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