Polytope of Type {4,54,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,54,4}*1728d
if this polytope has a name.
Group : SmallGroup(1728,20783)
Rank : 4
Schlafli Type : {4,54,4}
Number of vertices, edges, etc : 4, 108, 108, 4
Order of s0s1s2s3 : 54
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-Orientable
Flat
Self-Dual
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 : {4,27,4}*864
3-fold quotients : {4,18,4}*576d
6-fold quotients : {4,9,4}*288
9-fold quotients : {4,6,4}*192d
18-fold quotients : {4,3,4}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)( 8, 16)
( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)
( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)
( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)
( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)
( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)
( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)
(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)
(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)
(145,153)(146,154)(147,155)(148,156)(149,157)(150,158)(151,159)(152,160)
(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)
(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)
(193,201)(194,202)(195,203)(196,204)(197,205)(198,206)(199,207)(200,208)
(209,217)(210,218)(211,219)(212,220)(213,221)(214,222)(215,223)(216,224)
(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)(232,240)
(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)(248,256)
(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)(264,272)
(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)(280,288)
(289,297)(290,298)(291,299)(292,300)(293,301)(294,302)(295,303)(296,304)
(305,313)(306,314)(307,315)(308,316)(309,317)(310,318)(311,319)(312,320)
(321,329)(322,330)(323,331)(324,332)(325,333)(326,334)(327,335)(328,336)
(337,345)(338,346)(339,347)(340,348)(341,349)(342,350)(343,351)(344,352)
(353,361)(354,362)(355,363)(356,364)(357,365)(358,366)(359,367)(360,368)
(369,377)(370,378)(371,379)(372,380)(373,381)(374,382)(375,383)(376,384)
(385,393)(386,394)(387,395)(388,396)(389,397)(390,398)(391,399)(392,400)
(401,409)(402,410)(403,411)(404,412)(405,413)(406,414)(407,415)(408,416)
(417,425)(418,426)(419,427)(420,428)(421,429)(422,430)(423,431)(424,432)
(433,441)(434,442)(435,443)(436,444)(437,445)(438,446)(439,447)(440,448)
(449,457)(450,458)(451,459)(452,460)(453,461)(454,462)(455,463)(456,464)
(465,473)(466,474)(467,475)(468,476)(469,477)(470,478)(471,479)(472,480)
(481,489)(482,490)(483,491)(484,492)(485,493)(486,494)(487,495)(488,496)
(497,505)(498,506)(499,507)(500,508)(501,509)(502,510)(503,511)(504,512)
(513,521)(514,522)(515,523)(516,524)(517,525)(518,526)(519,527)(520,528)
(529,537)(530,538)(531,539)(532,540)(533,541)(534,542)(535,543)(536,544)
(545,553)(546,554)(547,555)(548,556)(549,557)(550,558)(551,559)(552,560)
(561,569)(562,570)(563,571)(564,572)(565,573)(566,574)(567,575)(568,576)
(577,585)(578,586)(579,587)(580,588)(581,589)(582,590)(583,591)(584,592)
(593,601)(594,602)(595,603)(596,604)(597,605)(598,606)(599,607)(600,608)
(609,617)(610,618)(611,619)(612,620)(613,621)(614,622)(615,623)(616,624)
(625,633)(626,634)(627,635)(628,636)(629,637)(630,638)(631,639)(632,640)
(641,649)(642,650)(643,651)(644,652)(645,653)(646,654)(647,655)(648,656)
(657,665)(658,666)(659,667)(660,668)(661,669)(662,670)(663,671)(664,672)
(673,681)(674,682)(675,683)(676,684)(677,685)(678,686)(679,687)(680,688)
(689,697)(690,698)(691,699)(692,700)(693,701)(694,702)(695,703)(696,704)
(705,713)(706,714)(707,715)(708,716)(709,717)(710,718)(711,719)(712,720)
(721,729)(722,730)(723,731)(724,732)(725,733)(726,734)(727,735)(728,736)
(737,745)(738,746)(739,747)(740,748)(741,749)(742,750)(743,751)(744,752)
(753,761)(754,762)(755,763)(756,764)(757,765)(758,766)(759,767)(760,768)
(769,777)(770,778)(771,779)(772,780)(773,781)(774,782)(775,783)(776,784)
(785,793)(786,794)(787,795)(788,796)(789,797)(790,798)(791,799)(792,800)
(801,809)(802,810)(803,811)(804,812)(805,813)(806,814)(807,815)(808,816)
(817,825)(818,826)(819,827)(820,828)(821,829)(822,830)(823,831)(824,832)
(833,841)(834,842)(835,843)(836,844)(837,845)(838,846)(839,847)(840,848)
(849,857)(850,858)(851,859)(852,860)(853,861)(854,862)(855,863)(856,864);;
s1 := ( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 33)( 18, 34)
( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 45)( 26, 46)
( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 49,129)( 50,130)
( 51,132)( 52,131)( 53,133)( 54,134)( 55,136)( 56,135)( 57,141)( 58,142)
( 59,144)( 60,143)( 61,137)( 62,138)( 63,140)( 64,139)( 65,113)( 66,114)
( 67,116)( 68,115)( 69,117)( 70,118)( 71,120)( 72,119)( 73,125)( 74,126)
( 75,128)( 76,127)( 77,121)( 78,122)( 79,124)( 80,123)( 81, 97)( 82, 98)
( 83,100)( 84, 99)( 85,101)( 86,102)( 87,104)( 88,103)( 89,109)( 90,110)
( 91,112)( 92,111)( 93,105)( 94,106)( 95,108)( 96,107)(145,417)(146,418)
(147,420)(148,419)(149,421)(150,422)(151,424)(152,423)(153,429)(154,430)
(155,432)(156,431)(157,425)(158,426)(159,428)(160,427)(161,401)(162,402)
(163,404)(164,403)(165,405)(166,406)(167,408)(168,407)(169,413)(170,414)
(171,416)(172,415)(173,409)(174,410)(175,412)(176,411)(177,385)(178,386)
(179,388)(180,387)(181,389)(182,390)(183,392)(184,391)(185,397)(186,398)
(187,400)(188,399)(189,393)(190,394)(191,396)(192,395)(193,369)(194,370)
(195,372)(196,371)(197,373)(198,374)(199,376)(200,375)(201,381)(202,382)
(203,384)(204,383)(205,377)(206,378)(207,380)(208,379)(209,353)(210,354)
(211,356)(212,355)(213,357)(214,358)(215,360)(216,359)(217,365)(218,366)
(219,368)(220,367)(221,361)(222,362)(223,364)(224,363)(225,337)(226,338)
(227,340)(228,339)(229,341)(230,342)(231,344)(232,343)(233,349)(234,350)
(235,352)(236,351)(237,345)(238,346)(239,348)(240,347)(241,321)(242,322)
(243,324)(244,323)(245,325)(246,326)(247,328)(248,327)(249,333)(250,334)
(251,336)(252,335)(253,329)(254,330)(255,332)(256,331)(257,305)(258,306)
(259,308)(260,307)(261,309)(262,310)(263,312)(264,311)(265,317)(266,318)
(267,320)(268,319)(269,313)(270,314)(271,316)(272,315)(273,289)(274,290)
(275,292)(276,291)(277,293)(278,294)(279,296)(280,295)(281,301)(282,302)
(283,304)(284,303)(285,297)(286,298)(287,300)(288,299)(435,436)(439,440)
(441,445)(442,446)(443,448)(444,447)(449,465)(450,466)(451,468)(452,467)
(453,469)(454,470)(455,472)(456,471)(457,477)(458,478)(459,480)(460,479)
(461,473)(462,474)(463,476)(464,475)(481,561)(482,562)(483,564)(484,563)
(485,565)(486,566)(487,568)(488,567)(489,573)(490,574)(491,576)(492,575)
(493,569)(494,570)(495,572)(496,571)(497,545)(498,546)(499,548)(500,547)
(501,549)(502,550)(503,552)(504,551)(505,557)(506,558)(507,560)(508,559)
(509,553)(510,554)(511,556)(512,555)(513,529)(514,530)(515,532)(516,531)
(517,533)(518,534)(519,536)(520,535)(521,541)(522,542)(523,544)(524,543)
(525,537)(526,538)(527,540)(528,539)(577,849)(578,850)(579,852)(580,851)
(581,853)(582,854)(583,856)(584,855)(585,861)(586,862)(587,864)(588,863)
(589,857)(590,858)(591,860)(592,859)(593,833)(594,834)(595,836)(596,835)
(597,837)(598,838)(599,840)(600,839)(601,845)(602,846)(603,848)(604,847)
(605,841)(606,842)(607,844)(608,843)(609,817)(610,818)(611,820)(612,819)
(613,821)(614,822)(615,824)(616,823)(617,829)(618,830)(619,832)(620,831)
(621,825)(622,826)(623,828)(624,827)(625,801)(626,802)(627,804)(628,803)
(629,805)(630,806)(631,808)(632,807)(633,813)(634,814)(635,816)(636,815)
(637,809)(638,810)(639,812)(640,811)(641,785)(642,786)(643,788)(644,787)
(645,789)(646,790)(647,792)(648,791)(649,797)(650,798)(651,800)(652,799)
(653,793)(654,794)(655,796)(656,795)(657,769)(658,770)(659,772)(660,771)
(661,773)(662,774)(663,776)(664,775)(665,781)(666,782)(667,784)(668,783)
(669,777)(670,778)(671,780)(672,779)(673,753)(674,754)(675,756)(676,755)
(677,757)(678,758)(679,760)(680,759)(681,765)(682,766)(683,768)(684,767)
(685,761)(686,762)(687,764)(688,763)(689,737)(690,738)(691,740)(692,739)
(693,741)(694,742)(695,744)(696,743)(697,749)(698,750)(699,752)(700,751)
(701,745)(702,746)(703,748)(704,747)(705,721)(706,722)(707,724)(708,723)
(709,725)(710,726)(711,728)(712,727)(713,733)(714,734)(715,736)(716,735)
(717,729)(718,730)(719,732)(720,731);;
s2 := ( 1,577)( 2,580)( 3,579)( 4,578)( 5,589)( 6,592)( 7,591)( 8,590)
( 9,585)( 10,588)( 11,587)( 12,586)( 13,581)( 14,584)( 15,583)( 16,582)
( 17,609)( 18,612)( 19,611)( 20,610)( 21,621)( 22,624)( 23,623)( 24,622)
( 25,617)( 26,620)( 27,619)( 28,618)( 29,613)( 30,616)( 31,615)( 32,614)
( 33,593)( 34,596)( 35,595)( 36,594)( 37,605)( 38,608)( 39,607)( 40,606)
( 41,601)( 42,604)( 43,603)( 44,602)( 45,597)( 46,600)( 47,599)( 48,598)
( 49,705)( 50,708)( 51,707)( 52,706)( 53,717)( 54,720)( 55,719)( 56,718)
( 57,713)( 58,716)( 59,715)( 60,714)( 61,709)( 62,712)( 63,711)( 64,710)
( 65,689)( 66,692)( 67,691)( 68,690)( 69,701)( 70,704)( 71,703)( 72,702)
( 73,697)( 74,700)( 75,699)( 76,698)( 77,693)( 78,696)( 79,695)( 80,694)
( 81,673)( 82,676)( 83,675)( 84,674)( 85,685)( 86,688)( 87,687)( 88,686)
( 89,681)( 90,684)( 91,683)( 92,682)( 93,677)( 94,680)( 95,679)( 96,678)
( 97,657)( 98,660)( 99,659)(100,658)(101,669)(102,672)(103,671)(104,670)
(105,665)(106,668)(107,667)(108,666)(109,661)(110,664)(111,663)(112,662)
(113,641)(114,644)(115,643)(116,642)(117,653)(118,656)(119,655)(120,654)
(121,649)(122,652)(123,651)(124,650)(125,645)(126,648)(127,647)(128,646)
(129,625)(130,628)(131,627)(132,626)(133,637)(134,640)(135,639)(136,638)
(137,633)(138,636)(139,635)(140,634)(141,629)(142,632)(143,631)(144,630)
(145,433)(146,436)(147,435)(148,434)(149,445)(150,448)(151,447)(152,446)
(153,441)(154,444)(155,443)(156,442)(157,437)(158,440)(159,439)(160,438)
(161,465)(162,468)(163,467)(164,466)(165,477)(166,480)(167,479)(168,478)
(169,473)(170,476)(171,475)(172,474)(173,469)(174,472)(175,471)(176,470)
(177,449)(178,452)(179,451)(180,450)(181,461)(182,464)(183,463)(184,462)
(185,457)(186,460)(187,459)(188,458)(189,453)(190,456)(191,455)(192,454)
(193,561)(194,564)(195,563)(196,562)(197,573)(198,576)(199,575)(200,574)
(201,569)(202,572)(203,571)(204,570)(205,565)(206,568)(207,567)(208,566)
(209,545)(210,548)(211,547)(212,546)(213,557)(214,560)(215,559)(216,558)
(217,553)(218,556)(219,555)(220,554)(221,549)(222,552)(223,551)(224,550)
(225,529)(226,532)(227,531)(228,530)(229,541)(230,544)(231,543)(232,542)
(233,537)(234,540)(235,539)(236,538)(237,533)(238,536)(239,535)(240,534)
(241,513)(242,516)(243,515)(244,514)(245,525)(246,528)(247,527)(248,526)
(249,521)(250,524)(251,523)(252,522)(253,517)(254,520)(255,519)(256,518)
(257,497)(258,500)(259,499)(260,498)(261,509)(262,512)(263,511)(264,510)
(265,505)(266,508)(267,507)(268,506)(269,501)(270,504)(271,503)(272,502)
(273,481)(274,484)(275,483)(276,482)(277,493)(278,496)(279,495)(280,494)
(281,489)(282,492)(283,491)(284,490)(285,485)(286,488)(287,487)(288,486)
(289,849)(290,852)(291,851)(292,850)(293,861)(294,864)(295,863)(296,862)
(297,857)(298,860)(299,859)(300,858)(301,853)(302,856)(303,855)(304,854)
(305,833)(306,836)(307,835)(308,834)(309,845)(310,848)(311,847)(312,846)
(313,841)(314,844)(315,843)(316,842)(317,837)(318,840)(319,839)(320,838)
(321,817)(322,820)(323,819)(324,818)(325,829)(326,832)(327,831)(328,830)
(329,825)(330,828)(331,827)(332,826)(333,821)(334,824)(335,823)(336,822)
(337,801)(338,804)(339,803)(340,802)(341,813)(342,816)(343,815)(344,814)
(345,809)(346,812)(347,811)(348,810)(349,805)(350,808)(351,807)(352,806)
(353,785)(354,788)(355,787)(356,786)(357,797)(358,800)(359,799)(360,798)
(361,793)(362,796)(363,795)(364,794)(365,789)(366,792)(367,791)(368,790)
(369,769)(370,772)(371,771)(372,770)(373,781)(374,784)(375,783)(376,782)
(377,777)(378,780)(379,779)(380,778)(381,773)(382,776)(383,775)(384,774)
(385,753)(386,756)(387,755)(388,754)(389,765)(390,768)(391,767)(392,766)
(393,761)(394,764)(395,763)(396,762)(397,757)(398,760)(399,759)(400,758)
(401,737)(402,740)(403,739)(404,738)(405,749)(406,752)(407,751)(408,750)
(409,745)(410,748)(411,747)(412,746)(413,741)(414,744)(415,743)(416,742)
(417,721)(418,724)(419,723)(420,722)(421,733)(422,736)(423,735)(424,734)
(425,729)(426,732)(427,731)(428,730)(429,725)(430,728)(431,727)(432,726);;
s3 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)
( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)
( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)
( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)
( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)
(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)
(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)
(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)
(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)
(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)
(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)
(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)
(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)
(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)
(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272)
(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)(287,288)
(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)(303,304)
(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)(319,320)
(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)(335,336)
(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)(351,352)
(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)(367,368)
(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)(383,384)
(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)(399,400)
(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)(415,416)
(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)(431,432)
(433,434)(435,436)(437,438)(439,440)(441,442)(443,444)(445,446)(447,448)
(449,450)(451,452)(453,454)(455,456)(457,458)(459,460)(461,462)(463,464)
(465,466)(467,468)(469,470)(471,472)(473,474)(475,476)(477,478)(479,480)
(481,482)(483,484)(485,486)(487,488)(489,490)(491,492)(493,494)(495,496)
(497,498)(499,500)(501,502)(503,504)(505,506)(507,508)(509,510)(511,512)
(513,514)(515,516)(517,518)(519,520)(521,522)(523,524)(525,526)(527,528)
(529,530)(531,532)(533,534)(535,536)(537,538)(539,540)(541,542)(543,544)
(545,546)(547,548)(549,550)(551,552)(553,554)(555,556)(557,558)(559,560)
(561,562)(563,564)(565,566)(567,568)(569,570)(571,572)(573,574)(575,576)
(577,578)(579,580)(581,582)(583,584)(585,586)(587,588)(589,590)(591,592)
(593,594)(595,596)(597,598)(599,600)(601,602)(603,604)(605,606)(607,608)
(609,610)(611,612)(613,614)(615,616)(617,618)(619,620)(621,622)(623,624)
(625,626)(627,628)(629,630)(631,632)(633,634)(635,636)(637,638)(639,640)
(641,642)(643,644)(645,646)(647,648)(649,650)(651,652)(653,654)(655,656)
(657,658)(659,660)(661,662)(663,664)(665,666)(667,668)(669,670)(671,672)
(673,674)(675,676)(677,678)(679,680)(681,682)(683,684)(685,686)(687,688)
(689,690)(691,692)(693,694)(695,696)(697,698)(699,700)(701,702)(703,704)
(705,706)(707,708)(709,710)(711,712)(713,714)(715,716)(717,718)(719,720)
(721,722)(723,724)(725,726)(727,728)(729,730)(731,732)(733,734)(735,736)
(737,738)(739,740)(741,742)(743,744)(745,746)(747,748)(749,750)(751,752)
(753,754)(755,756)(757,758)(759,760)(761,762)(763,764)(765,766)(767,768)
(769,770)(771,772)(773,774)(775,776)(777,778)(779,780)(781,782)(783,784)
(785,786)(787,788)(789,790)(791,792)(793,794)(795,796)(797,798)(799,800)
(801,802)(803,804)(805,806)(807,808)(809,810)(811,812)(813,814)(815,816)
(817,818)(819,820)(821,822)(823,824)(825,826)(827,828)(829,830)(831,832)
(833,834)(835,836)(837,838)(839,840)(841,842)(843,844)(845,846)(847,848)
(849,850)(851,852)(853,854)(855,856)(857,858)(859,860)(861,862)(863,864);;
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, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s0*s1,
s3*s2*s1*s3*s2*s3*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)
( 8, 16)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)
( 24, 32)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)
( 40, 48)( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)
( 56, 64)( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)
( 72, 80)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)
( 88, 96)( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)
(104,112)(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)
(120,128)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)
(136,144)(145,153)(146,154)(147,155)(148,156)(149,157)(150,158)(151,159)
(152,160)(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)
(168,176)(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)
(184,192)(193,201)(194,202)(195,203)(196,204)(197,205)(198,206)(199,207)
(200,208)(209,217)(210,218)(211,219)(212,220)(213,221)(214,222)(215,223)
(216,224)(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)
(232,240)(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)
(248,256)(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)
(264,272)(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)
(280,288)(289,297)(290,298)(291,299)(292,300)(293,301)(294,302)(295,303)
(296,304)(305,313)(306,314)(307,315)(308,316)(309,317)(310,318)(311,319)
(312,320)(321,329)(322,330)(323,331)(324,332)(325,333)(326,334)(327,335)
(328,336)(337,345)(338,346)(339,347)(340,348)(341,349)(342,350)(343,351)
(344,352)(353,361)(354,362)(355,363)(356,364)(357,365)(358,366)(359,367)
(360,368)(369,377)(370,378)(371,379)(372,380)(373,381)(374,382)(375,383)
(376,384)(385,393)(386,394)(387,395)(388,396)(389,397)(390,398)(391,399)
(392,400)(401,409)(402,410)(403,411)(404,412)(405,413)(406,414)(407,415)
(408,416)(417,425)(418,426)(419,427)(420,428)(421,429)(422,430)(423,431)
(424,432)(433,441)(434,442)(435,443)(436,444)(437,445)(438,446)(439,447)
(440,448)(449,457)(450,458)(451,459)(452,460)(453,461)(454,462)(455,463)
(456,464)(465,473)(466,474)(467,475)(468,476)(469,477)(470,478)(471,479)
(472,480)(481,489)(482,490)(483,491)(484,492)(485,493)(486,494)(487,495)
(488,496)(497,505)(498,506)(499,507)(500,508)(501,509)(502,510)(503,511)
(504,512)(513,521)(514,522)(515,523)(516,524)(517,525)(518,526)(519,527)
(520,528)(529,537)(530,538)(531,539)(532,540)(533,541)(534,542)(535,543)
(536,544)(545,553)(546,554)(547,555)(548,556)(549,557)(550,558)(551,559)
(552,560)(561,569)(562,570)(563,571)(564,572)(565,573)(566,574)(567,575)
(568,576)(577,585)(578,586)(579,587)(580,588)(581,589)(582,590)(583,591)
(584,592)(593,601)(594,602)(595,603)(596,604)(597,605)(598,606)(599,607)
(600,608)(609,617)(610,618)(611,619)(612,620)(613,621)(614,622)(615,623)
(616,624)(625,633)(626,634)(627,635)(628,636)(629,637)(630,638)(631,639)
(632,640)(641,649)(642,650)(643,651)(644,652)(645,653)(646,654)(647,655)
(648,656)(657,665)(658,666)(659,667)(660,668)(661,669)(662,670)(663,671)
(664,672)(673,681)(674,682)(675,683)(676,684)(677,685)(678,686)(679,687)
(680,688)(689,697)(690,698)(691,699)(692,700)(693,701)(694,702)(695,703)
(696,704)(705,713)(706,714)(707,715)(708,716)(709,717)(710,718)(711,719)
(712,720)(721,729)(722,730)(723,731)(724,732)(725,733)(726,734)(727,735)
(728,736)(737,745)(738,746)(739,747)(740,748)(741,749)(742,750)(743,751)
(744,752)(753,761)(754,762)(755,763)(756,764)(757,765)(758,766)(759,767)
(760,768)(769,777)(770,778)(771,779)(772,780)(773,781)(774,782)(775,783)
(776,784)(785,793)(786,794)(787,795)(788,796)(789,797)(790,798)(791,799)
(792,800)(801,809)(802,810)(803,811)(804,812)(805,813)(806,814)(807,815)
(808,816)(817,825)(818,826)(819,827)(820,828)(821,829)(822,830)(823,831)
(824,832)(833,841)(834,842)(835,843)(836,844)(837,845)(838,846)(839,847)
(840,848)(849,857)(850,858)(851,859)(852,860)(853,861)(854,862)(855,863)
(856,864);
s1 := Sym(864)!( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 33)
( 18, 34)( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 45)
( 26, 46)( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 49,129)
( 50,130)( 51,132)( 52,131)( 53,133)( 54,134)( 55,136)( 56,135)( 57,141)
( 58,142)( 59,144)( 60,143)( 61,137)( 62,138)( 63,140)( 64,139)( 65,113)
( 66,114)( 67,116)( 68,115)( 69,117)( 70,118)( 71,120)( 72,119)( 73,125)
( 74,126)( 75,128)( 76,127)( 77,121)( 78,122)( 79,124)( 80,123)( 81, 97)
( 82, 98)( 83,100)( 84, 99)( 85,101)( 86,102)( 87,104)( 88,103)( 89,109)
( 90,110)( 91,112)( 92,111)( 93,105)( 94,106)( 95,108)( 96,107)(145,417)
(146,418)(147,420)(148,419)(149,421)(150,422)(151,424)(152,423)(153,429)
(154,430)(155,432)(156,431)(157,425)(158,426)(159,428)(160,427)(161,401)
(162,402)(163,404)(164,403)(165,405)(166,406)(167,408)(168,407)(169,413)
(170,414)(171,416)(172,415)(173,409)(174,410)(175,412)(176,411)(177,385)
(178,386)(179,388)(180,387)(181,389)(182,390)(183,392)(184,391)(185,397)
(186,398)(187,400)(188,399)(189,393)(190,394)(191,396)(192,395)(193,369)
(194,370)(195,372)(196,371)(197,373)(198,374)(199,376)(200,375)(201,381)
(202,382)(203,384)(204,383)(205,377)(206,378)(207,380)(208,379)(209,353)
(210,354)(211,356)(212,355)(213,357)(214,358)(215,360)(216,359)(217,365)
(218,366)(219,368)(220,367)(221,361)(222,362)(223,364)(224,363)(225,337)
(226,338)(227,340)(228,339)(229,341)(230,342)(231,344)(232,343)(233,349)
(234,350)(235,352)(236,351)(237,345)(238,346)(239,348)(240,347)(241,321)
(242,322)(243,324)(244,323)(245,325)(246,326)(247,328)(248,327)(249,333)
(250,334)(251,336)(252,335)(253,329)(254,330)(255,332)(256,331)(257,305)
(258,306)(259,308)(260,307)(261,309)(262,310)(263,312)(264,311)(265,317)
(266,318)(267,320)(268,319)(269,313)(270,314)(271,316)(272,315)(273,289)
(274,290)(275,292)(276,291)(277,293)(278,294)(279,296)(280,295)(281,301)
(282,302)(283,304)(284,303)(285,297)(286,298)(287,300)(288,299)(435,436)
(439,440)(441,445)(442,446)(443,448)(444,447)(449,465)(450,466)(451,468)
(452,467)(453,469)(454,470)(455,472)(456,471)(457,477)(458,478)(459,480)
(460,479)(461,473)(462,474)(463,476)(464,475)(481,561)(482,562)(483,564)
(484,563)(485,565)(486,566)(487,568)(488,567)(489,573)(490,574)(491,576)
(492,575)(493,569)(494,570)(495,572)(496,571)(497,545)(498,546)(499,548)
(500,547)(501,549)(502,550)(503,552)(504,551)(505,557)(506,558)(507,560)
(508,559)(509,553)(510,554)(511,556)(512,555)(513,529)(514,530)(515,532)
(516,531)(517,533)(518,534)(519,536)(520,535)(521,541)(522,542)(523,544)
(524,543)(525,537)(526,538)(527,540)(528,539)(577,849)(578,850)(579,852)
(580,851)(581,853)(582,854)(583,856)(584,855)(585,861)(586,862)(587,864)
(588,863)(589,857)(590,858)(591,860)(592,859)(593,833)(594,834)(595,836)
(596,835)(597,837)(598,838)(599,840)(600,839)(601,845)(602,846)(603,848)
(604,847)(605,841)(606,842)(607,844)(608,843)(609,817)(610,818)(611,820)
(612,819)(613,821)(614,822)(615,824)(616,823)(617,829)(618,830)(619,832)
(620,831)(621,825)(622,826)(623,828)(624,827)(625,801)(626,802)(627,804)
(628,803)(629,805)(630,806)(631,808)(632,807)(633,813)(634,814)(635,816)
(636,815)(637,809)(638,810)(639,812)(640,811)(641,785)(642,786)(643,788)
(644,787)(645,789)(646,790)(647,792)(648,791)(649,797)(650,798)(651,800)
(652,799)(653,793)(654,794)(655,796)(656,795)(657,769)(658,770)(659,772)
(660,771)(661,773)(662,774)(663,776)(664,775)(665,781)(666,782)(667,784)
(668,783)(669,777)(670,778)(671,780)(672,779)(673,753)(674,754)(675,756)
(676,755)(677,757)(678,758)(679,760)(680,759)(681,765)(682,766)(683,768)
(684,767)(685,761)(686,762)(687,764)(688,763)(689,737)(690,738)(691,740)
(692,739)(693,741)(694,742)(695,744)(696,743)(697,749)(698,750)(699,752)
(700,751)(701,745)(702,746)(703,748)(704,747)(705,721)(706,722)(707,724)
(708,723)(709,725)(710,726)(711,728)(712,727)(713,733)(714,734)(715,736)
(716,735)(717,729)(718,730)(719,732)(720,731);
s2 := Sym(864)!( 1,577)( 2,580)( 3,579)( 4,578)( 5,589)( 6,592)( 7,591)
( 8,590)( 9,585)( 10,588)( 11,587)( 12,586)( 13,581)( 14,584)( 15,583)
( 16,582)( 17,609)( 18,612)( 19,611)( 20,610)( 21,621)( 22,624)( 23,623)
( 24,622)( 25,617)( 26,620)( 27,619)( 28,618)( 29,613)( 30,616)( 31,615)
( 32,614)( 33,593)( 34,596)( 35,595)( 36,594)( 37,605)( 38,608)( 39,607)
( 40,606)( 41,601)( 42,604)( 43,603)( 44,602)( 45,597)( 46,600)( 47,599)
( 48,598)( 49,705)( 50,708)( 51,707)( 52,706)( 53,717)( 54,720)( 55,719)
( 56,718)( 57,713)( 58,716)( 59,715)( 60,714)( 61,709)( 62,712)( 63,711)
( 64,710)( 65,689)( 66,692)( 67,691)( 68,690)( 69,701)( 70,704)( 71,703)
( 72,702)( 73,697)( 74,700)( 75,699)( 76,698)( 77,693)( 78,696)( 79,695)
( 80,694)( 81,673)( 82,676)( 83,675)( 84,674)( 85,685)( 86,688)( 87,687)
( 88,686)( 89,681)( 90,684)( 91,683)( 92,682)( 93,677)( 94,680)( 95,679)
( 96,678)( 97,657)( 98,660)( 99,659)(100,658)(101,669)(102,672)(103,671)
(104,670)(105,665)(106,668)(107,667)(108,666)(109,661)(110,664)(111,663)
(112,662)(113,641)(114,644)(115,643)(116,642)(117,653)(118,656)(119,655)
(120,654)(121,649)(122,652)(123,651)(124,650)(125,645)(126,648)(127,647)
(128,646)(129,625)(130,628)(131,627)(132,626)(133,637)(134,640)(135,639)
(136,638)(137,633)(138,636)(139,635)(140,634)(141,629)(142,632)(143,631)
(144,630)(145,433)(146,436)(147,435)(148,434)(149,445)(150,448)(151,447)
(152,446)(153,441)(154,444)(155,443)(156,442)(157,437)(158,440)(159,439)
(160,438)(161,465)(162,468)(163,467)(164,466)(165,477)(166,480)(167,479)
(168,478)(169,473)(170,476)(171,475)(172,474)(173,469)(174,472)(175,471)
(176,470)(177,449)(178,452)(179,451)(180,450)(181,461)(182,464)(183,463)
(184,462)(185,457)(186,460)(187,459)(188,458)(189,453)(190,456)(191,455)
(192,454)(193,561)(194,564)(195,563)(196,562)(197,573)(198,576)(199,575)
(200,574)(201,569)(202,572)(203,571)(204,570)(205,565)(206,568)(207,567)
(208,566)(209,545)(210,548)(211,547)(212,546)(213,557)(214,560)(215,559)
(216,558)(217,553)(218,556)(219,555)(220,554)(221,549)(222,552)(223,551)
(224,550)(225,529)(226,532)(227,531)(228,530)(229,541)(230,544)(231,543)
(232,542)(233,537)(234,540)(235,539)(236,538)(237,533)(238,536)(239,535)
(240,534)(241,513)(242,516)(243,515)(244,514)(245,525)(246,528)(247,527)
(248,526)(249,521)(250,524)(251,523)(252,522)(253,517)(254,520)(255,519)
(256,518)(257,497)(258,500)(259,499)(260,498)(261,509)(262,512)(263,511)
(264,510)(265,505)(266,508)(267,507)(268,506)(269,501)(270,504)(271,503)
(272,502)(273,481)(274,484)(275,483)(276,482)(277,493)(278,496)(279,495)
(280,494)(281,489)(282,492)(283,491)(284,490)(285,485)(286,488)(287,487)
(288,486)(289,849)(290,852)(291,851)(292,850)(293,861)(294,864)(295,863)
(296,862)(297,857)(298,860)(299,859)(300,858)(301,853)(302,856)(303,855)
(304,854)(305,833)(306,836)(307,835)(308,834)(309,845)(310,848)(311,847)
(312,846)(313,841)(314,844)(315,843)(316,842)(317,837)(318,840)(319,839)
(320,838)(321,817)(322,820)(323,819)(324,818)(325,829)(326,832)(327,831)
(328,830)(329,825)(330,828)(331,827)(332,826)(333,821)(334,824)(335,823)
(336,822)(337,801)(338,804)(339,803)(340,802)(341,813)(342,816)(343,815)
(344,814)(345,809)(346,812)(347,811)(348,810)(349,805)(350,808)(351,807)
(352,806)(353,785)(354,788)(355,787)(356,786)(357,797)(358,800)(359,799)
(360,798)(361,793)(362,796)(363,795)(364,794)(365,789)(366,792)(367,791)
(368,790)(369,769)(370,772)(371,771)(372,770)(373,781)(374,784)(375,783)
(376,782)(377,777)(378,780)(379,779)(380,778)(381,773)(382,776)(383,775)
(384,774)(385,753)(386,756)(387,755)(388,754)(389,765)(390,768)(391,767)
(392,766)(393,761)(394,764)(395,763)(396,762)(397,757)(398,760)(399,759)
(400,758)(401,737)(402,740)(403,739)(404,738)(405,749)(406,752)(407,751)
(408,750)(409,745)(410,748)(411,747)(412,746)(413,741)(414,744)(415,743)
(416,742)(417,721)(418,724)(419,723)(420,722)(421,733)(422,736)(423,735)
(424,734)(425,729)(426,732)(427,731)(428,730)(429,725)(430,728)(431,727)
(432,726);
s3 := Sym(864)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)
( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)
( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)
( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)
( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)
( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)
( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)
(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)
(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)
(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)
(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)
(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)
(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)
(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)
(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)
(239,240)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)
(255,256)(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)
(271,272)(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)
(287,288)(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)
(303,304)(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)
(319,320)(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)
(335,336)(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)
(351,352)(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)
(367,368)(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)
(383,384)(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)
(399,400)(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)
(415,416)(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)
(431,432)(433,434)(435,436)(437,438)(439,440)(441,442)(443,444)(445,446)
(447,448)(449,450)(451,452)(453,454)(455,456)(457,458)(459,460)(461,462)
(463,464)(465,466)(467,468)(469,470)(471,472)(473,474)(475,476)(477,478)
(479,480)(481,482)(483,484)(485,486)(487,488)(489,490)(491,492)(493,494)
(495,496)(497,498)(499,500)(501,502)(503,504)(505,506)(507,508)(509,510)
(511,512)(513,514)(515,516)(517,518)(519,520)(521,522)(523,524)(525,526)
(527,528)(529,530)(531,532)(533,534)(535,536)(537,538)(539,540)(541,542)
(543,544)(545,546)(547,548)(549,550)(551,552)(553,554)(555,556)(557,558)
(559,560)(561,562)(563,564)(565,566)(567,568)(569,570)(571,572)(573,574)
(575,576)(577,578)(579,580)(581,582)(583,584)(585,586)(587,588)(589,590)
(591,592)(593,594)(595,596)(597,598)(599,600)(601,602)(603,604)(605,606)
(607,608)(609,610)(611,612)(613,614)(615,616)(617,618)(619,620)(621,622)
(623,624)(625,626)(627,628)(629,630)(631,632)(633,634)(635,636)(637,638)
(639,640)(641,642)(643,644)(645,646)(647,648)(649,650)(651,652)(653,654)
(655,656)(657,658)(659,660)(661,662)(663,664)(665,666)(667,668)(669,670)
(671,672)(673,674)(675,676)(677,678)(679,680)(681,682)(683,684)(685,686)
(687,688)(689,690)(691,692)(693,694)(695,696)(697,698)(699,700)(701,702)
(703,704)(705,706)(707,708)(709,710)(711,712)(713,714)(715,716)(717,718)
(719,720)(721,722)(723,724)(725,726)(727,728)(729,730)(731,732)(733,734)
(735,736)(737,738)(739,740)(741,742)(743,744)(745,746)(747,748)(749,750)
(751,752)(753,754)(755,756)(757,758)(759,760)(761,762)(763,764)(765,766)
(767,768)(769,770)(771,772)(773,774)(775,776)(777,778)(779,780)(781,782)
(783,784)(785,786)(787,788)(789,790)(791,792)(793,794)(795,796)(797,798)
(799,800)(801,802)(803,804)(805,806)(807,808)(809,810)(811,812)(813,814)
(815,816)(817,818)(819,820)(821,822)(823,824)(825,826)(827,828)(829,830)
(831,832)(833,834)(835,836)(837,838)(839,840)(841,842)(843,844)(845,846)
(847,848)(849,850)(851,852)(853,854)(855,856)(857,858)(859,860)(861,862)
(863,864);
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,
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s0*s1, s3*s2*s1*s3*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope