)(127,400)(128,398)
(129,405)(130,397)(131,404)(132,402)(133,403)(134,401)(135,399)(136,418)
(137,416)(138,423)(139,415)(140,422)(141,420)(142,421)(143,419)(144,417)
(145,409)(146,407)(147,414)(148,406)(149,413)(150,411)(151,412)(152,410)
(153,408)(154,427)(155,425)(156,432)(157,424)(158,431)(159,429)(160,430)
(161,428)(162,426)(163,337)(164,335)(165,342)(166,334)(167,341)(168,339)
(169,340)(170,338)(171,336)(172,328)(173,326)(174,333)(175,325)(176,332)
(177,330)(178,331)(179,329)(180,327)(181,346)(182,344)(183,351)(184,343)
(185,350)(186,348)(187,349)(188,347)(189,345)(190,364)(191,362)(192,369)
(193,361)(194,368)(195,366)(196,367)(197,365)(198,363)(199,355)(200,353)
(201,360)(202,352)(203,359)(204,357)(205,358)(206,356)(207,354)(208,373)
(209,371)(210,378)(211,370)(212,377)(213,375)(214,376)(215,374)(216,372)
(433,769)(434,767)(435,774)(436,766)(437,773)(438,771)(439,772)(440,770)
(441,768)(442,760)(443,758)(444,765)(445,757)(446,764)(447,762)(448,763)
(449,761)(450,759)(451,778)(452,776)(453,783)(454,775)(455,782)(456,780)
(457,781)(458,779)(459,777)(460,796)(461,794)(462,801)(463,793)(464,800)
(465,798)(466,799)(467,797)(468,795)(469,787)(470,785)(471,792)(472,784)
(473,791)(474,789)(475,790)(476,788)(477,786)(478,805)(479,803)(480,810)
(481,802)(482,809)(483,807)(484,808)(485,806)(486,804)(487,850)(488,848)
(489,855)(490,847)(491,854)(492,852)(493,853)(494,851)(495,849)(496,841)
(497,839)(498,846)(499,838)(500,845)(501,843)(502,844)(503,842)(504,840)
(505,859)(506,857)(507,864)(508,856)(509,863)(510,861)(511,862)(512,860)
(513,858)(514,823)(515,821)(516,828)(517,820)(518,827)(519,825)(520,826)
(521,824)(522,822)(523,814)(524,812)(525,819)(526,811)(527,818)(528,816)
(529,817)(530,815)(531,813)(532,832)(533,830)(534,837)(535,829)(536,836)
(537,834)(538,835)(539,833)(540,831)(541,661)(542,659)(543,666)(544,658)
(545,665)(546,663)(547,664)(548,662)(549,660)(550,652)(551,650)(552,657)
(553,649)(554,656)(555,654)(556,655)(557,653)(558,651)(559,670)(560,668)
(561,675)(562,667)(563,674)(564,672)(565,673)(566,671)(567,669)(568,688)
(569,686)(570,693)(571,685)(572,692)(573,690)(574,691)(575,689)(576,687)
(577,679)(578,677)(579,684)(580,676)(581,683)(582,681)(583,682)(584,680)
(585,678)(586,697)(587,695)(588,702)(589,694)(590,701)(591,699)(592,700)
(593,698)(594,696)(595,742)(596,740)(597,747)(598,739)(599,746)(600,744)
(601,745)(602,743)(603,741)(604,733)(605,731)(606,738)(607,730)(608,737)
(609,735)(610,736)(611,734)(612,732)(613,751)(614,749)(615,756)(616,748)
(617,755)(618,753)(619,754)(620,752)(621,750)(622,715)(623,713)(624,720)
(625,712)(626,719)(627,717)(628,718)(629,716)(630,714)(631,706)(632,704)
(633,711)(634,703)(635,710)(636,708)(637,709)(638,707)(639,705)(640,724)
(641,722)(642,729)(643,721)(644,728)(645,726)(646,727)(647,725)(648,723);;
s2 := ( 1,433)( 2,434)( 3,435)( 4,441)( 5,439)( 6,440)( 7,437)( 8,438)
( 9,436)( 10,442)( 11,443)( 12,444)( 13,450)( 14,448)( 15,449)( 16,446)
( 17,447)( 18,445)( 19,451)( 20,452)( 21,453)( 22,459)( 23,457)( 24,458)
( 25,455)( 26,456)( 27,454)( 28,460)( 29,461)( 30,462)( 31,468)( 32,466)
( 33,467)( 34,464)( 35,465)( 36,463)( 37,469)( 38,470)( 39,471)( 40,477)
( 41,475)( 42,476)( 43,473)( 44,474)( 45,472)( 46,478)( 47,479)( 48,480)
( 49,486)( 50,484)( 51,485)( 52,482)( 53,483)( 54,481)( 55,514)( 56,515)
( 57,516)( 58,522)( 59,520)( 60,521)( 61,518)( 62,519)( 63,517)( 64,523)
( 65,524)( 66,525)( 67,531)( 68,529)( 69,530)( 70,527)( 71,528)( 72,526)
( 73,532)( 74,533)( 75,534)( 76,540)( 77,538)( 78,539)( 79,536)( 80,537)
( 81,535)( 82,487)( 83,488)( 84,489)( 85,495)( 86,493)( 87,494)( 88,491)
( 89,492)( 90,490)( 91,496)( 92,497)( 93,498)( 94,504)( 95,502)( 96,503)
( 97,500)( 98,501)( 99,499)(100,505)(101,506)(102,507)(103,513)(104,511)
(105,512)(106,509)(107,510)(108,508)(109,595)(110,596)(111,597)(112,603)
(113,601)(114,602)(115,599)(116,600)(117,598)(118,604)(119,605)(120,606)
(121,612)(122,610)(123,611)(124,608)(125,609)(126,607)(127,613)(128,614)
(129,615)(130,621)(131,619)(132,620)(133,617)(134,618)(135,616)(136,622)
(137,623)(138,624)(139,630)(140,628)(141,629)(142,626)(143,627)(144,625)
(145,631)(146,632)(147,633)(148,639)(149,637)(150,638)(151,635)(152,636)
(153,634)(154,640)(155,641)(156,642)(157,648)(158,646)(159,647)(160,644)
(161,645)(162,643)(163,541)(164,542)(165,543)(166,549)(167,547)(168,548)
(169,545)(170,546)(171,544)(172,550)(173,551)(174,552)(175,558)(176,556)
(177,557)(178,554)(179,555)(180,553)(181,559)(182,560)(183,561)(184,567)
(185,565)(186,566)(187,563)(188,564)(189,562)(190,568)(191,569)(192,570)
(193,576)(194,574)(195,575)(196,572)(197,573)(198,571)(199,577)(200,578)
(201,579)(202,585)(203,583)(204,584)(205,581)(206,582)(207,580)(208,586)
(209,587)(210,588)(211,594)(212,592)(213,593)(214,590)(215,591)(216,589)
(217,730)(218,731)(219,732)(220,738)(221,736)(222,737)(223,734)(224,735)
(225,733)(226,739)(227,740)(228,741)(229,747)(230,745)(231,746)(232,743)
(233,744)(234,742)(235,748)(236,749)(237,750)(238,756)(239,754)(240,755)
(241,752)(242,753)(243,751)(244,703)(245,704)(246,705)(247,711)(248,709)
(249,710)(250,707)(251,708)(252,706)(253,712)(254,713)(255,714)(256,720)
(257,718)(258,719)(259,716)(260,717)(261,715)(262,721)(263,722)(264,723)
(265,729)(266,727)(267,728)(268,725)(269,726)(270,724)(271,676)(272,677)
(273,678)(274,684)(275,682)(276,683)(277,680)(278,681)(279,679)(280,685)
(281,686)(282,687)(283,693)(284,691)(285,692)(286,689)(287,690)(288,688)
(289,694)(290,695)(291,696)(292,702)(293,700)(294,701)(295,698)(296,699)
(297,697)(298,649)(299,650)(300,651)(301,657)(302,655)(303,656)(304,653)
(305,654)(306,652)(307,658)(308,659)(309,660)(310,666)(311,664)(312,665)
(313,662)(314,663)(315,661)(316,667)(317,668)(318,669)(319,675)(320,673)
(321,674)(322,671)(323,672)(324,670)(325,757)(326,758)(327,759)(328,765)
(329,763)(330,764)(331,761)(332,762)(333,760)(334,766)(335,767)(336,768)
(337,774)(338,772)(339,773)(340,770)(341,771)(342,769)(343,775)(344,776)
(345,777)(346,783)(347,781)(348,782)(349,779)(350,780)(351,778)(352,784)
(353,785)(354,786)(355,792)(356,790)(357,791)(358,788)(359,789)(360,787)
(361,793)(362,794)(363,795)(364,801)(365,799)(366,800)(367,797)(368,798)
(369,796)(370,802)(371,803)(372,804)(373,810)(374,808)(375,809)(376,806)
(377,807)(378,805)(379,838)(380,839)(381,840)(382,846)(383,844)(384,845)
(385,842)(386,843)(387,841)(388,847)(389,848)(390,849)(391,855)(392,853)
(393,854)(394,851)(395,852)(396,850)(397,856)(398,857)(399,858)(400,864)
(401,862)(402,863)(403,860)(404,861)(405,859)(406,811)(407,812)(408,813)
(409,819)(410,817)(411,818)(412,815)(413,816)(414,814)(415,820)(416,821)
(417,822)(418,828)(419,826)(420,827)(421,824)(422,825)(423,823)(424,829)
(425,830)(426,831)(427,837)(428,835)(429,836)(430,833)(431,834)(432,832);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(864)!( 1,325)( 2,327)( 3,326)( 4,331)( 5,333)( 6,332)( 7,328)
( 8,330)( 9,329)( 10,343)( 11,345)( 12,344)( 13,349)( 14,351)( 15,350)
( 16,346)( 17,348)( 18,347)( 19,334)( 20,336)( 21,335)( 22,340)( 23,342)
( 24,341)( 25,337)( 26,339)( 27,338)( 28,352)( 29,354)( 30,353)( 31,358)
( 32,360)( 33,359)( 34,355)( 35,357)( 36,356)( 37,370)( 38,372)( 39,371)
( 40,376)( 41,378)( 42,377)( 43,373)( 44,375)( 45,374)( 46,361)( 47,363)
( 48,362)( 49,367)( 50,369)( 51,368)( 52,364)( 53,366)( 54,365)( 55,379)
( 56,381)( 57,380)( 58,385)( 59,387)( 60,386)( 61,382)( 62,384)( 63,383)
( 64,397)( 65,399)( 66,398)( 67,403)( 68,405)( 69,404)( 70,400)( 71,402)
( 72,401)( 73,388)( 74,390)( 75,389)( 76,394)( 77,396)( 78,395)( 79,391)
( 80,393)( 81,392)( 82,406)( 83,408)( 84,407)( 85,412)( 86,414)( 87,413)
( 88,409)( 89,411)( 90,410)( 91,424)( 92,426)( 93,425)( 94,430)( 95,432)
( 96,431)( 97,427)( 98,429)( 99,428)(100,415)(101,417)(102,416)(103,421)
(104,423)(105,422)(106,418)(107,420)(108,419)(109,298)(110,300)(111,299)
(112,304)(113,306)(114,305)(115,301)(116,303)(117,302)(118,316)(119,318)
(120,317)(121,322)(122,324)(123,323)(124,319)(125,321)(126,320)(127,307)
(128,309)(129,308)(130,313)(131,315)(132,314)(133,310)(134,312)(135,311)
(136,271)(137,273)(138,272)(139,277)(140,279)(141,278)(142,274)(143,276)
(144,275)(145,289)(146,291)(147,290)(148,295)(149,297)(150,296)(151,292)
(152,294)(153,293)(154,280)(155,282)(156,281)(157,286)(158,288)(159,287)
(160,283)(161,285)(162,284)(163,217)(164,219)(165,218)(166,223)(167,225)
(168,224)(169,220)(170,222)(171,221)(172,235)(173,237)(174,236)(175,241)
(176,243)(177,242)(178,238)(179,240)(180,239)(181,226)(182,228)(183,227)
(184,232)(185,234)(186,233)(187,229)(188,231)(189,230)(190,244)(191,246)
(192,245)(193,250)(194,252)(195,251)(196,247)(197,249)(198,248)(199,262)
(200,264)(201,263)(202,268)(203,270)(204,269)(205,265)(206,267)(207,266)
(208,253)(209,255)(210,254)(211,259)(212,261)(213,260)(214,256)(215,258)
(216,257)(433,757)(434,759)(435,758)(436,763)(437,765)(438,764)(439,760)
(440,762)(441,761)(442,775)(443,777)(444,776)(445,781)(446,783)(447,782)
(448,778)(449,780)(450,779)(451,766)(452,768)(453,767)(454,772)(455,774)
(456,773)(457,769)(458,771)(459,770)(460,784)(461,786)(462,785)(463,790)
(464,792)(465,791)(466,787)(467,789)(468,788)(469,802)(470,804)(471,803)
(472,808)(473,810)(474,809)(475,805)(476,807)(477,806)(478,793)(479,795)
(480,794)(481,799)(482,801)(483,800)(484,796)(485,798)(486,797)(487,811)
(488,813)(489,812)(490,817)(491,819)(492,818)(493,814)(494,816)(495,815)
(496,829)(497,831)(498,830)(499,835)(500,837)(501,836)(502,832)(503,834)
(504,833)(505,820)(506,822)(507,821)(508,826)(509,828)(510,827)(511,823)
(512,825)(513,824)(514,838)(515,840)(516,839)(517,844)(518,846)(519,845)
(520,841)(521,843)(522,842)(523,856)(524,858)(525,857)(526,862)(527,864)
(528,863)(529,859)(530,861)(531,860)(532,847)(533,849)(534,848)(535,853)
(536,855)(537,854)(538,850)(539,852)(540,851)(541,730)(542,732)(543,731)
(544,736)(545,738)(546,737)(547,733)(548,735)(549,734)(550,748)(551,750)
(552,749)(553,754)(554,756)(555,755)(556,751)(557,753)(558,752)(559,739)
(560,741)(561,740)(562,745)(563,747)(564,746)(565,742)(566,744)(567,743)
(568,703)(569,705)(570,704)(571,709)(572,711)(573,710)(574,706)(575,708)
(576,707)(577,721)(578,723)(579,722)(580,727)(581,729)(582,728)(583,724)
(584,726)(585,725)(586,712)(587,714)(588,713)(589,718)(590,720)(591,719)
(592,715)(593,717)(594,716)(595,649)(596,651)(597,650)(598,655)(599,657)
(600,656)(601,652)(602,654)(603,653)(604,667)(605,669)(606,668)(607,673)
(608,675)(609,674)(610,670)(611,672)(612,671)(613,658)(614,660)(615,659)
(616,664)(617,666)(618,665)(619,661)(620,663)(621,662)(622,676)(623,678)
(624,677)(625,682)(626,684)(627,683)(628,679)(629,681)(630,680)(631,694)
(632,696)(633,695)(634,700)(635,702)(636,701)(637,697)(638,699)(639,698)
(640,685)(641,687)(642,686)(643,691)(644,693)(645,692)(646,688)(647,690)
(648,689);
s1 := Sym(864)!( 1,229)( 2,227)( 3,234)( 4,226)( 5,233)( 6,231)( 7,232)
( 8,230)( 9,228)( 10,220)( 11,218)( 12,225)( 13,217)( 14,224)( 15,222)
( 16,223)( 17,221)( 18,219)( 19,238)( 20,236)( 21,243)( 22,235)( 23,242)
( 24,240)( 25,241)( 26,239)( 27,237)( 28,256)( 29,254)( 30,261)( 31,253)
( 32,260)( 33,258)( 34,259)( 35,257)( 36,255)( 37,247)( 38,245)( 39,252)
( 40,244)( 41,251)( 42,249)( 43,250)( 44,248)( 45,246)( 46,265)( 47,263)
( 48,270)( 49,262)( 50,269)( 51,267)( 52,268)( 53,266)( 54,264)( 55,310)
( 56,308)( 57,315)( 58,307)( 59,314)( 60,312)( 61,313)( 62,311)( 63,309)
( 64,301)( 65,299)( 66,306)( 67,298)( 68,305)( 69,303)( 70,304)( 71,302)
( 72,300)( 73,319)( 74,317)( 75,324)( 76,316)( 77,323)( 78,321)( 79,322)
( 80,320)( 81,318)( 82,283)( 83,281)( 84,288)( 85,280)( 86,287)( 87,285)
( 88,286)( 89,284)( 90,282)( 91,274)( 92,272)( 93,279)( 94,271)( 95,278)
( 96,276)( 97,277)( 98,275)( 99,273)(100,292)(101,290)(102,297)(103,289)
(104,296)(105,294)(106,295)(107,293)(108,291)(109,391)(110,389)(111,396)
(112,388)(113,395)(114,393)(115,394)(116,392)(117,390)(118,382)(119,380)
(120,387)(121,379)(122,386)(123,384)(124,385)(125,383)(126,381)(127,400)
(128,398)(129,405)(130,397)(131,404)(132,402)(133,403)(134,401)(135,399)
(136,418)(137,416)(138,423)(139,415)(140,422)(141,420)(142,421)(143,419)
(144,417)(145,409)(146,407)(147,414)(148,406)(149,413)(150,411)(151,412)
(152,410)(153,408)(154,427)(155,425)(156,432)(157,424)(158,431)(159,429)
(160,430)(161,428)(162,426)(163,337)(164,335)(165,342)(166,334)(167,341)
(168,339)(169,340)(170,338)(171,336)(172,328)(173,326)(174,333)(175,325)
(176,332)(177,330)(178,331)(179,329)(180,327)(181,346)(182,344)(183,351)
(184,343)(185,350)(186,348)(187,349)(188,347)(189,345)(190,364)(191,362)
(192,369)(193,361)(194,368)(195,366)(196,367)(197,365)(198,363)(199,355)
(200,353)(201,360)(202,352)(203,359)(204,357)(205,358)(206,356)(207,354)
(208,373)(209,371)(210,378)(211,370)(212,377)(213,375)(214,376)(215,374)
(216,372)(433,769)(434,767)(435,774)(436,766)(437,773)(438,771)(439,772)
(440,770)(441,768)(442,760)(443,758)(444,765)(445,757)(446,764)(447,762)
(448,763)(449,761)(450,759)(451,778)(452,776)(453,783)(454,775)(455,782)
(456,780)(457,781)(458,779)(459,777)(460,796)(461,794)(462,801)(463,793)
(464,800)(465,798)(466,799)(467,797)(468,795)(469,787)(470,785)(471,792)
(472,784)(473,791)(474,789)(475,790)(476,788)(477,786)(478,805)(479,803)
(480,810)(481,802)(482,809)(483,807)(484,808)(485,806)(486,804)(487,850)
(488,848)(489,855)(490,847)(491,854)(492,852)(493,853)(494,851)(495,849)
(496,841)(497,839)(498,846)(499,838)(500,845)(501,843)(502,844)(503,842)
(504,840)(505,859)(506,857)(507,864)(508,856)(509,863)(510,861)(511,862)
(512,860)(513,858)(514,823)(515,821)(516,828)(517,820)(518,827)(519,825)
(520,826)(521,824)(522,822)(523,814)(524,812)(525,819)(526,811)(527,818)
(528,816)(529,817)(530,815)(531,813)(532,832)(533,830)(534,837)(535,829)
(536,836)(537,834)(538,835)(539,833)(540,831)(541,661)(542,659)(543,666)
(544,658)(545,665)(546,663)(547,664)(548,662)(549,660)(550,652)(551,650)
(552,657)(553,649)(554,656)(555,654)(556,655)(557,653)(558,651)(559,670)
(560,668)(561,675)(562,667)(563,674)(564,672)(565,673)(566,671)(567,669)
(568,688)(569,686)(570,693)(571,685)(572,692)(573,690)(574,691)(575,689)
(576,687)(577,679)(578,677)(579,684)(580,676)(581,683)(582,681)(583,682)
(584,680)(585,678)(586,697)(587,695)(588,702)(589,694)(590,701)(591,699)
(592,700)(593,698)(594,696)(595,742)(596,740)(597,747)(598,739)(599,746)
(600,744)(601,745)(602,743)(603,741)(604,733)(605,731)(606,738)(607,730)
(608,737)(609,735)(610,736)(611,734)(612,732)(613,751)(614,749)(615,756)
(616,748)(617,755)(618,753)(619,754)(620,752)(621,750)(622,715)(623,713)
(624,720)(625,712)(626,719)(627,717)(628,718)(629,716)(630,714)(631,706)
(632,704)(633,711)(634,703)(635,710)(636,708)(637,709)(638,707)(639,705)
(640,724)(641,722)(642,729)(643,721)(644,728)(645,726)(646,727)(647,725)
(648,723);
s2 := Sym(864)!( 1,433)( 2,434)( 3,435)( 4,441)( 5,439)( 6,440)( 7,437)
( 8,438)( 9,436)( 10,442)( 11,443)( 12,444)( 13,450)( 14,448)( 15,449)
( 16,446)( 17,447)( 18,445)( 19,451)( 20,452)( 21,453)( 22,459)( 23,457)
( 24,458)( 25,455)( 26,456)( 27,454)( 28,460)( 29,461)( 30,462)( 31,468)
( 32,466)( 33,467)( 34,464)( 35,465)( 36,463)( 37,469)( 38,470)( 39,471)
( 40,477)( 41,475)( 42,476)( 43,473)( 44,474)( 45,472)( 46,478)( 47,479)
( 48,480)( 49,486)( 50,484)( 51,485)( 52,482)( 53,483)( 54,481)( 55,514)
( 56,515)( 57,516)( 58,522)( 59,520)( 60,521)( 61,518)( 62,519)( 63,517)
( 64,523)( 65,524)( 66,525)( 67,531)( 68,529)( 69,530)( 70,527)( 71,528)
( 72,526)( 73,532)( 74,533)( 75,534)( 76,540)( 77,538)( 78,539)( 79,536)
( 80,537)( 81,535)( 82,487)( 83,488)( 84,489)( 85,495)( 86,493)( 87,494)
( 88,491)( 89,492)( 90,490)( 91,496)( 92,497)( 93,498)( 94,504)( 95,502)
( 96,503)( 97,500)( 98,501)( 99,499)(100,505)(101,506)(102,507)(103,513)
(104,511)(105,512)(106,509)(107,510)(108,508)(109,595)(110,596)(111,597)
(112,603)(113,601)(114,602)(115,599)(116,600)(117,598)(118,604)(119,605)
(120,606)(121,612)(122,610)(123,611)(124,608)(125,609)(126,607)(127,613)
(128,614)(129,615)(130,621)(131,619)(132,620)(133,617)(134,618)(135,616)
(136,622)(137,623)(138,624)(139,630)(140,628)(141,629)(142,626)(143,627)
(144,625)(145,631)(146,632)(147,633)(148,639)(149,637)(150,638)(151,635)
(152,636)(153,634)(154,640)(155,641)(156,642)(157,648)(158,646)(159,647)
(160,644)(161,645)(162,643)(163,541)(164,542)(165,543)(166,549)(167,547)
(168,548)(169,545)(170,546)(171,544)(172,550)(173,551)(174,552)(175,558)
(176,556)(177,557)(178,554)(179,555)(180,553)(181,559)(182,560)(183,561)
(184,567)(185,565)(186,566)(187,563)(188,564)(189,562)(190,568)(191,569)
(192,570)(193,576)(194,574)(195,575)(196,572)(197,573)(198,571)(199,577)
(200,578)(201,579)(202,585)(203,583)(204,584)(205,581)(206,582)(207,580)
(208,586)(209,587)(210,588)(211,594)(212,592)(213,593)(214,590)(215,591)
(216,589)(217,730)(218,731)(219,732)(220,738)(221,736)(222,737)(223,734)
(224,735)(225,733)(226,739)(227,740)(228,741)(229,747)(230,745)(231,746)
(232,743)(233,744)(234,742)(235,748)(236,749)(237,750)(238,756)(239,754)
(240,755)(241,752)(242,753)(243,751)(244,703)(245,704)(246,705)(247,711)
(248,709)(249,710)(250,707)(251,708)(252,706)(253,712)(254,713)(255,714)
(256,720)(257,718)(258,719)(259,716)(260,717)(261,715)(262,721)(263,722)
(264,723)(265,729)(266,727)(267,728)(268,725)(269,726)(270,724)(271,676)
(272,677)(273,678)(274,684)(275,682)(276,683)(277,680)(278,681)(279,679)
(280,685)(281,686)(282,687)(283,693)(284,691)(285,692)(286,689)(287,690)
(288,688)(289,694)(290,695)(291,696)(292,702)(293,700)(294,701)(295,698)
(296,699)(297,697)(298,649)(299,650)(300,651)(301,657)(302,655)(303,656)
(304,653)(305,654)(306,652)(307,658)(308,659)(309,660)(310,666)(311,664)
(312,665)(313,662)(314,663)(315,661)(316,667)(317,668)(318,669)(319,675)
(320,673)(321,674)(322,671)(323,672)(324,670)(325,757)(326,758)(327,759)
(328,765)(329,763)(330,764)(331,761)(332,762)(333,760)(334,766)(335,767)
(336,768)(337,774)(338,772)(339,773)(340,770)(341,771)(342,769)(343,775)
(344,776)(345,777)(346,783)(347,781)(348,782)(349,779)(350,780)(351,778)
(352,784)(353,785)(354,786)(355,792)(356,790)(357,791)(358,788)(359,789)
(360,787)(361,793)(362,794)(363,795)(364,801)(365,799)(366,800)(367,797)
(368,798)(369,796)(370,802)(371,803)(372,804)(373,810)(374,808)(375,809)
(376,806)(377,807)(378,805)(379,838)(380,839)(381,840)(382,846)(383,844)
(384,845)(385,842)(386,843)(387,841)(388,847)(389,848)(390,849)(391,855)
(392,853)(393,854)(394,851)(395,852)(396,850)(397,856)(398,857)(399,858)
(400,864)(401,862)(402,863)(403,860)(404,861)(405,859)(406,811)(407,812)
(408,813)(409,819)(410,817)(411,818)(412,815)(413,816)(414,814)(415,820)
(416,821)(417,822)(418,828)(419,826)(420,827)(421,824)(422,825)(423,823)
(424,829)(425,830)(426,831)(427,837)(428,835)(429,836)(430,833)(431,834)
(432,832);
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope