Polytope of Type {6,8,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,8,6}*1728a
if this polytope has a name.
Group : SmallGroup(1728,46549)
Rank : 4
Schlafli Type : {6,8,6}
Number of vertices, edges, etc : 18, 72, 72, 6
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
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 : {6,4,6}*864b
   3-fold quotients : {6,8,2}*576
   4-fold quotients : {6,4,6}*432a
   6-fold quotients : {6,4,2}*288
   9-fold quotients : {2,8,6}*192
   12-fold quotients : {6,4,2}*144
   18-fold quotients : {2,4,6}*96a
   27-fold quotients : {2,8,2}*64
   36-fold quotients : {2,2,6}*48
   54-fold quotients : {2,4,2}*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 := (  1,163)(  2,165)(  3,164)(  4,169)(  5,171)(  6,170)(  7,166)(  8,168)
(  9,167)( 10,172)( 11,174)( 12,173)( 13,178)( 14,180)( 15,179)( 16,175)
( 17,177)( 18,176)( 19,181)( 20,183)( 21,182)( 22,187)( 23,189)( 24,188)
( 25,184)( 26,186)( 27,185)( 28,190)( 29,192)( 30,191)( 31,196)( 32,198)
( 33,197)( 34,193)( 35,195)( 36,194)( 37,199)( 38,201)( 39,200)( 40,205)
( 41,207)( 42,206)( 43,202)( 44,204)( 45,203)( 46,208)( 47,210)( 48,209)
( 49,214)( 50,216)( 51,215)( 52,211)( 53,213)( 54,212)( 55,136)( 56,138)
( 57,137)( 58,142)( 59,144)( 60,143)( 61,139)( 62,141)( 63,140)( 64,145)
( 65,147)( 66,146)( 67,151)( 68,153)( 69,152)( 70,148)( 71,150)( 72,149)
( 73,154)( 74,156)( 75,155)( 76,160)( 77,162)( 78,161)( 79,157)( 80,159)
( 81,158)( 82,109)( 83,111)( 84,110)( 85,115)( 86,117)( 87,116)( 88,112)
( 89,114)( 90,113)( 91,118)( 92,120)( 93,119)( 94,124)( 95,126)( 96,125)
( 97,121)( 98,123)( 99,122)(100,127)(101,129)(102,128)(103,133)(104,135)
(105,134)(106,130)(107,132)(108,131)(217,379)(218,381)(219,380)(220,385)
(221,387)(222,386)(223,382)(224,384)(225,383)(226,388)(227,390)(228,389)
(229,394)(230,396)(231,395)(232,391)(233,393)(234,392)(235,397)(236,399)
(237,398)(238,403)(239,405)(240,404)(241,400)(242,402)(243,401)(244,406)
(245,408)(246,407)(247,412)(248,414)(249,413)(250,409)(251,411)(252,410)
(253,415)(254,417)(255,416)(256,421)(257,423)(258,422)(259,418)(260,420)
(261,419)(262,424)(263,426)(264,425)(265,430)(266,432)(267,431)(268,427)
(269,429)(270,428)(271,352)(272,354)(273,353)(274,358)(275,360)(276,359)
(277,355)(278,357)(279,356)(280,361)(281,363)(282,362)(283,367)(284,369)
(285,368)(286,364)(287,366)(288,365)(289,370)(290,372)(291,371)(292,376)
(293,378)(294,377)(295,373)(296,375)(297,374)(298,325)(299,327)(300,326)
(301,331)(302,333)(303,332)(304,328)(305,330)(306,329)(307,334)(308,336)
(309,335)(310,340)(311,342)(312,341)(313,337)(314,339)(315,338)(316,343)
(317,345)(318,344)(319,349)(320,351)(321,350)(322,346)(323,348)(324,347)
(433,595)(434,597)(435,596)(436,601)(437,603)(438,602)(439,598)(440,600)
(441,599)(442,604)(443,606)(444,605)(445,610)(446,612)(447,611)(448,607)
(449,609)(450,608)(451,613)(452,615)(453,614)(454,619)(455,621)(456,620)
(457,616)(458,618)(459,617)(460,622)(461,624)(462,623)(463,628)(464,630)
(465,629)(466,625)(467,627)(468,626)(469,631)(470,633)(471,632)(472,637)
(473,639)(474,638)(475,634)(476,636)(477,635)(478,640)(479,642)(480,641)
(481,646)(482,648)(483,647)(484,643)(485,645)(486,644)(487,568)(488,570)
(489,569)(490,574)(491,576)(492,575)(493,571)(494,573)(495,572)(496,577)
(497,579)(498,578)(499,583)(500,585)(501,584)(502,580)(503,582)(504,581)
(505,586)(506,588)(507,587)(508,592)(509,594)(510,593)(511,589)(512,591)
(513,590)(514,541)(515,543)(516,542)(517,547)(518,549)(519,548)(520,544)
(521,546)(522,545)(523,550)(524,552)(525,551)(526,556)(527,558)(528,557)
(529,553)(530,555)(531,554)(532,559)(533,561)(534,560)(535,565)(536,567)
(537,566)(538,562)(539,564)(540,563)(649,811)(650,813)(651,812)(652,817)
(653,819)(654,818)(655,814)(656,816)(657,815)(658,820)(659,822)(660,821)
(661,826)(662,828)(663,827)(664,823)(665,825)(666,824)(667,829)(668,831)
(669,830)(670,835)(671,837)(672,836)(673,832)(674,834)(675,833)(676,838)
(677,840)(678,839)(679,844)(680,846)(681,845)(682,841)(683,843)(684,842)
(685,847)(686,849)(687,848)(688,853)(689,855)(690,854)(691,850)(692,852)
(693,851)(694,856)(695,858)(696,857)(697,862)(698,864)(699,863)(700,859)
(701,861)(702,860)(703,784)(704,786)(705,785)(706,790)(707,792)(708,791)
(709,787)(710,789)(711,788)(712,793)(713,795)(714,794)(715,799)(716,801)
(717,800)(718,796)(719,798)(720,797)(721,802)(722,804)(723,803)(724,808)
(725,810)(726,809)(727,805)(728,807)(729,806)(730,757)(731,759)(732,758)
(733,763)(734,765)(735,764)(736,760)(737,762)(738,761)(739,766)(740,768)
(741,767)(742,772)(743,774)(744,773)(745,769)(746,771)(747,770)(748,775)
(749,777)(750,776)(751,781)(752,783)(753,782)(754,778)(755,780)(756,779);;
s1 := (  1,  4)(  3,  9)(  5,  8)( 10, 13)( 12, 18)( 14, 17)( 19, 22)( 21, 27)
( 23, 26)( 28, 31)( 30, 36)( 32, 35)( 37, 40)( 39, 45)( 41, 44)( 46, 49)
( 48, 54)( 50, 53)( 55, 85)( 56, 83)( 57, 90)( 58, 82)( 59, 89)( 60, 87)
( 61, 88)( 62, 86)( 63, 84)( 64, 94)( 65, 92)( 66, 99)( 67, 91)( 68, 98)
( 69, 96)( 70, 97)( 71, 95)( 72, 93)( 73,103)( 74,101)( 75,108)( 76,100)
( 77,107)( 78,105)( 79,106)( 80,104)( 81,102)(109,139)(110,137)(111,144)
(112,136)(113,143)(114,141)(115,142)(116,140)(117,138)(118,148)(119,146)
(120,153)(121,145)(122,152)(123,150)(124,151)(125,149)(126,147)(127,157)
(128,155)(129,162)(130,154)(131,161)(132,159)(133,160)(134,158)(135,156)
(163,166)(165,171)(167,170)(172,175)(174,180)(176,179)(181,184)(183,189)
(185,188)(190,193)(192,198)(194,197)(199,202)(201,207)(203,206)(208,211)
(210,216)(212,215)(217,220)(219,225)(221,224)(226,229)(228,234)(230,233)
(235,238)(237,243)(239,242)(244,247)(246,252)(248,251)(253,256)(255,261)
(257,260)(262,265)(264,270)(266,269)(271,301)(272,299)(273,306)(274,298)
(275,305)(276,303)(277,304)(278,302)(279,300)(280,310)(281,308)(282,315)
(283,307)(284,314)(285,312)(286,313)(287,311)(288,309)(289,319)(290,317)
(291,324)(292,316)(293,323)(294,321)(295,322)(296,320)(297,318)(325,355)
(326,353)(327,360)(328,352)(329,359)(330,357)(331,358)(332,356)(333,354)
(334,364)(335,362)(336,369)(337,361)(338,368)(339,366)(340,367)(341,365)
(342,363)(343,373)(344,371)(345,378)(346,370)(347,377)(348,375)(349,376)
(350,374)(351,372)(379,382)(381,387)(383,386)(388,391)(390,396)(392,395)
(397,400)(399,405)(401,404)(406,409)(408,414)(410,413)(415,418)(417,423)
(419,422)(424,427)(426,432)(428,431)(433,490)(434,488)(435,495)(436,487)
(437,494)(438,492)(439,493)(440,491)(441,489)(442,499)(443,497)(444,504)
(445,496)(446,503)(447,501)(448,502)(449,500)(450,498)(451,508)(452,506)
(453,513)(454,505)(455,512)(456,510)(457,511)(458,509)(459,507)(460,517)
(461,515)(462,522)(463,514)(464,521)(465,519)(466,520)(467,518)(468,516)
(469,526)(470,524)(471,531)(472,523)(473,530)(474,528)(475,529)(476,527)
(477,525)(478,535)(479,533)(480,540)(481,532)(482,539)(483,537)(484,538)
(485,536)(486,534)(541,625)(542,623)(543,630)(544,622)(545,629)(546,627)
(547,628)(548,626)(549,624)(550,634)(551,632)(552,639)(553,631)(554,638)
(555,636)(556,637)(557,635)(558,633)(559,643)(560,641)(561,648)(562,640)
(563,647)(564,645)(565,646)(566,644)(567,642)(568,598)(569,596)(570,603)
(571,595)(572,602)(573,600)(574,601)(575,599)(576,597)(577,607)(578,605)
(579,612)(580,604)(581,611)(582,609)(583,610)(584,608)(585,606)(586,616)
(587,614)(588,621)(589,613)(590,620)(591,618)(592,619)(593,617)(594,615)
(649,706)(650,704)(651,711)(652,703)(653,710)(654,708)(655,709)(656,707)
(657,705)(658,715)(659,713)(660,720)(661,712)(662,719)(663,717)(664,718)
(665,716)(666,714)(667,724)(668,722)(669,729)(670,721)(671,728)(672,726)
(673,727)(674,725)(675,723)(676,733)(677,731)(678,738)(679,730)(680,737)
(681,735)(682,736)(683,734)(684,732)(685,742)(686,740)(687,747)(688,739)
(689,746)(690,744)(691,745)(692,743)(693,741)(694,751)(695,749)(696,756)
(697,748)(698,755)(699,753)(700,754)(701,752)(702,750)(757,841)(758,839)
(759,846)(760,838)(761,845)(762,843)(763,844)(764,842)(765,840)(766,850)
(767,848)(768,855)(769,847)(770,854)(771,852)(772,853)(773,851)(774,849)
(775,859)(776,857)(777,864)(778,856)(779,863)(780,861)(781,862)(782,860)
(783,858)(784,814)(785,812)(786,819)(787,811)(788,818)(789,816)(790,817)
(791,815)(792,813)(793,823)(794,821)(795,828)(796,820)(797,827)(798,825)
(799,826)(800,824)(801,822)(802,832)(803,830)(804,837)(805,829)(806,836)
(807,834)(808,835)(809,833)(810,831);;
s2 := (  1,649)(  2,650)(  3,651)(  4,657)(  5,655)(  6,656)(  7,653)(  8,654)
(  9,652)( 10,667)( 11,668)( 12,669)( 13,675)( 14,673)( 15,674)( 16,671)
( 17,672)( 18,670)( 19,658)( 20,659)( 21,660)( 22,666)( 23,664)( 24,665)
( 25,662)( 26,663)( 27,661)( 28,676)( 29,677)( 30,678)( 31,684)( 32,682)
( 33,683)( 34,680)( 35,681)( 36,679)( 37,694)( 38,695)( 39,696)( 40,702)
( 41,700)( 42,701)( 43,698)( 44,699)( 45,697)( 46,685)( 47,686)( 48,687)
( 49,693)( 50,691)( 51,692)( 52,689)( 53,690)( 54,688)( 55,730)( 56,731)
( 57,732)( 58,738)( 59,736)( 60,737)( 61,734)( 62,735)( 63,733)( 64,748)
( 65,749)( 66,750)( 67,756)( 68,754)( 69,755)( 70,752)( 71,753)( 72,751)
( 73,739)( 74,740)( 75,741)( 76,747)( 77,745)( 78,746)( 79,743)( 80,744)
( 81,742)( 82,703)( 83,704)( 84,705)( 85,711)( 86,709)( 87,710)( 88,707)
( 89,708)( 90,706)( 91,721)( 92,722)( 93,723)( 94,729)( 95,727)( 96,728)
( 97,725)( 98,726)( 99,724)(100,712)(101,713)(102,714)(103,720)(104,718)
(105,719)(106,716)(107,717)(108,715)(109,784)(110,785)(111,786)(112,792)
(113,790)(114,791)(115,788)(116,789)(117,787)(118,802)(119,803)(120,804)
(121,810)(122,808)(123,809)(124,806)(125,807)(126,805)(127,793)(128,794)
(129,795)(130,801)(131,799)(132,800)(133,797)(134,798)(135,796)(136,757)
(137,758)(138,759)(139,765)(140,763)(141,764)(142,761)(143,762)(144,760)
(145,775)(146,776)(147,777)(148,783)(149,781)(150,782)(151,779)(152,780)
(153,778)(154,766)(155,767)(156,768)(157,774)(158,772)(159,773)(160,770)
(161,771)(162,769)(163,811)(164,812)(165,813)(166,819)(167,817)(168,818)
(169,815)(170,816)(171,814)(172,829)(173,830)(174,831)(175,837)(176,835)
(177,836)(178,833)(179,834)(180,832)(181,820)(182,821)(183,822)(184,828)
(185,826)(186,827)(187,824)(188,825)(189,823)(190,838)(191,839)(192,840)
(193,846)(194,844)(195,845)(196,842)(197,843)(198,841)(199,856)(200,857)
(201,858)(202,864)(203,862)(204,863)(205,860)(206,861)(207,859)(208,847)
(209,848)(210,849)(211,855)(212,853)(213,854)(214,851)(215,852)(216,850)
(217,433)(218,434)(219,435)(220,441)(221,439)(222,440)(223,437)(224,438)
(225,436)(226,451)(227,452)(228,453)(229,459)(230,457)(231,458)(232,455)
(233,456)(234,454)(235,442)(236,443)(237,444)(238,450)(239,448)(240,449)
(241,446)(242,447)(243,445)(244,460)(245,461)(246,462)(247,468)(248,466)
(249,467)(250,464)(251,465)(252,463)(253,478)(254,479)(255,480)(256,486)
(257,484)(258,485)(259,482)(260,483)(261,481)(262,469)(263,470)(264,471)
(265,477)(266,475)(267,476)(268,473)(269,474)(270,472)(271,514)(272,515)
(273,516)(274,522)(275,520)(276,521)(277,518)(278,519)(279,517)(280,532)
(281,533)(282,534)(283,540)(284,538)(285,539)(286,536)(287,537)(288,535)
(289,523)(290,524)(291,525)(292,531)(293,529)(294,530)(295,527)(296,528)
(297,526)(298,487)(299,488)(300,489)(301,495)(302,493)(303,494)(304,491)
(305,492)(306,490)(307,505)(308,506)(309,507)(310,513)(311,511)(312,512)
(313,509)(314,510)(315,508)(316,496)(317,497)(318,498)(319,504)(320,502)
(321,503)(322,500)(323,501)(324,499)(325,568)(326,569)(327,570)(328,576)
(329,574)(330,575)(331,572)(332,573)(333,571)(334,586)(335,587)(336,588)
(337,594)(338,592)(339,593)(340,590)(341,591)(342,589)(343,577)(344,578)
(345,579)(346,585)(347,583)(348,584)(349,581)(350,582)(351,580)(352,541)
(353,542)(354,543)(355,549)(356,547)(357,548)(358,545)(359,546)(360,544)
(361,559)(362,560)(363,561)(364,567)(365,565)(366,566)(367,563)(368,564)
(369,562)(370,550)(371,551)(372,552)(373,558)(374,556)(375,557)(376,554)
(377,555)(378,553)(379,595)(380,596)(381,597)(382,603)(383,601)(384,602)
(385,599)(386,600)(387,598)(388,613)(389,614)(390,615)(391,621)(392,619)
(393,620)(394,617)(395,618)(396,616)(397,604)(398,605)(399,606)(400,612)
(401,610)(402,611)(403,608)(404,609)(405,607)(406,622)(407,623)(408,624)
(409,630)(410,628)(411,629)(412,626)(413,627)(414,625)(415,640)(416,641)
(417,642)(418,648)(419,646)(420,647)(421,644)(422,645)(423,643)(424,631)
(425,632)(426,633)(427,639)(428,637)(429,638)(430,635)(431,636)(432,634);;
s3 := (  1,226)(  2,227)(  3,228)(  4,229)(  5,230)(  6,231)(  7,232)(  8,233)
(  9,234)( 10,217)( 11,218)( 12,219)( 13,220)( 14,221)( 15,222)( 16,223)
( 17,224)( 18,225)( 19,235)( 20,236)( 21,237)( 22,238)( 23,239)( 24,240)
( 25,241)( 26,242)( 27,243)( 28,253)( 29,254)( 30,255)( 31,256)( 32,257)
( 33,258)( 34,259)( 35,260)( 36,261)( 37,244)( 38,245)( 39,246)( 40,247)
( 41,248)( 42,249)( 43,250)( 44,251)( 45,252)( 46,262)( 47,263)( 48,264)
( 49,265)( 50,266)( 51,267)( 52,268)( 53,269)( 54,270)( 55,280)( 56,281)
( 57,282)( 58,283)( 59,284)( 60,285)( 61,286)( 62,287)( 63,288)( 64,271)
( 65,272)( 66,273)( 67,274)( 68,275)( 69,276)( 70,277)( 71,278)( 72,279)
( 73,289)( 74,290)( 75,291)( 76,292)( 77,293)( 78,294)( 79,295)( 80,296)
( 81,297)( 82,307)( 83,308)( 84,309)( 85,310)( 86,311)( 87,312)( 88,313)
( 89,314)( 90,315)( 91,298)( 92,299)( 93,300)( 94,301)( 95,302)( 96,303)
( 97,304)( 98,305)( 99,306)(100,316)(101,317)(102,318)(103,319)(104,320)
(105,321)(106,322)(107,323)(108,324)(109,334)(110,335)(111,336)(112,337)
(113,338)(114,339)(115,340)(116,341)(117,342)(118,325)(119,326)(120,327)
(121,328)(122,329)(123,330)(124,331)(125,332)(126,333)(127,343)(128,344)
(129,345)(130,346)(131,347)(132,348)(133,349)(134,350)(135,351)(136,361)
(137,362)(138,363)(139,364)(140,365)(141,366)(142,367)(143,368)(144,369)
(145,352)(146,353)(147,354)(148,355)(149,356)(150,357)(151,358)(152,359)
(153,360)(154,370)(155,371)(156,372)(157,373)(158,374)(159,375)(160,376)
(161,377)(162,378)(163,388)(164,389)(165,390)(166,391)(167,392)(168,393)
(169,394)(170,395)(171,396)(172,379)(173,380)(174,381)(175,382)(176,383)
(177,384)(178,385)(179,386)(180,387)(181,397)(182,398)(183,399)(184,400)
(185,401)(186,402)(187,403)(188,404)(189,405)(190,415)(191,416)(192,417)
(193,418)(194,419)(195,420)(196,421)(197,422)(198,423)(199,406)(200,407)
(201,408)(202,409)(203,410)(204,411)(205,412)(206,413)(207,414)(208,424)
(209,425)(210,426)(211,427)(212,428)(213,429)(214,430)(215,431)(216,432)
(433,658)(434,659)(435,660)(436,661)(437,662)(438,663)(439,664)(440,665)
(441,666)(442,649)(443,650)(444,651)(445,652)(446,653)(447,654)(448,655)
(449,656)(450,657)(451,667)(452,668)(453,669)(454,670)(455,671)(456,672)
(457,673)(458,674)(459,675)(460,685)(461,686)(462,687)(463,688)(464,689)
(465,690)(466,691)(467,692)(468,693)(469,676)(470,677)(471,678)(472,679)
(473,680)(474,681)(475,682)(476,683)(477,684)(478,694)(479,695)(480,696)
(481,697)(482,698)(483,699)(484,700)(485,701)(486,702)(487,712)(488,713)
(489,714)(490,715)(491,716)(492,717)(493,718)(494,719)(495,720)(496,703)
(497,704)(498,705)(499,706)(500,707)(501,708)(502,709)(503,710)(504,711)
(505,721)(506,722)(507,723)(508,724)(509,725)(510,726)(511,727)(512,728)
(513,729)(514,739)(515,740)(516,741)(517,742)(518,743)(519,744)(520,745)
(521,746)(522,747)(523,730)(524,731)(525,732)(526,733)(527,734)(528,735)
(529,736)(530,737)(531,738)(532,748)(533,749)(534,750)(535,751)(536,752)
(537,753)(538,754)(539,755)(540,756)(541,766)(542,767)(543,768)(544,769)
(545,770)(546,771)(547,772)(548,773)(549,774)(550,757)(551,758)(552,759)
(553,760)(554,761)(555,762)(556,763)(557,764)(558,765)(559,775)(560,776)
(561,777)(562,778)(563,779)(564,780)(565,781)(566,782)(567,783)(568,793)
(569,794)(570,795)(571,796)(572,797)(573,798)(574,799)(575,800)(576,801)
(577,784)(578,785)(579,786)(580,787)(581,788)(582,789)(583,790)(584,791)
(585,792)(586,802)(587,803)(588,804)(589,805)(590,806)(591,807)(592,808)
(593,809)(594,810)(595,820)(596,821)(597,822)(598,823)(599,824)(600,825)
(601,826)(602,827)(603,828)(604,811)(605,812)(606,813)(607,814)(608,815)
(609,816)(610,817)(611,818)(612,819)(613,829)(614,830)(615,831)(616,832)
(617,833)(618,834)(619,835)(620,836)(621,837)(622,847)(623,848)(624,849)
(625,850)(626,851)(627,852)(628,853)(629,854)(630,855)(631,838)(632,839)
(633,840)(634,841)(635,842)(636,843)(637,844)(638,845)(639,846)(640,856)
(641,857)(642,858)(643,859)(644,860)(645,861)(646,862)(647,863)(648,864);;
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, s1*s2*s3*s2*s1*s2*s3*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
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)!(  1,163)(  2,165)(  3,164)(  4,169)(  5,171)(  6,170)(  7,166)
(  8,168)(  9,167)( 10,172)( 11,174)( 12,173)( 13,178)( 14,180)( 15,179)
( 16,175)( 17,177)( 18,176)( 19,181)( 20,183)( 21,182)( 22,187)( 23,189)
( 24,188)( 25,184)( 26,186)( 27,185)( 28,190)( 29,192)( 30,191)( 31,196)
( 32,198)( 33,197)( 34,193)( 35,195)( 36,194)( 37,199)( 38,201)( 39,200)
( 40,205)( 41,207)( 42,206)( 43,202)( 44,204)( 45,203)( 46,208)( 47,210)
( 48,209)( 49,214)( 50,216)( 51,215)( 52,211)( 53,213)( 54,212)( 55,136)
( 56,138)( 57,137)( 58,142)( 59,144)( 60,143)( 61,139)( 62,141)( 63,140)
( 64,145)( 65,147)( 66,146)( 67,151)( 68,153)( 69,152)( 70,148)( 71,150)
( 72,149)( 73,154)( 74,156)( 75,155)( 76,160)( 77,162)( 78,161)( 79,157)
( 80,159)( 81,158)( 82,109)( 83,111)( 84,110)( 85,115)( 86,117)( 87,116)
( 88,112)( 89,114)( 90,113)( 91,118)( 92,120)( 93,119)( 94,124)( 95,126)
( 96,125)( 97,121)( 98,123)( 99,122)(100,127)(101,129)(102,128)(103,133)
(104,135)(105,134)(106,130)(107,132)(108,131)(217,379)(218,381)(219,380)
(220,385)(221,387)(222,386)(223,382)(224,384)(225,383)(226,388)(227,390)
(228,389)(229,394)(230,396)(231,395)(232,391)(233,393)(234,392)(235,397)
(236,399)(237,398)(238,403)(239,405)(240,404)(241,400)(242,402)(243,401)
(244,406)(245,408)(246,407)(247,412)(248,414)(249,413)(250,409)(251,411)
(252,410)(253,415)(254,417)(255,416)(256,421)(257,423)(258,422)(259,418)
(260,420)(261,419)(262,424)(263,426)(264,425)(265,430)(266,432)(267,431)
(268,427)(269,429)(270,428)(271,352)(272,354)(273,353)(274,358)(275,360)
(276,359)(277,355)(278,357)(279,356)(280,361)(281,363)(282,362)(283,367)
(284,369)(285,368)(286,364)(287,366)(288,365)(289,370)(290,372)(291,371)
(292,376)(293,378)(294,377)(295,373)(296,375)(297,374)(298,325)(299,327)
(300,326)(301,331)(302,333)(303,332)(304,328)(305,330)(306,329)(307,334)
(308,336)(309,335)(310,340)(311,342)(312,341)(313,337)(314,339)(315,338)
(316,343)(317,345)(318,344)(319,349)(320,351)(321,350)(322,346)(323,348)
(324,347)(433,595)(434,597)(435,596)(436,601)(437,603)(438,602)(439,598)
(440,600)(441,599)(442,604)(443,606)(444,605)(445,610)(446,612)(447,611)
(448,607)(449,609)(450,608)(451,613)(452,615)(453,614)(454,619)(455,621)
(456,620)(457,616)(458,618)(459,617)(460,622)(461,624)(462,623)(463,628)
(464,630)(465,629)(466,625)(467,627)(468,626)(469,631)(470,633)(471,632)
(472,637)(473,639)(474,638)(475,634)(476,636)(477,635)(478,640)(479,642)
(480,641)(481,646)(482,648)(483,647)(484,643)(485,645)(486,644)(487,568)
(488,570)(489,569)(490,574)(491,576)(492,575)(493,571)(494,573)(495,572)
(496,577)(497,579)(498,578)(499,583)(500,585)(501,584)(502,580)(503,582)
(504,581)(505,586)(506,588)(507,587)(508,592)(509,594)(510,593)(511,589)
(512,591)(513,590)(514,541)(515,543)(516,542)(517,547)(518,549)(519,548)
(520,544)(521,546)(522,545)(523,550)(524,552)(525,551)(526,556)(527,558)
(528,557)(529,553)(530,555)(531,554)(532,559)(533,561)(534,560)(535,565)
(536,567)(537,566)(538,562)(539,564)(540,563)(649,811)(650,813)(651,812)
(652,817)(653,819)(654,818)(655,814)(656,816)(657,815)(658,820)(659,822)
(660,821)(661,826)(662,828)(663,827)(664,823)(665,825)(666,824)(667,829)
(668,831)(669,830)(670,835)(671,837)(672,836)(673,832)(674,834)(675,833)
(676,838)(677,840)(678,839)(679,844)(680,846)(681,845)(682,841)(683,843)
(684,842)(685,847)(686,849)(687,848)(688,853)(689,855)(690,854)(691,850)
(692,852)(693,851)(694,856)(695,858)(696,857)(697,862)(698,864)(699,863)
(700,859)(701,861)(702,860)(703,784)(704,786)(705,785)(706,790)(707,792)
(708,791)(709,787)(710,789)(711,788)(712,793)(713,795)(714,794)(715,799)
(716,801)(717,800)(718,796)(719,798)(720,797)(721,802)(722,804)(723,803)
(724,808)(725,810)(726,809)(727,805)(728,807)(729,806)(730,757)(731,759)
(732,758)(733,763)(734,765)(735,764)(736,760)(737,762)(738,761)(739,766)
(740,768)(741,767)(742,772)(743,774)(744,773)(745,769)(746,771)(747,770)
(748,775)(749,777)(750,776)(751,781)(752,783)(753,782)(754,778)(755,780)
(756,779);
s1 := Sym(864)!(  1,  4)(  3,  9)(  5,  8)( 10, 13)( 12, 18)( 14, 17)( 19, 22)
( 21, 27)( 23, 26)( 28, 31)( 30, 36)( 32, 35)( 37, 40)( 39, 45)( 41, 44)
( 46, 49)( 48, 54)( 50, 53)( 55, 85)( 56, 83)( 57, 90)( 58, 82)( 59, 89)
( 60, 87)( 61, 88)( 62, 86)( 63, 84)( 64, 94)( 65, 92)( 66, 99)( 67, 91)
( 68, 98)( 69, 96)( 70, 97)( 71, 95)( 72, 93)( 73,103)( 74,101)( 75,108)
( 76,100)( 77,107)( 78,105)( 79,106)( 80,104)( 81,102)(109,139)(110,137)
(111,144)(112,136)(113,143)(114,141)(115,142)(116,140)(117,138)(118,148)
(119,146)(120,153)(121,145)(122,152)(123,150)(124,151)(125,149)(126,147)
(127,157)(128,155)(129,162)(130,154)(131,161)(132,159)(133,160)(134,158)
(135,156)(163,166)(165,171)(167,170)(172,175)(174,180)(176,179)(181,184)
(183,189)(185,188)(190,193)(192,198)(194,197)(199,202)(201,207)(203,206)
(208,211)(210,216)(212,215)(217,220)(219,225)(221,224)(226,229)(228,234)
(230,233)(235,238)(237,243)(239,242)(244,247)(246,252)(248,251)(253,256)
(255,261)(257,260)(262,265)(264,270)(266,269)(271,301)(272,299)(273,306)
(274,298)(275,305)(276,303)(277,304)(278,302)(279,300)(280,310)(281,308)
(282,315)(283,307)(284,314)(285,312)(286,313)(287,311)(288,309)(289,319)
(290,317)(291,324)(292,316)(293,323)(294,321)(295,322)(296,320)(297,318)
(325,355)(326,353)(327,360)(328,352)(329,359)(330,357)(331,358)(332,356)
(333,354)(334,364)(335,362)(336,369)(337,361)(338,368)(339,366)(340,367)
(341,365)(342,363)(343,373)(344,371)(345,378)(346,370)(347,377)(348,375)
(349,376)(350,374)(351,372)(379,382)(381,387)(383,386)(388,391)(390,396)
(392,395)(397,400)(399,405)(401,404)(406,409)(408,414)(410,413)(415,418)
(417,423)(419,422)(424,427)(426,432)(428,431)(433,490)(434,488)(435,495)
(436,487)(437,494)(438,492)(439,493)(440,491)(441,489)(442,499)(443,497)
(444,504)(445,496)(446,503)(447,501)(448,502)(449,500)(450,498)(451,508)
(452,506)(453,513)(454,505)(455,512)(456,510)(457,511)(458,509)(459,507)
(460,517)(461,515)(462,522)(463,514)(464,521)(465,519)(466,520)(467,518)
(468,516)(469,526)(470,524)(471,531)(472,523)(473,530)(474,528)(475,529)
(476,527)(477,525)(478,535)(479,533)(480,540)(481,532)(482,539)(483,537)
(484,538)(485,536)(486,534)(541,625)(542,623)(543,630)(544,622)(545,629)
(546,627)(547,628)(548,626)(549,624)(550,634)(551,632)(552,639)(553,631)
(554,638)(555,636)(556,637)(557,635)(558,633)(559,643)(560,641)(561,648)
(562,640)(563,647)(564,645)(565,646)(566,644)(567,642)(568,598)(569,596)
(570,603)(571,595)(572,602)(573,600)(574,601)(575,599)(576,597)(577,607)
(578,605)(579,612)(580,604)(581,611)(582,609)(583,610)(584,608)(585,606)
(586,616)(587,614)(588,621)(589,613)(590,620)(591,618)(592,619)(593,617)
(594,615)(649,706)(650,704)(651,711)(652,703)(653,710)(654,708)(655,709)
(656,707)(657,705)(658,715)(659,713)(660,720)(661,712)(662,719)(663,717)
(664,718)(665,716)(666,714)(667,724)(668,722)(669,729)(670,721)(671,728)
(672,726)(673,727)(674,725)(675,723)(676,733)(677,731)(678,738)(679,730)
(680,737)(681,735)(682,736)(683,734)(684,732)(685,742)(686,740)(687,747)
(688,739)(689,746)(690,744)(691,745)(692,743)(693,741)(694,751)(695,749)
(696,756)(697,748)(698,755)(699,753)(700,754)(701,752)(702,750)(757,841)
(758,839)(759,846)(760,838)(761,845)(762,843)(763,844)(764,842)(765,840)
(766,850)(767,848)(768,855)(769,847)(770,854)(771,852)(772,853)(773,851)
(774,849)(775,859)(776,857)(777,864)(778,856)(779,863)(780,861)(781,862)
(782,860)(783,858)(784,814)(785,812)(786,819)(787,811)(788,818)(789,816)
(790,817)(791,815)(792,813)(793,823)(794,821)(795,828)(796,820)(797,827)
(798,825)(799,826)(800,824)(801,822)(802,832)(803,830)(804,837)(805,829)
(806,836)(807,834)(808,835)(809,833)(810,831);
s2 := Sym(864)!(  1,649)(  2,650)(  3,651)(  4,657)(  5,655)(  6,656)(  7,653)
(  8,654)(  9,652)( 10,667)( 11,668)( 12,669)( 13,675)( 14,673)( 15,674)
( 16,671)( 17,672)( 18,670)( 19,658)( 20,659)( 21,660)( 22,666)( 23,664)
( 24,665)( 25,662)( 26,663)( 27,661)( 28,676)( 29,677)( 30,678)( 31,684)
( 32,682)( 33,683)( 34,680)( 35,681)( 36,679)( 37,694)( 38,695)( 39,696)
( 40,702)( 41,700)( 42,701)( 43,698)( 44,699)( 45,697)( 46,685)( 47,686)
( 48,687)( 49,693)( 50,691)( 51,692)( 52,689)( 53,690)( 54,688)( 55,730)
( 56,731)( 57,732)( 58,738)( 59,736)( 60,737)( 61,734)( 62,735)( 63,733)
( 64,748)( 65,749)( 66,750)( 67,756)( 68,754)( 69,755)( 70,752)( 71,753)
( 72,751)( 73,739)( 74,740)( 75,741)( 76,747)( 77,745)( 78,746)( 79,743)
( 80,744)( 81,742)( 82,703)( 83,704)( 84,705)( 85,711)( 86,709)( 87,710)
( 88,707)( 89,708)( 90,706)( 91,721)( 92,722)( 93,723)( 94,729)( 95,727)
( 96,728)( 97,725)( 98,726)( 99,724)(100,712)(101,713)(102,714)(103,720)
(104,718)(105,719)(106,716)(107,717)(108,715)(109,784)(110,785)(111,786)
(112,792)(113,790)(114,791)(115,788)(116,789)(117,787)(118,802)(119,803)
(120,804)(121,810)(122,808)(123,809)(124,806)(125,807)(126,805)(127,793)
(128,794)(129,795)(130,801)(131,799)(132,800)(133,797)(134,798)(135,796)
(136,757)(137,758)(138,759)(139,765)(140,763)(141,764)(142,761)(143,762)
(144,760)(145,775)(146,776)(147,777)(148,783)(149,781)(150,782)(151,779)
(152,780)(153,778)(154,766)(155,767)(156,768)(157,774)(158,772)(159,773)
(160,770)(161,771)(162,769)(163,811)(164,812)(165,813)(166,819)(167,817)
(168,818)(169,815)(170,816)(171,814)(172,829)(173,830)(174,831)(175,837)
(176,835)(177,836)(178,833)(179,834)(180,832)(181,820)(182,821)(183,822)
(184,828)(185,826)(186,827)(187,824)(188,825)(189,823)(190,838)(191,839)
(192,840)(193,846)(194,844)(195,845)(196,842)(197,843)(198,841)(199,856)
(200,857)(201,858)(202,864)(203,862)(204,863)(205,860)(206,861)(207,859)
(208,847)(209,848)(210,849)(211,855)(212,853)(213,854)(214,851)(215,852)
(216,850)(217,433)(218,434)(219,435)(220,441)(221,439)(222,440)(223,437)
(224,438)(225,436)(226,451)(227,452)(228,453)(229,459)(230,457)(231,458)
(232,455)(233,456)(234,454)(235,442)(236,443)(237,444)(238,450)(239,448)
(240,449)(241,446)(242,447)(243,445)(244,460)(245,461)(246,462)(247,468)
(248,466)(249,467)(250,464)(251,465)(252,463)(253,478)(254,479)(255,480)
(256,486)(257,484)(258,485)(259,482)(260,483)(261,481)(262,469)(263,470)
(264,471)(265,477)(266,475)(267,476)(268,473)(269,474)(270,472)(271,514)
(272,515)(273,516)(274,522)(275,520)(276,521)(277,518)(278,519)(279,517)
(280,532)(281,533)(282,534)(283,540)(284,538)(285,539)(286,536)(287,537)
(288,535)(289,523)(290,524)(291,525)(292,531)(293,529)(294,530)(295,527)
(296,528)(297,526)(298,487)(299,488)(300,489)(301,495)(302,493)(303,494)
(304,491)(305,492)(306,490)(307,505)(308,506)(309,507)(310,513)(311,511)
(312,512)(313,509)(314,510)(315,508)(316,496)(317,497)(318,498)(319,504)
(320,502)(321,503)(322,500)(323,501)(324,499)(325,568)(326,569)(327,570)
(328,576)(329,574)(330,575)(331,572)(332,573)(333,571)(334,586)(335,587)
(336,588)(337,594)(338,592)(339,593)(340,590)(341,591)(342,589)(343,577)
(344,578)(345,579)(346,585)(347,583)(348,584)(349,581)(350,582)(351,580)
(352,541)(353,542)(354,543)(355,549)(356,547)(357,548)(358,545)(359,546)
(360,544)(361,559)(362,560)(363,561)(364,567)(365,565)(366,566)(367,563)
(368,564)(369,562)(370,550)(371,551)(372,552)(373,558)(374,556)(375,557)
(376,554)(377,555)(378,553)(379,595)(380,596)(381,597)(382,603)(383,601)
(384,602)(385,599)(386,600)(387,598)(388,613)(389,614)(390,615)(391,621)
(392,619)(393,620)(394,617)(395,618)(396,616)(397,604)(398,605)(399,606)
(400,612)(401,610)(402,611)(403,608)(404,609)(405,607)(406,622)(407,623)
(408,624)(409,630)(410,628)(411,629)(412,626)(413,627)(414,625)(415,640)
(416,641)(417,642)(418,648)(419,646)(420,647)(421,644)(422,645)(423,643)
(424,631)(425,632)(426,633)(427,639)(428,637)(429,638)(430,635)(431,636)
(432,634);
s3 := Sym(864)!(  1,226)(  2,227)(  3,228)(  4,229)(  5,230)(  6,231)(  7,232)
(  8,233)(  9,234)( 10,217)( 11,218)( 12,219)( 13,220)( 14,221)( 15,222)
( 16,223)( 17,224)( 18,225)( 19,235)( 20,236)( 21,237)( 22,238)( 23,239)
( 24,240)( 25,241)( 26,242)( 27,243)( 28,253)( 29,254)( 30,255)( 31,256)
( 32,257)( 33,258)( 34,259)( 35,260)( 36,261)( 37,244)( 38,245)( 39,246)
( 40,247)( 41,248)( 42,249)( 43,250)( 44,251)( 45,252)( 46,262)( 47,263)
( 48,264)( 49,265)( 50,266)( 51,267)( 52,268)( 53,269)( 54,270)( 55,280)
( 56,281)( 57,282)( 58,283)( 59,284)( 60,285)( 61,286)( 62,287)( 63,288)
( 64,271)( 65,272)( 66,273)( 67,274)( 68,275)( 69,276)( 70,277)( 71,278)
( 72,279)( 73,289)( 74,290)( 75,291)( 76,292)( 77,293)( 78,294)( 79,295)
( 80,296)( 81,297)( 82,307)( 83,308)( 84,309)( 85,310)( 86,311)( 87,312)
( 88,313)( 89,314)( 90,315)( 91,298)( 92,299)( 93,300)( 94,301)( 95,302)
( 96,303)( 97,304)( 98,305)( 99,306)(100,316)(101,317)(102,318)(103,319)
(104,320)(105,321)(106,322)(107,323)(108,324)(109,334)(110,335)(111,336)
(112,337)(113,338)(114,339)(115,340)(116,341)(117,342)(118,325)(119,326)
(120,327)(121,328)(122,329)(123,330)(124,331)(125,332)(126,333)(127,343)
(128,344)(129,345)(130,346)(131,347)(132,348)(133,349)(134,350)(135,351)
(136,361)(137,362)(138,363)(139,364)(140,365)(141,366)(142,367)(143,368)
(144,369)(145,352)(146,353)(147,354)(148,355)(149,356)(150,357)(151,358)
(152,359)(153,360)(154,370)(155,371)(156,372)(157,373)(158,374)(159,375)
(160,376)(161,377)(162,378)(163,388)(164,389)(165,390)(166,391)(167,392)
(168,393)(169,394)(170,395)(171,396)(172,379)(173,380)(174,381)(175,382)
(176,383)(177,384)(178,385)(179,386)(180,387)(181,397)(182,398)(183,399)
(184,400)(185,401)(186,402)(187,403)(188,404)(189,405)(190,415)(191,416)
(192,417)(193,418)(194,419)(195,420)(196,421)(197,422)(198,423)(199,406)
(200,407)(201,408)(202,409)(203,410)(204,411)(205,412)(206,413)(207,414)
(208,424)(209,425)(210,426)(211,427)(212,428)(213,429)(214,430)(215,431)
(216,432)(433,658)(434,659)(435,660)(436,661)(437,662)(438,663)(439,664)
(440,665)(441,666)(442,649)(443,650)(444,651)(445,652)(446,653)(447,654)
(448,655)(449,656)(450,657)(451,667)(452,668)(453,669)(454,670)(455,671)
(456,672)(457,673)(458,674)(459,675)(460,685)(461,686)(462,687)(463,688)
(464,689)(465,690)(466,691)(467,692)(468,693)(469,676)(470,677)(471,678)
(472,679)(473,680)(474,681)(475,682)(476,683)(477,684)(478,694)(479,695)
(480,696)(481,697)(482,698)(483,699)(484,700)(485,701)(486,702)(487,712)
(488,713)(489,714)(490,715)(491,716)(492,717)(493,718)(494,719)(495,720)
(496,703)(497,704)(498,705)(499,706)(500,707)(501,708)(502,709)(503,710)
(504,711)(505,721)(506,722)(507,723)(508,724)(509,725)(510,726)(511,727)
(512,728)(513,729)(514,739)(515,740)(516,741)(517,742)(518,743)(519,744)
(520,745)(521,746)(522,747)(523,730)(524,731)(525,732)(526,733)(527,734)
(528,735)(529,736)(530,737)(531,738)(532,748)(533,749)(534,750)(535,751)
(536,752)(537,753)(538,754)(539,755)(540,756)(541,766)(542,767)(543,768)
(544,769)(545,770)(546,771)(547,772)(548,773)(549,774)(550,757)(551,758)
(552,759)(553,760)(554,761)(555,762)(556,763)(557,764)(558,765)(559,775)
(560,776)(561,777)(562,778)(563,779)(564,780)(565,781)(566,782)(567,783)
(568,793)(569,794)(570,795)(571,796)(572,797)(573,798)(574,799)(575,800)
(576,801)(577,784)(578,785)(579,786)(580,787)(581,788)(582,789)(583,790)
(584,791)(585,792)(586,802)(587,803)(588,804)(589,805)(590,806)(591,807)
(592,808)(593,809)(594,810)(595,820)(596,821)(597,822)(598,823)(599,824)
(600,825)(601,826)(602,827)(603,828)(604,811)(605,812)(606,813)(607,814)
(608,815)(609,816)(610,817)(611,818)(612,819)(613,829)(614,830)(615,831)
(616,832)(617,833)(618,834)(619,835)(620,836)(621,837)(622,847)(623,848)
(624,849)(625,850)(626,851)(627,852)(628,853)(629,854)(630,855)(631,838)
(632,839)(633,840)(634,841)(635,842)(636,843)(637,844)(638,845)(639,846)
(640,856)(641,857)(642,858)(643,859)(644,860)(645,861)(646,862)(647,863)
(648,864);
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, 
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope