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Polytope of Type {4,6,36}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,36}*1728a
Also Known As : {{4,6|2},{6,36|2}}. if this polytope has another name.
Group : SmallGroup(1728,14196)
Rank : 4
Schlafli Type : {4,6,36}
Number of vertices, edges, etc : 4, 12, 108, 36
Order of s0s1s2s3 : 36
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 : {2,6,36}*864a, {4,6,18}*864a
   3-fold quotients : {4,2,36}*576, {4,6,12}*576a
   4-fold quotients : {2,6,18}*432a
   6-fold quotients : {2,2,36}*288, {4,2,18}*288, {2,6,12}*288a, {4,6,6}*288a
   9-fold quotients : {4,2,12}*192, {4,6,4}*192a
   12-fold quotients : {4,2,9}*144, {2,2,18}*144, {2,6,6}*144a
   18-fold quotients : {2,2,12}*96, {2,6,4}*96a, {4,2,6}*96, {4,6,2}*96a
   24-fold quotients : {2,2,9}*72
   27-fold quotients : {4,2,4}*64
   36-fold quotients : {4,2,3}*48, {2,2,6}*48, {2,6,2}*48
   54-fold quotients : {2,2,4}*32, {4,2,2}*32
   72-fold quotients : {2,2,3}*24, {2,3,2}*24
   108-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,217)(  2,218)(  3,219)(  4,220)(  5,221)(  6,222)(  7,223)(  8,224)
(  9,225)( 10,226)( 11,227)( 12,228)( 13,229)( 14,230)( 15,231)( 16,232)
( 17,233)( 18,234)( 19,235)( 20,236)( 21,237)( 22,238)( 23,239)( 24,240)
( 25,241)( 26,242)( 27,243)( 28,244)( 29,245)( 30,246)( 31,247)( 32,248)
( 33,249)( 34,250)( 35,251)( 36,252)( 37,253)( 38,254)( 39,255)( 40,256)
( 41,257)( 42,258)( 43,259)( 44,260)( 45,261)( 46,262)( 47,263)( 48,264)
( 49,265)( 50,266)( 51,267)( 52,268)( 53,269)( 54,270)( 55,271)( 56,272)
( 57,273)( 58,274)( 59,275)( 60,276)( 61,277)( 62,278)( 63,279)( 64,280)
( 65,281)( 66,282)( 67,283)( 68,284)( 69,285)( 70,286)( 71,287)( 72,288)
( 73,289)( 74,290)( 75,291)( 76,292)( 77,293)( 78,294)( 79,295)( 80,296)
( 81,297)( 82,298)( 83,299)( 84,300)( 85,301)( 86,302)( 87,303)( 88,304)
( 89,305)( 90,306)( 91,307)( 92,308)( 93,309)( 94,310)( 95,311)( 96,312)
( 97,313)( 98,314)( 99,315)(100,316)(101,317)(102,318)(103,319)(104,320)
(105,321)(106,322)(107,323)(108,324)(109,379)(110,380)(111,381)(112,382)
(113,383)(114,384)(115,385)(116,386)(117,387)(118,388)(119,389)(120,390)
(121,391)(122,392)(123,393)(124,394)(125,395)(126,396)(127,397)(128,398)
(129,399)(130,400)(131,401)(132,402)(133,403)(134,404)(135,405)(136,406)
(137,407)(138,408)(139,409)(140,410)(141,411)(142,412)(143,413)(144,414)
(145,415)(146,416)(147,417)(148,418)(149,419)(150,420)(151,421)(152,422)
(153,423)(154,424)(155,425)(156,426)(157,427)(158,428)(159,429)(160,430)
(161,431)(162,432)(163,325)(164,326)(165,327)(166,328)(167,329)(168,330)
(169,331)(170,332)(171,333)(172,334)(173,335)(174,336)(175,337)(176,338)
(177,339)(178,340)(179,341)(180,342)(181,343)(182,344)(183,345)(184,346)
(185,347)(186,348)(187,349)(188,350)(189,351)(190,352)(191,353)(192,354)
(193,355)(194,356)(195,357)(196,358)(197,359)(198,360)(199,361)(200,362)
(201,363)(202,364)(203,365)(204,366)(205,367)(206,368)(207,369)(208,370)
(209,371)(210,372)(211,373)(212,374)(213,375)(214,376)(215,377)(216,378)
(433,649)(434,650)(435,651)(436,652)(437,653)(438,654)(439,655)(440,656)
(441,657)(442,658)(443,659)(444,660)(445,661)(446,662)(447,663)(448,664)
(449,665)(450,666)(451,667)(452,668)(453,669)(454,670)(455,671)(456,672)
(457,673)(458,674)(459,675)(460,676)(461,677)(462,678)(463,679)(464,680)
(465,681)(466,682)(467,683)(468,684)(469,685)(470,686)(471,687)(472,688)
(473,689)(474,690)(475,691)(476,692)(477,693)(478,694)(479,695)(480,696)
(481,697)(482,698)(483,699)(484,700)(485,701)(486,702)(487,703)(488,704)
(489,705)(490,706)(491,707)(492,708)(493,709)(494,710)(495,711)(496,712)
(497,713)(498,714)(499,715)(500,716)(501,717)(502,718)(503,719)(504,720)
(505,721)(506,722)(507,723)(508,724)(509,725)(510,726)(511,727)(512,728)
(513,729)(514,730)(515,731)(516,732)(517,733)(518,734)(519,735)(520,736)
(521,737)(522,738)(523,739)(524,740)(525,741)(526,742)(527,743)(528,744)
(529,745)(530,746)(531,747)(532,748)(533,749)(534,750)(535,751)(536,752)
(537,753)(538,754)(539,755)(540,756)(541,811)(542,812)(543,813)(544,814)
(545,815)(546,816)(547,817)(548,818)(549,819)(550,820)(551,821)(552,822)
(553,823)(554,824)(555,825)(556,826)(557,827)(558,828)(559,829)(560,830)
(561,831)(562,832)(563,833)(564,834)(565,835)(566,836)(567,837)(568,838)
(569,839)(570,840)(571,841)(572,842)(573,843)(574,844)(575,845)(576,846)
(577,847)(578,848)(579,849)(580,850)(581,851)(582,852)(583,853)(584,854)
(585,855)(586,856)(587,857)(588,858)(589,859)(590,860)(591,861)(592,862)
(593,863)(594,864)(595,757)(596,758)(597,759)(598,760)(599,761)(600,762)
(601,763)(602,764)(603,765)(604,766)(605,767)(606,768)(607,769)(608,770)
(609,771)(610,772)(611,773)(612,774)(613,775)(614,776)(615,777)(616,778)
(617,779)(618,780)(619,781)(620,782)(621,783)(622,784)(623,785)(624,786)
(625,787)(626,788)(627,789)(628,790)(629,791)(630,792)(631,793)(632,794)
(633,795)(634,796)(635,797)(636,798)(637,799)(638,800)(639,801)(640,802)
(641,803)(642,804)(643,805)(644,806)(645,807)(646,808)(647,809)(648,810);;
s1 := (  1,541)(  2,542)(  3,543)(  4,547)(  5,548)(  6,549)(  7,544)(  8,545)
(  9,546)( 10,550)( 11,551)( 12,552)( 13,556)( 14,557)( 15,558)( 16,553)
( 17,554)( 18,555)( 19,559)( 20,560)( 21,561)( 22,565)( 23,566)( 24,567)
( 25,562)( 26,563)( 27,564)( 28,568)( 29,569)( 30,570)( 31,574)( 32,575)
( 33,576)( 34,571)( 35,572)( 36,573)( 37,577)( 38,578)( 39,579)( 40,583)
( 41,584)( 42,585)( 43,580)( 44,581)( 45,582)( 46,586)( 47,587)( 48,588)
( 49,592)( 50,593)( 51,594)( 52,589)( 53,590)( 54,591)( 55,595)( 56,596)
( 57,597)( 58,601)( 59,602)( 60,603)( 61,598)( 62,599)( 63,600)( 64,604)
( 65,605)( 66,606)( 67,610)( 68,611)( 69,612)( 70,607)( 71,608)( 72,609)
( 73,613)( 74,614)( 75,615)( 76,619)( 77,620)( 78,621)( 79,616)( 80,617)
( 81,618)( 82,622)( 83,623)( 84,624)( 85,628)( 86,629)( 87,630)( 88,625)
( 89,626)( 90,627)( 91,631)( 92,632)( 93,633)( 94,637)( 95,638)( 96,639)
( 97,634)( 98,635)( 99,636)(100,640)(101,641)(102,642)(103,646)(104,647)
(105,648)(106,643)(107,644)(108,645)(109,460)(110,461)(111,462)(112,466)
(113,467)(114,468)(115,463)(116,464)(117,465)(118,469)(119,470)(120,471)
(121,475)(122,476)(123,477)(124,472)(125,473)(126,474)(127,478)(128,479)
(129,480)(130,484)(131,485)(132,486)(133,481)(134,482)(135,483)(136,433)
(137,434)(138,435)(139,439)(140,440)(141,441)(142,436)(143,437)(144,438)
(145,442)(146,443)(147,444)(148,448)(149,449)(150,450)(151,445)(152,446)
(153,447)(154,451)(155,452)(156,453)(157,457)(158,458)(159,459)(160,454)
(161,455)(162,456)(163,514)(164,515)(165,516)(166,520)(167,521)(168,522)
(169,517)(170,518)(171,519)(172,523)(173,524)(174,525)(175,529)(176,530)
(177,531)(178,526)(179,527)(180,528)(181,532)(182,533)(183,534)(184,538)
(185,539)(186,540)(187,535)(188,536)(189,537)(190,487)(191,488)(192,489)
(193,493)(194,494)(195,495)(196,490)(197,491)(198,492)(199,496)(200,497)
(201,498)(202,502)(203,503)(204,504)(205,499)(206,500)(207,501)(208,505)
(209,506)(210,507)(211,511)(212,512)(213,513)(214,508)(215,509)(216,510)
(217,757)(218,758)(219,759)(220,763)(221,764)(222,765)(223,760)(224,761)
(225,762)(226,766)(227,767)(228,768)(229,772)(230,773)(231,774)(232,769)
(233,770)(234,771)(235,775)(236,776)(237,777)(238,781)(239,782)(240,783)
(241,778)(242,779)(243,780)(244,784)(245,785)(246,786)(247,790)(248,791)
(249,792)(250,787)(251,788)(252,789)(253,793)(254,794)(255,795)(256,799)
(257,800)(258,801)(259,796)(260,797)(261,798)(262,802)(263,803)(264,804)
(265,808)(266,809)(267,810)(268,805)(269,806)(270,807)(271,811)(272,812)
(273,813)(274,817)(275,818)(276,819)(277,814)(278,815)(279,816)(280,820)
(281,821)(282,822)(283,826)(284,827)(285,828)(286,823)(287,824)(288,825)
(289,829)(290,830)(291,831)(292,835)(293,836)(294,837)(295,832)(296,833)
(297,834)(298,838)(299,839)(300,840)(301,844)(302,845)(303,846)(304,841)
(305,842)(306,843)(307,847)(308,848)(309,849)(310,853)(311,854)(312,855)
(313,850)(314,851)(315,852)(316,856)(317,857)(318,858)(319,862)(320,863)
(321,864)(322,859)(323,860)(324,861)(325,676)(326,677)(327,678)(328,682)
(329,683)(330,684)(331,679)(332,680)(333,681)(334,685)(335,686)(336,687)
(337,691)(338,692)(339,693)(340,688)(341,689)(342,690)(343,694)(344,695)
(345,696)(346,700)(347,701)(348,702)(349,697)(350,698)(351,699)(352,649)
(353,650)(354,651)(355,655)(356,656)(357,657)(358,652)(359,653)(360,654)
(361,658)(362,659)(363,660)(364,664)(365,665)(366,666)(367,661)(368,662)
(369,663)(370,667)(371,668)(372,669)(373,673)(374,674)(375,675)(376,670)
(377,671)(378,672)(379,730)(380,731)(381,732)(382,736)(383,737)(384,738)
(385,733)(386,734)(387,735)(388,739)(389,740)(390,741)(391,745)(392,746)
(393,747)(394,742)(395,743)(396,744)(397,748)(398,749)(399,750)(400,754)
(401,755)(402,756)(403,751)(404,752)(405,753)(406,703)(407,704)(408,705)
(409,709)(410,710)(411,711)(412,706)(413,707)(414,708)(415,712)(416,713)
(417,714)(418,718)(419,719)(420,720)(421,715)(422,716)(423,717)(424,721)
(425,722)(426,723)(427,727)(428,728)(429,729)(430,724)(431,725)(432,726);;
s2 := (  1,436)(  2,438)(  3,437)(  4,433)(  5,435)(  6,434)(  7,439)(  8,441)
(  9,440)( 10,456)( 11,455)( 12,454)( 13,453)( 14,452)( 15,451)( 16,459)
( 17,458)( 18,457)( 19,447)( 20,446)( 21,445)( 22,444)( 23,443)( 24,442)
( 25,450)( 26,449)( 27,448)( 28,463)( 29,465)( 30,464)( 31,460)( 32,462)
( 33,461)( 34,466)( 35,468)( 36,467)( 37,483)( 38,482)( 39,481)( 40,480)
( 41,479)( 42,478)( 43,486)( 44,485)( 45,484)( 46,474)( 47,473)( 48,472)
( 49,471)( 50,470)( 51,469)( 52,477)( 53,476)( 54,475)( 55,490)( 56,492)
( 57,491)( 58,487)( 59,489)( 60,488)( 61,493)( 62,495)( 63,494)( 64,510)
( 65,509)( 66,508)( 67,507)( 68,506)( 69,505)( 70,513)( 71,512)( 72,511)
( 73,501)( 74,500)( 75,499)( 76,498)( 77,497)( 78,496)( 79,504)( 80,503)
( 81,502)( 82,517)( 83,519)( 84,518)( 85,514)( 86,516)( 87,515)( 88,520)
( 89,522)( 90,521)( 91,537)( 92,536)( 93,535)( 94,534)( 95,533)( 96,532)
( 97,540)( 98,539)( 99,538)(100,528)(101,527)(102,526)(103,525)(104,524)
(105,523)(106,531)(107,530)(108,529)(109,571)(110,573)(111,572)(112,568)
(113,570)(114,569)(115,574)(116,576)(117,575)(118,591)(119,590)(120,589)
(121,588)(122,587)(123,586)(124,594)(125,593)(126,592)(127,582)(128,581)
(129,580)(130,579)(131,578)(132,577)(133,585)(134,584)(135,583)(136,544)
(137,546)(138,545)(139,541)(140,543)(141,542)(142,547)(143,549)(144,548)
(145,564)(146,563)(147,562)(148,561)(149,560)(150,559)(151,567)(152,566)
(153,565)(154,555)(155,554)(156,553)(157,552)(158,551)(159,550)(160,558)
(161,557)(162,556)(163,625)(164,627)(165,626)(166,622)(167,624)(168,623)
(169,628)(170,630)(171,629)(172,645)(173,644)(174,643)(175,642)(176,641)
(177,640)(178,648)(179,647)(180,646)(181,636)(182,635)(183,634)(184,633)
(185,632)(186,631)(187,639)(188,638)(189,637)(190,598)(191,600)(192,599)
(193,595)(194,597)(195,596)(196,601)(197,603)(198,602)(199,618)(200,617)
(201,616)(202,615)(203,614)(204,613)(205,621)(206,620)(207,619)(208,609)
(209,608)(210,607)(211,606)(212,605)(213,604)(214,612)(215,611)(216,610)
(217,652)(218,654)(219,653)(220,649)(221,651)(222,650)(223,655)(224,657)
(225,656)(226,672)(227,671)(228,670)(229,669)(230,668)(231,667)(232,675)
(233,674)(234,673)(235,663)(236,662)(237,661)(238,660)(239,659)(240,658)
(241,666)(242,665)(243,664)(244,679)(245,681)(246,680)(247,676)(248,678)
(249,677)(250,682)(251,684)(252,683)(253,699)(254,698)(255,697)(256,696)
(257,695)(258,694)(259,702)(260,701)(261,700)(262,690)(263,689)(264,688)
(265,687)(266,686)(267,685)(268,693)(269,692)(270,691)(271,706)(272,708)
(273,707)(274,703)(275,705)(276,704)(277,709)(278,711)(279,710)(280,726)
(281,725)(282,724)(283,723)(284,722)(285,721)(286,729)(287,728)(288,727)
(289,717)(290,716)(291,715)(292,714)(293,713)(294,712)(295,720)(296,719)
(297,718)(298,733)(299,735)(300,734)(301,730)(302,732)(303,731)(304,736)
(305,738)(306,737)(307,753)(308,752)(309,751)(310,750)(311,749)(312,748)
(313,756)(314,755)(315,754)(316,744)(317,743)(318,742)(319,741)(320,740)
(321,739)(322,747)(323,746)(324,745)(325,787)(326,789)(327,788)(328,784)
(329,786)(330,785)(331,790)(332,792)(333,791)(334,807)(335,806)(336,805)
(337,804)(338,803)(339,802)(340,810)(341,809)(342,808)(343,798)(344,797)
(345,796)(346,795)(347,794)(348,793)(349,801)(350,800)(351,799)(352,760)
(353,762)(354,761)(355,757)(356,759)(357,758)(358,763)(359,765)(360,764)
(361,780)(362,779)(363,778)(364,777)(365,776)(366,775)(367,783)(368,782)
(369,781)(370,771)(371,770)(372,769)(373,768)(374,767)(375,766)(376,774)
(377,773)(378,772)(379,841)(380,843)(381,842)(382,838)(383,840)(384,839)
(385,844)(386,846)(387,845)(388,861)(389,860)(390,859)(391,858)(392,857)
(393,856)(394,864)(395,863)(396,862)(397,852)(398,851)(399,850)(400,849)
(401,848)(402,847)(403,855)(404,854)(405,853)(406,814)(407,816)(408,815)
(409,811)(410,813)(411,812)(412,817)(413,819)(414,818)(415,834)(416,833)
(417,832)(418,831)(419,830)(420,829)(421,837)(422,836)(423,835)(424,825)
(425,824)(426,823)(427,822)(428,821)(429,820)(430,828)(431,827)(432,826);;
s3 := (  1, 10)(  2, 12)(  3, 11)(  4, 13)(  5, 15)(  6, 14)(  7, 16)(  8, 18)
(  9, 17)( 19, 21)( 22, 24)( 25, 27)( 28, 37)( 29, 39)( 30, 38)( 31, 40)
( 32, 42)( 33, 41)( 34, 43)( 35, 45)( 36, 44)( 46, 48)( 49, 51)( 52, 54)
( 55, 64)( 56, 66)( 57, 65)( 58, 67)( 59, 69)( 60, 68)( 61, 70)( 62, 72)
( 63, 71)( 73, 75)( 76, 78)( 79, 81)( 82, 91)( 83, 93)( 84, 92)( 85, 94)
( 86, 96)( 87, 95)( 88, 97)( 89, 99)( 90, 98)(100,102)(103,105)(106,108)
(109,145)(110,147)(111,146)(112,148)(113,150)(114,149)(115,151)(116,153)
(117,152)(118,136)(119,138)(120,137)(121,139)(122,141)(123,140)(124,142)
(125,144)(126,143)(127,156)(128,155)(129,154)(130,159)(131,158)(132,157)
(133,162)(134,161)(135,160)(163,199)(164,201)(165,200)(166,202)(167,204)
(168,203)(169,205)(170,207)(171,206)(172,190)(173,192)(174,191)(175,193)
(176,195)(177,194)(178,196)(179,198)(180,197)(181,210)(182,209)(183,208)
(184,213)(185,212)(186,211)(187,216)(188,215)(189,214)(217,226)(218,228)
(219,227)(220,229)(221,231)(222,230)(223,232)(224,234)(225,233)(235,237)
(238,240)(241,243)(244,253)(245,255)(246,254)(247,256)(248,258)(249,257)
(250,259)(251,261)(252,260)(262,264)(265,267)(268,270)(271,280)(272,282)
(273,281)(274,283)(275,285)(276,284)(277,286)(278,288)(279,287)(289,291)
(292,294)(295,297)(298,307)(299,309)(300,308)(301,310)(302,312)(303,311)
(304,313)(305,315)(306,314)(316,318)(319,321)(322,324)(325,361)(326,363)
(327,362)(328,364)(329,366)(330,365)(331,367)(332,369)(333,368)(334,352)
(335,354)(336,353)(337,355)(338,357)(339,356)(340,358)(341,360)(342,359)
(343,372)(344,371)(345,370)(346,375)(347,374)(348,373)(349,378)(350,377)
(351,376)(379,415)(380,417)(381,416)(382,418)(383,420)(384,419)(385,421)
(386,423)(387,422)(388,406)(389,408)(390,407)(391,409)(392,411)(393,410)
(394,412)(395,414)(396,413)(397,426)(398,425)(399,424)(400,429)(401,428)
(402,427)(403,432)(404,431)(405,430)(433,469)(434,471)(435,470)(436,472)
(437,474)(438,473)(439,475)(440,477)(441,476)(442,460)(443,462)(444,461)
(445,463)(446,465)(447,464)(448,466)(449,468)(450,467)(451,480)(452,479)
(453,478)(454,483)(455,482)(456,481)(457,486)(458,485)(459,484)(487,523)
(488,525)(489,524)(490,526)(491,528)(492,527)(493,529)(494,531)(495,530)
(496,514)(497,516)(498,515)(499,517)(500,519)(501,518)(502,520)(503,522)
(504,521)(505,534)(506,533)(507,532)(508,537)(509,536)(510,535)(511,540)
(512,539)(513,538)(541,550)(542,552)(543,551)(544,553)(545,555)(546,554)
(547,556)(548,558)(549,557)(559,561)(562,564)(565,567)(568,577)(569,579)
(570,578)(571,580)(572,582)(573,581)(574,583)(575,585)(576,584)(586,588)
(589,591)(592,594)(595,604)(596,606)(597,605)(598,607)(599,609)(600,608)
(601,610)(602,612)(603,611)(613,615)(616,618)(619,621)(622,631)(623,633)
(624,632)(625,634)(626,636)(627,635)(628,637)(629,639)(630,638)(640,642)
(643,645)(646,648)(649,685)(650,687)(651,686)(652,688)(653,690)(654,689)
(655,691)(656,693)(657,692)(658,676)(659,678)(660,677)(661,679)(662,681)
(663,680)(664,682)(665,684)(666,683)(667,696)(668,695)(669,694)(670,699)
(671,698)(672,697)(673,702)(674,701)(675,700)(703,739)(704,741)(705,740)
(706,742)(707,744)(708,743)(709,745)(710,747)(711,746)(712,730)(713,732)
(714,731)(715,733)(716,735)(717,734)(718,736)(719,738)(720,737)(721,750)
(722,749)(723,748)(724,753)(725,752)(726,751)(727,756)(728,755)(729,754)
(757,766)(758,768)(759,767)(760,769)(761,771)(762,770)(763,772)(764,774)
(765,773)(775,777)(778,780)(781,783)(784,793)(785,795)(786,794)(787,796)
(788,798)(789,797)(790,799)(791,801)(792,800)(802,804)(805,807)(808,810)
(811,820)(812,822)(813,821)(814,823)(815,825)(816,824)(817,826)(818,828)
(819,827)(829,831)(832,834)(835,837)(838,847)(839,849)(840,848)(841,850)
(842,852)(843,851)(844,853)(845,855)(846,854)(856,858)(859,861)(862,864);;
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, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(864)!(  1,217)(  2,218)(  3,219)(  4,220)(  5,221)(  6,222)(  7,223)
(  8,224)(  9,225)( 10,226)( 11,227)( 12,228)( 13,229)( 14,230)( 15,231)
( 16,232)( 17,233)( 18,234)( 19,235)( 20,236)( 21,237)( 22,238)( 23,239)
( 24,240)( 25,241)( 26,242)( 27,243)( 28,244)( 29,245)( 30,246)( 31,247)
( 32,248)( 33,249)( 34,250)( 35,251)( 36,252)( 37,253)( 38,254)( 39,255)
( 40,256)( 41,257)( 42,258)( 43,259)( 44,260)( 45,261)( 46,262)( 47,263)
( 48,264)( 49,265)( 50,266)( 51,267)( 52,268)( 53,269)( 54,270)( 55,271)
( 56,272)( 57,273)( 58,274)( 59,275)( 60,276)( 61,277)( 62,278)( 63,279)
( 64,280)( 65,281)( 66,282)( 67,283)( 68,284)( 69,285)( 70,286)( 71,287)
( 72,288)( 73,289)( 74,290)( 75,291)( 76,292)( 77,293)( 78,294)( 79,295)
( 80,296)( 81,297)( 82,298)( 83,299)( 84,300)( 85,301)( 86,302)( 87,303)
( 88,304)( 89,305)( 90,306)( 91,307)( 92,308)( 93,309)( 94,310)( 95,311)
( 96,312)( 97,313)( 98,314)( 99,315)(100,316)(101,317)(102,318)(103,319)
(104,320)(105,321)(106,322)(107,323)(108,324)(109,379)(110,380)(111,381)
(112,382)(113,383)(114,384)(115,385)(116,386)(117,387)(118,388)(119,389)
(120,390)(121,391)(122,392)(123,393)(124,394)(125,395)(126,396)(127,397)
(128,398)(129,399)(130,400)(131,401)(132,402)(133,403)(134,404)(135,405)
(136,406)(137,407)(138,408)(139,409)(140,410)(141,411)(142,412)(143,413)
(144,414)(145,415)(146,416)(147,417)(148,418)(149,419)(150,420)(151,421)
(152,422)(153,423)(154,424)(155,425)(156,426)(157,427)(158,428)(159,429)
(160,430)(161,431)(162,432)(163,325)(164,326)(165,327)(166,328)(167,329)
(168,330)(169,331)(170,332)(171,333)(172,334)(173,335)(174,336)(175,337)
(176,338)(177,339)(178,340)(179,341)(180,342)(181,343)(182,344)(183,345)
(184,346)(185,347)(186,348)(187,349)(188,350)(189,351)(190,352)(191,353)
(192,354)(193,355)(194,356)(195,357)(196,358)(197,359)(198,360)(199,361)
(200,362)(201,363)(202,364)(203,365)(204,366)(205,367)(206,368)(207,369)
(208,370)(209,371)(210,372)(211,373)(212,374)(213,375)(214,376)(215,377)
(216,378)(433,649)(434,650)(435,651)(436,652)(437,653)(438,654)(439,655)
(440,656)(441,657)(442,658)(443,659)(444,660)(445,661)(446,662)(447,663)
(448,664)(449,665)(450,666)(451,667)(452,668)(453,669)(454,670)(455,671)
(456,672)(457,673)(458,674)(459,675)(460,676)(461,677)(462,678)(463,679)
(464,680)(465,681)(466,682)(467,683)(468,684)(469,685)(470,686)(471,687)
(472,688)(473,689)(474,690)(475,691)(476,692)(477,693)(478,694)(479,695)
(480,696)(481,697)(482,698)(483,699)(484,700)(485,701)(486,702)(487,703)
(488,704)(489,705)(490,706)(491,707)(492,708)(493,709)(494,710)(495,711)
(496,712)(497,713)(498,714)(499,715)(500,716)(501,717)(502,718)(503,719)
(504,720)(505,721)(506,722)(507,723)(508,724)(509,725)(510,726)(511,727)
(512,728)(513,729)(514,730)(515,731)(516,732)(517,733)(518,734)(519,735)
(520,736)(521,737)(522,738)(523,739)(524,740)(525,741)(526,742)(527,743)
(528,744)(529,745)(530,746)(531,747)(532,748)(533,749)(534,750)(535,751)
(536,752)(537,753)(538,754)(539,755)(540,756)(541,811)(542,812)(543,813)
(544,814)(545,815)(546,816)(547,817)(548,818)(549,819)(550,820)(551,821)
(552,822)(553,823)(554,824)(555,825)(556,826)(557,827)(558,828)(559,829)
(560,830)(561,831)(562,832)(563,833)(564,834)(565,835)(566,836)(567,837)
(568,838)(569,839)(570,840)(571,841)(572,842)(573,843)(574,844)(575,845)
(576,846)(577,847)(578,848)(579,849)(580,850)(581,851)(582,852)(583,853)
(584,854)(585,855)(586,856)(587,857)(588,858)(589,859)(590,860)(591,861)
(592,862)(593,863)(594,864)(595,757)(596,758)(597,759)(598,760)(599,761)
(600,762)(601,763)(602,764)(603,765)(604,766)(605,767)(606,768)(607,769)
(608,770)(609,771)(610,772)(611,773)(612,774)(613,775)(614,776)(615,777)
(616,778)(617,779)(618,780)(619,781)(620,782)(621,783)(622,784)(623,785)
(624,786)(625,787)(626,788)(627,789)(628,790)(629,791)(630,792)(631,793)
(632,794)(633,795)(634,796)(635,797)(636,798)(637,799)(638,800)(639,801)
(640,802)(641,803)(642,804)(643,805)(644,806)(645,807)(646,808)(647,809)
(648,810);
s1 := Sym(864)!(  1,541)(  2,542)(  3,543)(  4,547)(  5,548)(  6,549)(  7,544)
(  8,545)(  9,546)( 10,550)( 11,551)( 12,552)( 13,556)( 14,557)( 15,558)
( 16,553)( 17,554)( 18,555)( 19,559)( 20,560)( 21,561)( 22,565)( 23,566)
( 24,567)( 25,562)( 26,563)( 27,564)( 28,568)( 29,569)( 30,570)( 31,574)
( 32,575)( 33,576)( 34,571)( 35,572)( 36,573)( 37,577)( 38,578)( 39,579)
( 40,583)( 41,584)( 42,585)( 43,580)( 44,581)( 45,582)( 46,586)( 47,587)
( 48,588)( 49,592)( 50,593)( 51,594)( 52,589)( 53,590)( 54,591)( 55,595)
( 56,596)( 57,597)( 58,601)( 59,602)( 60,603)( 61,598)( 62,599)( 63,600)
( 64,604)( 65,605)( 66,606)( 67,610)( 68,611)( 69,612)( 70,607)( 71,608)
( 72,609)( 73,613)( 74,614)( 75,615)( 76,619)( 77,620)( 78,621)( 79,616)
( 80,617)( 81,618)( 82,622)( 83,623)( 84,624)( 85,628)( 86,629)( 87,630)
( 88,625)( 89,626)( 90,627)( 91,631)( 92,632)( 93,633)( 94,637)( 95,638)
( 96,639)( 97,634)( 98,635)( 99,636)(100,640)(101,641)(102,642)(103,646)
(104,647)(105,648)(106,643)(107,644)(108,645)(109,460)(110,461)(111,462)
(112,466)(113,467)(114,468)(115,463)(116,464)(117,465)(118,469)(119,470)
(120,471)(121,475)(122,476)(123,477)(124,472)(125,473)(126,474)(127,478)
(128,479)(129,480)(130,484)(131,485)(132,486)(133,481)(134,482)(135,483)
(136,433)(137,434)(138,435)(139,439)(140,440)(141,441)(142,436)(143,437)
(144,438)(145,442)(146,443)(147,444)(148,448)(149,449)(150,450)(151,445)
(152,446)(153,447)(154,451)(155,452)(156,453)(157,457)(158,458)(159,459)
(160,454)(161,455)(162,456)(163,514)(164,515)(165,516)(166,520)(167,521)
(168,522)(169,517)(170,518)(171,519)(172,523)(173,524)(174,525)(175,529)
(176,530)(177,531)(178,526)(179,527)(180,528)(181,532)(182,533)(183,534)
(184,538)(185,539)(186,540)(187,535)(188,536)(189,537)(190,487)(191,488)
(192,489)(193,493)(194,494)(195,495)(196,490)(197,491)(198,492)(199,496)
(200,497)(201,498)(202,502)(203,503)(204,504)(205,499)(206,500)(207,501)
(208,505)(209,506)(210,507)(211,511)(212,512)(213,513)(214,508)(215,509)
(216,510)(217,757)(218,758)(219,759)(220,763)(221,764)(222,765)(223,760)
(224,761)(225,762)(226,766)(227,767)(228,768)(229,772)(230,773)(231,774)
(232,769)(233,770)(234,771)(235,775)(236,776)(237,777)(238,781)(239,782)
(240,783)(241,778)(242,779)(243,780)(244,784)(245,785)(246,786)(247,790)
(248,791)(249,792)(250,787)(251,788)(252,789)(253,793)(254,794)(255,795)
(256,799)(257,800)(258,801)(259,796)(260,797)(261,798)(262,802)(263,803)
(264,804)(265,808)(266,809)(267,810)(268,805)(269,806)(270,807)(271,811)
(272,812)(273,813)(274,817)(275,818)(276,819)(277,814)(278,815)(279,816)
(280,820)(281,821)(282,822)(283,826)(284,827)(285,828)(286,823)(287,824)
(288,825)(289,829)(290,830)(291,831)(292,835)(293,836)(294,837)(295,832)
(296,833)(297,834)(298,838)(299,839)(300,840)(301,844)(302,845)(303,846)
(304,841)(305,842)(306,843)(307,847)(308,848)(309,849)(310,853)(311,854)
(312,855)(313,850)(314,851)(315,852)(316,856)(317,857)(318,858)(319,862)
(320,863)(321,864)(322,859)(323,860)(324,861)(325,676)(326,677)(327,678)
(328,682)(329,683)(330,684)(331,679)(332,680)(333,681)(334,685)(335,686)
(336,687)(337,691)(338,692)(339,693)(340,688)(341,689)(342,690)(343,694)
(344,695)(345,696)(346,700)(347,701)(348,702)(349,697)(350,698)(351,699)
(352,649)(353,650)(354,651)(355,655)(356,656)(357,657)(358,652)(359,653)
(360,654)(361,658)(362,659)(363,660)(364,664)(365,665)(366,666)(367,661)
(368,662)(369,663)(370,667)(371,668)(372,669)(373,673)(374,674)(375,675)
(376,670)(377,671)(378,672)(379,730)(380,731)(381,732)(382,736)(383,737)
(384,738)(385,733)(386,734)(387,735)(388,739)(389,740)(390,741)(391,745)
(392,746)(393,747)(394,742)(395,743)(396,744)(397,748)(398,749)(399,750)
(400,754)(401,755)(402,756)(403,751)(404,752)(405,753)(406,703)(407,704)
(408,705)(409,709)(410,710)(411,711)(412,706)(413,707)(414,708)(415,712)
(416,713)(417,714)(418,718)(419,719)(420,720)(421,715)(422,716)(423,717)
(424,721)(425,722)(426,723)(427,727)(428,728)(429,729)(430,724)(431,725)
(432,726);
s2 := Sym(864)!(  1,436)(  2,438)(  3,437)(  4,433)(  5,435)(  6,434)(  7,439)
(  8,441)(  9,440)( 10,456)( 11,455)( 12,454)( 13,453)( 14,452)( 15,451)
( 16,459)( 17,458)( 18,457)( 19,447)( 20,446)( 21,445)( 22,444)( 23,443)
( 24,442)( 25,450)( 26,449)( 27,448)( 28,463)( 29,465)( 30,464)( 31,460)
( 32,462)( 33,461)( 34,466)( 35,468)( 36,467)( 37,483)( 38,482)( 39,481)
( 40,480)( 41,479)( 42,478)( 43,486)( 44,485)( 45,484)( 46,474)( 47,473)
( 48,472)( 49,471)( 50,470)( 51,469)( 52,477)( 53,476)( 54,475)( 55,490)
( 56,492)( 57,491)( 58,487)( 59,489)( 60,488)( 61,493)( 62,495)( 63,494)
( 64,510)( 65,509)( 66,508)( 67,507)( 68,506)( 69,505)( 70,513)( 71,512)
( 72,511)( 73,501)( 74,500)( 75,499)( 76,498)( 77,497)( 78,496)( 79,504)
( 80,503)( 81,502)( 82,517)( 83,519)( 84,518)( 85,514)( 86,516)( 87,515)
( 88,520)( 89,522)( 90,521)( 91,537)( 92,536)( 93,535)( 94,534)( 95,533)
( 96,532)( 97,540)( 98,539)( 99,538)(100,528)(101,527)(102,526)(103,525)
(104,524)(105,523)(106,531)(107,530)(108,529)(109,571)(110,573)(111,572)
(112,568)(113,570)(114,569)(115,574)(116,576)(117,575)(118,591)(119,590)
(120,589)(121,588)(122,587)(123,586)(124,594)(125,593)(126,592)(127,582)
(128,581)(129,580)(130,579)(131,578)(132,577)(133,585)(134,584)(135,583)
(136,544)(137,546)(138,545)(139,541)(140,543)(141,542)(142,547)(143,549)
(144,548)(145,564)(146,563)(147,562)(148,561)(149,560)(150,559)(151,567)
(152,566)(153,565)(154,555)(155,554)(156,553)(157,552)(158,551)(159,550)
(160,558)(161,557)(162,556)(163,625)(164,627)(165,626)(166,622)(167,624)
(168,623)(169,628)(170,630)(171,629)(172,645)(173,644)(174,643)(175,642)
(176,641)(177,640)(178,648)(179,647)(180,646)(181,636)(182,635)(183,634)
(184,633)(185,632)(186,631)(187,639)(188,638)(189,637)(190,598)(191,600)
(192,599)(193,595)(194,597)(195,596)(196,601)(197,603)(198,602)(199,618)
(200,617)(201,616)(202,615)(203,614)(204,613)(205,621)(206,620)(207,619)
(208,609)(209,608)(210,607)(211,606)(212,605)(213,604)(214,612)(215,611)
(216,610)(217,652)(218,654)(219,653)(220,649)(221,651)(222,650)(223,655)
(224,657)(225,656)(226,672)(227,671)(228,670)(229,669)(230,668)(231,667)
(232,675)(233,674)(234,673)(235,663)(236,662)(237,661)(238,660)(239,659)
(240,658)(241,666)(242,665)(243,664)(244,679)(245,681)(246,680)(247,676)
(248,678)(249,677)(250,682)(251,684)(252,683)(253,699)(254,698)(255,697)
(256,696)(257,695)(258,694)(259,702)(260,701)(261,700)(262,690)(263,689)
(264,688)(265,687)(266,686)(267,685)(268,693)(269,692)(270,691)(271,706)
(272,708)(273,707)(274,703)(275,705)(276,704)(277,709)(278,711)(279,710)
(280,726)(281,725)(282,724)(283,723)(284,722)(285,721)(286,729)(287,728)
(288,727)(289,717)(290,716)(291,715)(292,714)(293,713)(294,712)(295,720)
(296,719)(297,718)(298,733)(299,735)(300,734)(301,730)(302,732)(303,731)
(304,736)(305,738)(306,737)(307,753)(308,752)(309,751)(310,750)(311,749)
(312,748)(313,756)(314,755)(315,754)(316,744)(317,743)(318,742)(319,741)
(320,740)(321,739)(322,747)(323,746)(324,745)(325,787)(326,789)(327,788)
(328,784)(329,786)(330,785)(331,790)(332,792)(333,791)(334,807)(335,806)
(336,805)(337,804)(338,803)(339,802)(340,810)(341,809)(342,808)(343,798)
(344,797)(345,796)(346,795)(347,794)(348,793)(349,801)(350,800)(351,799)
(352,760)(353,762)(354,761)(355,757)(356,759)(357,758)(358,763)(359,765)
(360,764)(361,780)(362,779)(363,778)(364,777)(365,776)(366,775)(367,783)
(368,782)(369,781)(370,771)(371,770)(372,769)(373,768)(374,767)(375,766)
(376,774)(377,773)(378,772)(379,841)(380,843)(381,842)(382,838)(383,840)
(384,839)(385,844)(386,846)(387,845)(388,861)(389,860)(390,859)(391,858)
(392,857)(393,856)(394,864)(395,863)(396,862)(397,852)(398,851)(399,850)
(400,849)(401,848)(402,847)(403,855)(404,854)(405,853)(406,814)(407,816)
(408,815)(409,811)(410,813)(411,812)(412,817)(413,819)(414,818)(415,834)
(416,833)(417,832)(418,831)(419,830)(420,829)(421,837)(422,836)(423,835)
(424,825)(425,824)(426,823)(427,822)(428,821)(429,820)(430,828)(431,827)
(432,826);
s3 := Sym(864)!(  1, 10)(  2, 12)(  3, 11)(  4, 13)(  5, 15)(  6, 14)(  7, 16)
(  8, 18)(  9, 17)( 19, 21)( 22, 24)( 25, 27)( 28, 37)( 29, 39)( 30, 38)
( 31, 40)( 32, 42)( 33, 41)( 34, 43)( 35, 45)( 36, 44)( 46, 48)( 49, 51)
( 52, 54)( 55, 64)( 56, 66)( 57, 65)( 58, 67)( 59, 69)( 60, 68)( 61, 70)
( 62, 72)( 63, 71)( 73, 75)( 76, 78)( 79, 81)( 82, 91)( 83, 93)( 84, 92)
( 85, 94)( 86, 96)( 87, 95)( 88, 97)( 89, 99)( 90, 98)(100,102)(103,105)
(106,108)(109,145)(110,147)(111,146)(112,148)(113,150)(114,149)(115,151)
(116,153)(117,152)(118,136)(119,138)(120,137)(121,139)(122,141)(123,140)
(124,142)(125,144)(126,143)(127,156)(128,155)(129,154)(130,159)(131,158)
(132,157)(133,162)(134,161)(135,160)(163,199)(164,201)(165,200)(166,202)
(167,204)(168,203)(169,205)(170,207)(171,206)(172,190)(173,192)(174,191)
(175,193)(176,195)(177,194)(178,196)(179,198)(180,197)(181,210)(182,209)
(183,208)(184,213)(185,212)(186,211)(187,216)(188,215)(189,214)(217,226)
(218,228)(219,227)(220,229)(221,231)(222,230)(223,232)(224,234)(225,233)
(235,237)(238,240)(241,243)(244,253)(245,255)(246,254)(247,256)(248,258)
(249,257)(250,259)(251,261)(252,260)(262,264)(265,267)(268,270)(271,280)
(272,282)(273,281)(274,283)(275,285)(276,284)(277,286)(278,288)(279,287)
(289,291)(292,294)(295,297)(298,307)(299,309)(300,308)(301,310)(302,312)
(303,311)(304,313)(305,315)(306,314)(316,318)(319,321)(322,324)(325,361)
(326,363)(327,362)(328,364)(329,366)(330,365)(331,367)(332,369)(333,368)
(334,352)(335,354)(336,353)(337,355)(338,357)(339,356)(340,358)(341,360)
(342,359)(343,372)(344,371)(345,370)(346,375)(347,374)(348,373)(349,378)
(350,377)(351,376)(379,415)(380,417)(381,416)(382,418)(383,420)(384,419)
(385,421)(386,423)(387,422)(388,406)(389,408)(390,407)(391,409)(392,411)
(393,410)(394,412)(395,414)(396,413)(397,426)(398,425)(399,424)(400,429)
(401,428)(402,427)(403,432)(404,431)(405,430)(433,469)(434,471)(435,470)
(436,472)(437,474)(438,473)(439,475)(440,477)(441,476)(442,460)(443,462)
(444,461)(445,463)(446,465)(447,464)(448,466)(449,468)(450,467)(451,480)
(452,479)(453,478)(454,483)(455,482)(456,481)(457,486)(458,485)(459,484)
(487,523)(488,525)(489,524)(490,526)(491,528)(492,527)(493,529)(494,531)
(495,530)(496,514)(497,516)(498,515)(499,517)(500,519)(501,518)(502,520)
(503,522)(504,521)(505,534)(506,533)(507,532)(508,537)(509,536)(510,535)
(511,540)(512,539)(513,538)(541,550)(542,552)(543,551)(544,553)(545,555)
(546,554)(547,556)(548,558)(549,557)(559,561)(562,564)(565,567)(568,577)
(569,579)(570,578)(571,580)(572,582)(573,581)(574,583)(575,585)(576,584)
(586,588)(589,591)(592,594)(595,604)(596,606)(597,605)(598,607)(599,609)
(600,608)(601,610)(602,612)(603,611)(613,615)(616,618)(619,621)(622,631)
(623,633)(624,632)(625,634)(626,636)(627,635)(628,637)(629,639)(630,638)
(640,642)(643,645)(646,648)(649,685)(650,687)(651,686)(652,688)(653,690)
(654,689)(655,691)(656,693)(657,692)(658,676)(659,678)(660,677)(661,679)
(662,681)(663,680)(664,682)(665,684)(666,683)(667,696)(668,695)(669,694)
(670,699)(671,698)(672,697)(673,702)(674,701)(675,700)(703,739)(704,741)
(705,740)(706,742)(707,744)(708,743)(709,745)(710,747)(711,746)(712,730)
(713,732)(714,731)(715,733)(716,735)(717,734)(718,736)(719,738)(720,737)
(721,750)(722,749)(723,748)(724,753)(725,752)(726,751)(727,756)(728,755)
(729,754)(757,766)(758,768)(759,767)(760,769)(761,771)(762,770)(763,772)
(764,774)(765,773)(775,777)(778,780)(781,783)(784,793)(785,795)(786,794)
(787,796)(788,798)(789,797)(790,799)(791,801)(792,800)(802,804)(805,807)
(808,810)(811,820)(812,822)(813,821)(814,823)(815,825)(816,824)(817,826)
(818,828)(819,827)(829,831)(832,834)(835,837)(838,847)(839,849)(840,848)
(841,850)(842,852)(843,851)(844,853)(845,855)(846,854)(856,858)(859,861)
(862,864);
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, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s3*s2*s1*s2*s3*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 
References : None.
to this polytope