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Polytope of Type {36,6,4}

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