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