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Polytope of Type {3,6,48}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,48}*1728b
if this polytope has a name.
Group : SmallGroup(1728,21263)
Rank : 4
Schlafli Type : {3,6,48}
Number of vertices, edges, etc : 3, 9, 144, 48
Order of s0s1s2s3 : 48
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 : {3,6,24}*864b
   3-fold quotients : {3,2,48}*576, {3,6,16}*576
   4-fold quotients : {3,6,12}*432b
   6-fold quotients : {3,2,24}*288, {3,6,8}*288
   8-fold quotients : {3,6,6}*216b
   9-fold quotients : {3,2,16}*192
   12-fold quotients : {3,2,12}*144, {3,6,4}*144
   18-fold quotients : {3,2,8}*96
   24-fold quotients : {3,2,6}*72, {3,6,2}*72
   36-fold quotients : {3,2,4}*48
   48-fold quotients : {3,2,3}*36
   72-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,649)(  2,650)(  3,651)(  4,655)(  5,656)(  6,657)(  7,652)(  8,653)
(  9,654)( 10,667)( 11,668)( 12,669)( 13,673)( 14,674)( 15,675)( 16,670)
( 17,671)( 18,672)( 19,658)( 20,659)( 21,660)( 22,664)( 23,665)( 24,666)
( 25,661)( 26,662)( 27,663)( 28,676)( 29,677)( 30,678)( 31,682)( 32,683)
( 33,684)( 34,679)( 35,680)( 36,681)( 37,694)( 38,695)( 39,696)( 40,700)
( 41,701)( 42,702)( 43,697)( 44,698)( 45,699)( 46,685)( 47,686)( 48,687)
( 49,691)( 50,692)( 51,693)( 52,688)( 53,689)( 54,690)( 55,703)( 56,704)
( 57,705)( 58,709)( 59,710)( 60,711)( 61,706)( 62,707)( 63,708)( 64,721)
( 65,722)( 66,723)( 67,727)( 68,728)( 69,729)( 70,724)( 71,725)( 72,726)
( 73,712)( 74,713)( 75,714)( 76,718)( 77,719)( 78,720)( 79,715)( 80,716)
( 81,717)( 82,730)( 83,731)( 84,732)( 85,736)( 86,737)( 87,738)( 88,733)
( 89,734)( 90,735)( 91,748)( 92,749)( 93,750)( 94,754)( 95,755)( 96,756)
( 97,751)( 98,752)( 99,753)(100,739)(101,740)(102,741)(103,745)(104,746)
(105,747)(106,742)(107,743)(108,744)(109,757)(110,758)(111,759)(112,763)
(113,764)(114,765)(115,760)(116,761)(117,762)(118,775)(119,776)(120,777)
(121,781)(122,782)(123,783)(124,778)(125,779)(126,780)(127,766)(128,767)
(129,768)(130,772)(131,773)(132,774)(133,769)(134,770)(135,771)(136,784)
(137,785)(138,786)(139,790)(140,791)(141,792)(142,787)(143,788)(144,789)
(145,802)(146,803)(147,804)(148,808)(149,809)(150,810)(151,805)(152,806)
(153,807)(154,793)(155,794)(156,795)(157,799)(158,800)(159,801)(160,796)
(161,797)(162,798)(163,811)(164,812)(165,813)(166,817)(167,818)(168,819)
(169,814)(170,815)(171,816)(172,829)(173,830)(174,831)(175,835)(176,836)
(177,837)(178,832)(179,833)(180,834)(181,820)(182,821)(183,822)(184,826)
(185,827)(186,828)(187,823)(188,824)(189,825)(190,838)(191,839)(192,840)
(193,844)(194,845)(195,846)(196,841)(197,842)(198,843)(199,856)(200,857)
(201,858)(202,862)(203,863)(204,864)(205,859)(206,860)(207,861)(208,847)
(209,848)(210,849)(211,853)(212,854)(213,855)(214,850)(215,851)(216,852)
(217,541)(218,542)(219,543)(220,547)(221,548)(222,549)(223,544)(224,545)
(225,546)(226,559)(227,560)(228,561)(229,565)(230,566)(231,567)(232,562)
(233,563)(234,564)(235,550)(236,551)(237,552)(238,556)(239,557)(240,558)
(241,553)(242,554)(243,555)(244,568)(245,569)(246,570)(247,574)(248,575)
(249,576)(250,571)(251,572)(252,573)(253,586)(254,587)(255,588)(256,592)
(257,593)(258,594)(259,589)(260,590)(261,591)(262,577)(263,578)(264,579)
(265,583)(266,584)(267,585)(268,580)(269,581)(270,582)(271,595)(272,596)
(273,597)(274,601)(275,602)(276,603)(277,598)(278,599)(279,600)(280,613)
(281,614)(282,615)(283,619)(284,620)(285,621)(286,616)(287,617)(288,618)
(289,604)(290,605)(291,606)(292,610)(293,611)(294,612)(295,607)(296,608)
(297,609)(298,622)(299,623)(300,624)(301,628)(302,629)(303,630)(304,625)
(305,626)(306,627)(307,640)(308,641)(309,642)(310,646)(311,647)(312,648)
(313,643)(314,644)(315,645)(316,631)(317,632)(318,633)(319,637)(320,638)
(321,639)(322,634)(323,635)(324,636)(325,514)(326,515)(327,516)(328,520)
(329,521)(330,522)(331,517)(332,518)(333,519)(334,532)(335,533)(336,534)
(337,538)(338,539)(339,540)(340,535)(341,536)(342,537)(343,523)(344,524)
(345,525)(346,529)(347,530)(348,531)(349,526)(350,527)(351,528)(352,487)
(353,488)(354,489)(355,493)(356,494)(357,495)(358,490)(359,491)(360,492)
(361,505)(362,506)(363,507)(364,511)(365,512)(366,513)(367,508)(368,509)
(369,510)(370,496)(371,497)(372,498)(373,502)(374,503)(375,504)(376,499)
(377,500)(378,501)(379,433)(380,434)(381,435)(382,439)(383,440)(384,441)
(385,436)(386,437)(387,438)(388,451)(389,452)(390,453)(391,457)(392,458)
(393,459)(394,454)(395,455)(396,456)(397,442)(398,443)(399,444)(400,448)
(401,449)(402,450)(403,445)(404,446)(405,447)(406,460)(407,461)(408,462)
(409,466)(410,467)(411,468)(412,463)(413,464)(414,465)(415,478)(416,479)
(417,480)(418,484)(419,485)(420,486)(421,481)(422,482)(423,483)(424,469)
(425,470)(426,471)(427,475)(428,476)(429,477)(430,472)(431,473)(432,474);;
s1 := (  1,661)(  2,662)(  3,663)(  4,658)(  5,659)(  6,660)(  7,664)(  8,665)
(  9,666)( 10,652)( 11,653)( 12,654)( 13,649)( 14,650)( 15,651)( 16,655)
( 17,656)( 18,657)( 19,670)( 20,671)( 21,672)( 22,667)( 23,668)( 24,669)
( 25,673)( 26,674)( 27,675)( 28,688)( 29,689)( 30,690)( 31,685)( 32,686)
( 33,687)( 34,691)( 35,692)( 36,693)( 37,679)( 38,680)( 39,681)( 40,676)
( 41,677)( 42,678)( 43,682)( 44,683)( 45,684)( 46,697)( 47,698)( 48,699)
( 49,694)( 50,695)( 51,696)( 52,700)( 53,701)( 54,702)( 55,715)( 56,716)
( 57,717)( 58,712)( 59,713)( 60,714)( 61,718)( 62,719)( 63,720)( 64,706)
( 65,707)( 66,708)( 67,703)( 68,704)( 69,705)( 70,709)( 71,710)( 72,711)
( 73,724)( 74,725)( 75,726)( 76,721)( 77,722)( 78,723)( 79,727)( 80,728)
( 81,729)( 82,742)( 83,743)( 84,744)( 85,739)( 86,740)( 87,741)( 88,745)
( 89,746)( 90,747)( 91,733)( 92,734)( 93,735)( 94,730)( 95,731)( 96,732)
( 97,736)( 98,737)( 99,738)(100,751)(101,752)(102,753)(103,748)(104,749)
(105,750)(106,754)(107,755)(108,756)(109,769)(110,770)(111,771)(112,766)
(113,767)(114,768)(115,772)(116,773)(117,774)(118,760)(119,761)(120,762)
(121,757)(122,758)(123,759)(124,763)(125,764)(126,765)(127,778)(128,779)
(129,780)(130,775)(131,776)(132,777)(133,781)(134,782)(135,783)(136,796)
(137,797)(138,798)(139,793)(140,794)(141,795)(142,799)(143,800)(144,801)
(145,787)(146,788)(147,789)(148,784)(149,785)(150,786)(151,790)(152,791)
(153,792)(154,805)(155,806)(156,807)(157,802)(158,803)(159,804)(160,808)
(161,809)(162,810)(163,823)(164,824)(165,825)(166,820)(167,821)(168,822)
(169,826)(170,827)(171,828)(172,814)(173,815)(174,816)(175,811)(176,812)
(177,813)(178,817)(179,818)(180,819)(181,832)(182,833)(183,834)(184,829)
(185,830)(186,831)(187,835)(188,836)(189,837)(190,850)(191,851)(192,852)
(193,847)(194,848)(195,849)(196,853)(197,854)(198,855)(199,841)(200,842)
(201,843)(202,838)(203,839)(204,840)(205,844)(206,845)(207,846)(208,859)
(209,860)(210,861)(211,856)(212,857)(213,858)(214,862)(215,863)(216,864)
(217,553)(218,554)(219,555)(220,550)(221,551)(222,552)(223,556)(224,557)
(225,558)(226,544)(227,545)(228,546)(229,541)(230,542)(231,543)(232,547)
(233,548)(234,549)(235,562)(236,563)(237,564)(238,559)(239,560)(240,561)
(241,565)(242,566)(243,567)(244,580)(245,581)(246,582)(247,577)(248,578)
(249,579)(250,583)(251,584)(252,585)(253,571)(254,572)(255,573)(256,568)
(257,569)(258,570)(259,574)(260,575)(261,576)(262,589)(263,590)(264,591)
(265,586)(266,587)(267,588)(268,592)(269,593)(270,594)(271,607)(272,608)
(273,609)(274,604)(275,605)(276,606)(277,610)(278,611)(279,612)(280,598)
(281,599)(282,600)(283,595)(284,596)(285,597)(286,601)(287,602)(288,603)
(289,616)(290,617)(291,618)(292,613)(293,614)(294,615)(295,619)(296,620)
(297,621)(298,634)(299,635)(300,636)(301,631)(302,632)(303,633)(304,637)
(305,638)(306,639)(307,625)(308,626)(309,627)(310,622)(311,623)(312,624)
(313,628)(314,629)(315,630)(316,643)(317,644)(318,645)(319,640)(320,641)
(321,642)(322,646)(323,647)(324,648)(325,526)(326,527)(327,528)(328,523)
(329,524)(330,525)(331,529)(332,530)(333,531)(334,517)(335,518)(336,519)
(337,514)(338,515)(339,516)(340,520)(341,521)(342,522)(343,535)(344,536)
(345,537)(346,532)(347,533)(348,534)(349,538)(350,539)(351,540)(352,499)
(353,500)(354,501)(355,496)(356,497)(357,498)(358,502)(359,503)(360,504)
(361,490)(362,491)(363,492)(364,487)(365,488)(366,489)(367,493)(368,494)
(369,495)(370,508)(371,509)(372,510)(373,505)(374,506)(375,507)(376,511)
(377,512)(378,513)(379,445)(380,446)(381,447)(382,442)(383,443)(384,444)
(385,448)(386,449)(387,450)(388,436)(389,437)(390,438)(391,433)(392,434)
(393,435)(394,439)(395,440)(396,441)(397,454)(398,455)(399,456)(400,451)
(401,452)(402,453)(403,457)(404,458)(405,459)(406,472)(407,473)(408,474)
(409,469)(410,470)(411,471)(412,475)(413,476)(414,477)(415,463)(416,464)
(417,465)(418,460)(419,461)(420,462)(421,466)(422,467)(423,468)(424,481)
(425,482)(426,483)(427,478)(428,479)(429,480)(430,484)(431,485)(432,486);;
s2 := (  1,433)(  2,435)(  3,434)(  4,436)(  5,438)(  6,437)(  7,439)(  8,441)
(  9,440)( 10,451)( 11,453)( 12,452)( 13,454)( 14,456)( 15,455)( 16,457)
( 17,459)( 18,458)( 19,442)( 20,444)( 21,443)( 22,445)( 23,447)( 24,446)
( 25,448)( 26,450)( 27,449)( 28,460)( 29,462)( 30,461)( 31,463)( 32,465)
( 33,464)( 34,466)( 35,468)( 36,467)( 37,478)( 38,480)( 39,479)( 40,481)
( 41,483)( 42,482)( 43,484)( 44,486)( 45,485)( 46,469)( 47,471)( 48,470)
( 49,472)( 50,474)( 51,473)( 52,475)( 53,477)( 54,476)( 55,514)( 56,516)
( 57,515)( 58,517)( 59,519)( 60,518)( 61,520)( 62,522)( 63,521)( 64,532)
( 65,534)( 66,533)( 67,535)( 68,537)( 69,536)( 70,538)( 71,540)( 72,539)
( 73,523)( 74,525)( 75,524)( 76,526)( 77,528)( 78,527)( 79,529)( 80,531)
( 81,530)( 82,487)( 83,489)( 84,488)( 85,490)( 86,492)( 87,491)( 88,493)
( 89,495)( 90,494)( 91,505)( 92,507)( 93,506)( 94,508)( 95,510)( 96,509)
( 97,511)( 98,513)( 99,512)(100,496)(101,498)(102,497)(103,499)(104,501)
(105,500)(106,502)(107,504)(108,503)(109,595)(110,597)(111,596)(112,598)
(113,600)(114,599)(115,601)(116,603)(117,602)(118,613)(119,615)(120,614)
(121,616)(122,618)(123,617)(124,619)(125,621)(126,620)(127,604)(128,606)
(129,605)(130,607)(131,609)(132,608)(133,610)(134,612)(135,611)(136,622)
(137,624)(138,623)(139,625)(140,627)(141,626)(142,628)(143,630)(144,629)
(145,640)(146,642)(147,641)(148,643)(149,645)(150,644)(151,646)(152,648)
(153,647)(154,631)(155,633)(156,632)(157,634)(158,636)(159,635)(160,637)
(161,639)(162,638)(163,541)(164,543)(165,542)(166,544)(167,546)(168,545)
(169,547)(170,549)(171,548)(172,559)(173,561)(174,560)(175,562)(176,564)
(177,563)(178,565)(179,567)(180,566)(181,550)(182,552)(183,551)(184,553)
(185,555)(186,554)(187,556)(188,558)(189,557)(190,568)(191,570)(192,569)
(193,571)(194,573)(195,572)(196,574)(197,576)(198,575)(199,586)(200,588)
(201,587)(202,589)(203,591)(204,590)(205,592)(206,594)(207,593)(208,577)
(209,579)(210,578)(211,580)(212,582)(213,581)(214,583)(215,585)(216,584)
(217,811)(218,813)(219,812)(220,814)(221,816)(222,815)(223,817)(224,819)
(225,818)(226,829)(227,831)(228,830)(229,832)(230,834)(231,833)(232,835)
(233,837)(234,836)(235,820)(236,822)(237,821)(238,823)(239,825)(240,824)
(241,826)(242,828)(243,827)(244,838)(245,840)(246,839)(247,841)(248,843)
(249,842)(250,844)(251,846)(252,845)(253,856)(254,858)(255,857)(256,859)
(257,861)(258,860)(259,862)(260,864)(261,863)(262,847)(263,849)(264,848)
(265,850)(266,852)(267,851)(268,853)(269,855)(270,854)(271,757)(272,759)
(273,758)(274,760)(275,762)(276,761)(277,763)(278,765)(279,764)(280,775)
(281,777)(282,776)(283,778)(284,780)(285,779)(286,781)(287,783)(288,782)
(289,766)(290,768)(291,767)(292,769)(293,771)(294,770)(295,772)(296,774)
(297,773)(298,784)(299,786)(300,785)(301,787)(302,789)(303,788)(304,790)
(305,792)(306,791)(307,802)(308,804)(309,803)(310,805)(311,807)(312,806)
(313,808)(314,810)(315,809)(316,793)(317,795)(318,794)(319,796)(320,798)
(321,797)(322,799)(323,801)(324,800)(325,703)(326,705)(327,704)(328,706)
(329,708)(330,707)(331,709)(332,711)(333,710)(334,721)(335,723)(336,722)
(337,724)(338,726)(339,725)(340,727)(341,729)(342,728)(343,712)(344,714)
(345,713)(346,715)(347,717)(348,716)(349,718)(350,720)(351,719)(352,730)
(353,732)(354,731)(355,733)(356,735)(357,734)(358,736)(359,738)(360,737)
(361,748)(362,750)(363,749)(364,751)(365,753)(366,752)(367,754)(368,756)
(369,755)(370,739)(371,741)(372,740)(373,742)(374,744)(375,743)(376,745)
(377,747)(378,746)(379,649)(380,651)(381,650)(382,652)(383,654)(384,653)
(385,655)(386,657)(387,656)(388,667)(389,669)(390,668)(391,670)(392,672)
(393,671)(394,673)(395,675)(396,674)(397,658)(398,660)(399,659)(400,661)
(401,663)(402,662)(403,664)(404,666)(405,665)(406,676)(407,678)(408,677)
(409,679)(410,681)(411,680)(412,682)(413,684)(414,683)(415,694)(416,696)
(417,695)(418,697)(419,699)(420,698)(421,700)(422,702)(423,701)(424,685)
(425,687)(426,686)(427,688)(428,690)(429,689)(430,691)(431,693)(432,692);;
s3 := (  1,  2)(  4,  5)(  7,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)
( 25, 26)( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 40, 41)( 43, 44)( 46, 47)
( 49, 50)( 52, 53)( 55, 83)( 56, 82)( 57, 84)( 58, 86)( 59, 85)( 60, 87)
( 61, 89)( 62, 88)( 63, 90)( 64, 92)( 65, 91)( 66, 93)( 67, 95)( 68, 94)
( 69, 96)( 70, 98)( 71, 97)( 72, 99)( 73,101)( 74,100)( 75,102)( 76,104)
( 77,103)( 78,105)( 79,107)( 80,106)( 81,108)(109,164)(110,163)(111,165)
(112,167)(113,166)(114,168)(115,170)(116,169)(117,171)(118,173)(119,172)
(120,174)(121,176)(122,175)(123,177)(124,179)(125,178)(126,180)(127,182)
(128,181)(129,183)(130,185)(131,184)(132,186)(133,188)(134,187)(135,189)
(136,191)(137,190)(138,192)(139,194)(140,193)(141,195)(142,197)(143,196)
(144,198)(145,200)(146,199)(147,201)(148,203)(149,202)(150,204)(151,206)
(152,205)(153,207)(154,209)(155,208)(156,210)(157,212)(158,211)(159,213)
(160,215)(161,214)(162,216)(217,380)(218,379)(219,381)(220,383)(221,382)
(222,384)(223,386)(224,385)(225,387)(226,389)(227,388)(228,390)(229,392)
(230,391)(231,393)(232,395)(233,394)(234,396)(235,398)(236,397)(237,399)
(238,401)(239,400)(240,402)(241,404)(242,403)(243,405)(244,407)(245,406)
(246,408)(247,410)(248,409)(249,411)(250,413)(251,412)(252,414)(253,416)
(254,415)(255,417)(256,419)(257,418)(258,420)(259,422)(260,421)(261,423)
(262,425)(263,424)(264,426)(265,428)(266,427)(267,429)(268,431)(269,430)
(270,432)(271,326)(272,325)(273,327)(274,329)(275,328)(276,330)(277,332)
(278,331)(279,333)(280,335)(281,334)(282,336)(283,338)(284,337)(285,339)
(286,341)(287,340)(288,342)(289,344)(290,343)(291,345)(292,347)(293,346)
(294,348)(295,350)(296,349)(297,351)(298,353)(299,352)(300,354)(301,356)
(302,355)(303,357)(304,359)(305,358)(306,360)(307,362)(308,361)(309,363)
(310,365)(311,364)(312,366)(313,368)(314,367)(315,369)(316,371)(317,370)
(318,372)(319,374)(320,373)(321,375)(322,377)(323,376)(324,378)(433,542)
(434,541)(435,543)(436,545)(437,544)(438,546)(439,548)(440,547)(441,549)
(442,551)(443,550)(444,552)(445,554)(446,553)(447,555)(448,557)(449,556)
(450,558)(451,560)(452,559)(453,561)(454,563)(455,562)(456,564)(457,566)
(458,565)(459,567)(460,569)(461,568)(462,570)(463,572)(464,571)(465,573)
(466,575)(467,574)(468,576)(469,578)(470,577)(471,579)(472,581)(473,580)
(474,582)(475,584)(476,583)(477,585)(478,587)(479,586)(480,588)(481,590)
(482,589)(483,591)(484,593)(485,592)(486,594)(487,623)(488,622)(489,624)
(490,626)(491,625)(492,627)(493,629)(494,628)(495,630)(496,632)(497,631)
(498,633)(499,635)(500,634)(501,636)(502,638)(503,637)(504,639)(505,641)
(506,640)(507,642)(508,644)(509,643)(510,645)(511,647)(512,646)(513,648)
(514,596)(515,595)(516,597)(517,599)(518,598)(519,600)(520,602)(521,601)
(522,603)(523,605)(524,604)(525,606)(526,608)(527,607)(528,609)(529,611)
(530,610)(531,612)(532,614)(533,613)(534,615)(535,617)(536,616)(537,618)
(538,620)(539,619)(540,621)(649,650)(652,653)(655,656)(658,659)(661,662)
(664,665)(667,668)(670,671)(673,674)(676,677)(679,680)(682,683)(685,686)
(688,689)(691,692)(694,695)(697,698)(700,701)(703,731)(704,730)(705,732)
(706,734)(707,733)(708,735)(709,737)(710,736)(711,738)(712,740)(713,739)
(714,741)(715,743)(716,742)(717,744)(718,746)(719,745)(720,747)(721,749)
(722,748)(723,750)(724,752)(725,751)(726,753)(727,755)(728,754)(729,756)
(757,812)(758,811)(759,813)(760,815)(761,814)(762,816)(763,818)(764,817)
(765,819)(766,821)(767,820)(768,822)(769,824)(770,823)(771,825)(772,827)
(773,826)(774,828)(775,830)(776,829)(777,831)(778,833)(779,832)(780,834)
(781,836)(782,835)(783,837)(784,839)(785,838)(786,840)(787,842)(788,841)
(789,843)(790,845)(791,844)(792,846)(793,848)(794,847)(795,849)(796,851)
(797,850)(798,852)(799,854)(800,853)(801,855)(802,857)(803,856)(804,858)
(805,860)(806,859)(807,861)(808,863)(809,862)(810,864);;
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, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
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*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)!(  1,649)(  2,650)(  3,651)(  4,655)(  5,656)(  6,657)(  7,652)
(  8,653)(  9,654)( 10,667)( 11,668)( 12,669)( 13,673)( 14,674)( 15,675)
( 16,670)( 17,671)( 18,672)( 19,658)( 20,659)( 21,660)( 22,664)( 23,665)
( 24,666)( 25,661)( 26,662)( 27,663)( 28,676)( 29,677)( 30,678)( 31,682)
( 32,683)( 33,684)( 34,679)( 35,680)( 36,681)( 37,694)( 38,695)( 39,696)
( 40,700)( 41,701)( 42,702)( 43,697)( 44,698)( 45,699)( 46,685)( 47,686)
( 48,687)( 49,691)( 50,692)( 51,693)( 52,688)( 53,689)( 54,690)( 55,703)
( 56,704)( 57,705)( 58,709)( 59,710)( 60,711)( 61,706)( 62,707)( 63,708)
( 64,721)( 65,722)( 66,723)( 67,727)( 68,728)( 69,729)( 70,724)( 71,725)
( 72,726)( 73,712)( 74,713)( 75,714)( 76,718)( 77,719)( 78,720)( 79,715)
( 80,716)( 81,717)( 82,730)( 83,731)( 84,732)( 85,736)( 86,737)( 87,738)
( 88,733)( 89,734)( 90,735)( 91,748)( 92,749)( 93,750)( 94,754)( 95,755)
( 96,756)( 97,751)( 98,752)( 99,753)(100,739)(101,740)(102,741)(103,745)
(104,746)(105,747)(106,742)(107,743)(108,744)(109,757)(110,758)(111,759)
(112,763)(113,764)(114,765)(115,760)(116,761)(117,762)(118,775)(119,776)
(120,777)(121,781)(122,782)(123,783)(124,778)(125,779)(126,780)(127,766)
(128,767)(129,768)(130,772)(131,773)(132,774)(133,769)(134,770)(135,771)
(136,784)(137,785)(138,786)(139,790)(140,791)(141,792)(142,787)(143,788)
(144,789)(145,802)(146,803)(147,804)(148,808)(149,809)(150,810)(151,805)
(152,806)(153,807)(154,793)(155,794)(156,795)(157,799)(158,800)(159,801)
(160,796)(161,797)(162,798)(163,811)(164,812)(165,813)(166,817)(167,818)
(168,819)(169,814)(170,815)(171,816)(172,829)(173,830)(174,831)(175,835)
(176,836)(177,837)(178,832)(179,833)(180,834)(181,820)(182,821)(183,822)
(184,826)(185,827)(186,828)(187,823)(188,824)(189,825)(190,838)(191,839)
(192,840)(193,844)(194,845)(195,846)(196,841)(197,842)(198,843)(199,856)
(200,857)(201,858)(202,862)(203,863)(204,864)(205,859)(206,860)(207,861)
(208,847)(209,848)(210,849)(211,853)(212,854)(213,855)(214,850)(215,851)
(216,852)(217,541)(218,542)(219,543)(220,547)(221,548)(222,549)(223,544)
(224,545)(225,546)(226,559)(227,560)(228,561)(229,565)(230,566)(231,567)
(232,562)(233,563)(234,564)(235,550)(236,551)(237,552)(238,556)(239,557)
(240,558)(241,553)(242,554)(243,555)(244,568)(245,569)(246,570)(247,574)
(248,575)(249,576)(250,571)(251,572)(252,573)(253,586)(254,587)(255,588)
(256,592)(257,593)(258,594)(259,589)(260,590)(261,591)(262,577)(263,578)
(264,579)(265,583)(266,584)(267,585)(268,580)(269,581)(270,582)(271,595)
(272,596)(273,597)(274,601)(275,602)(276,603)(277,598)(278,599)(279,600)
(280,613)(281,614)(282,615)(283,619)(284,620)(285,621)(286,616)(287,617)
(288,618)(289,604)(290,605)(291,606)(292,610)(293,611)(294,612)(295,607)
(296,608)(297,609)(298,622)(299,623)(300,624)(301,628)(302,629)(303,630)
(304,625)(305,626)(306,627)(307,640)(308,641)(309,642)(310,646)(311,647)
(312,648)(313,643)(314,644)(315,645)(316,631)(317,632)(318,633)(319,637)
(320,638)(321,639)(322,634)(323,635)(324,636)(325,514)(326,515)(327,516)
(328,520)(329,521)(330,522)(331,517)(332,518)(333,519)(334,532)(335,533)
(336,534)(337,538)(338,539)(339,540)(340,535)(341,536)(342,537)(343,523)
(344,524)(345,525)(346,529)(347,530)(348,531)(349,526)(350,527)(351,528)
(352,487)(353,488)(354,489)(355,493)(356,494)(357,495)(358,490)(359,491)
(360,492)(361,505)(362,506)(363,507)(364,511)(365,512)(366,513)(367,508)
(368,509)(369,510)(370,496)(371,497)(372,498)(373,502)(374,503)(375,504)
(376,499)(377,500)(378,501)(379,433)(380,434)(381,435)(382,439)(383,440)
(384,441)(385,436)(386,437)(387,438)(388,451)(389,452)(390,453)(391,457)
(392,458)(393,459)(394,454)(395,455)(396,456)(397,442)(398,443)(399,444)
(400,448)(401,449)(402,450)(403,445)(404,446)(405,447)(406,460)(407,461)
(408,462)(409,466)(410,467)(411,468)(412,463)(413,464)(414,465)(415,478)
(416,479)(417,480)(418,484)(419,485)(420,486)(421,481)(422,482)(423,483)
(424,469)(425,470)(426,471)(427,475)(428,476)(429,477)(430,472)(431,473)
(432,474);
s1 := Sym(864)!(  1,661)(  2,662)(  3,663)(  4,658)(  5,659)(  6,660)(  7,664)
(  8,665)(  9,666)( 10,652)( 11,653)( 12,654)( 13,649)( 14,650)( 15,651)
( 16,655)( 17,656)( 18,657)( 19,670)( 20,671)( 21,672)( 22,667)( 23,668)
( 24,669)( 25,673)( 26,674)( 27,675)( 28,688)( 29,689)( 30,690)( 31,685)
( 32,686)( 33,687)( 34,691)( 35,692)( 36,693)( 37,679)( 38,680)( 39,681)
( 40,676)( 41,677)( 42,678)( 43,682)( 44,683)( 45,684)( 46,697)( 47,698)
( 48,699)( 49,694)( 50,695)( 51,696)( 52,700)( 53,701)( 54,702)( 55,715)
( 56,716)( 57,717)( 58,712)( 59,713)( 60,714)( 61,718)( 62,719)( 63,720)
( 64,706)( 65,707)( 66,708)( 67,703)( 68,704)( 69,705)( 70,709)( 71,710)
( 72,711)( 73,724)( 74,725)( 75,726)( 76,721)( 77,722)( 78,723)( 79,727)
( 80,728)( 81,729)( 82,742)( 83,743)( 84,744)( 85,739)( 86,740)( 87,741)
( 88,745)( 89,746)( 90,747)( 91,733)( 92,734)( 93,735)( 94,730)( 95,731)
( 96,732)( 97,736)( 98,737)( 99,738)(100,751)(101,752)(102,753)(103,748)
(104,749)(105,750)(106,754)(107,755)(108,756)(109,769)(110,770)(111,771)
(112,766)(113,767)(114,768)(115,772)(116,773)(117,774)(118,760)(119,761)
(120,762)(121,757)(122,758)(123,759)(124,763)(125,764)(126,765)(127,778)
(128,779)(129,780)(130,775)(131,776)(132,777)(133,781)(134,782)(135,783)
(136,796)(137,797)(138,798)(139,793)(140,794)(141,795)(142,799)(143,800)
(144,801)(145,787)(146,788)(147,789)(148,784)(149,785)(150,786)(151,790)
(152,791)(153,792)(154,805)(155,806)(156,807)(157,802)(158,803)(159,804)
(160,808)(161,809)(162,810)(163,823)(164,824)(165,825)(166,820)(167,821)
(168,822)(169,826)(170,827)(171,828)(172,814)(173,815)(174,816)(175,811)
(176,812)(177,813)(178,817)(179,818)(180,819)(181,832)(182,833)(183,834)
(184,829)(185,830)(186,831)(187,835)(188,836)(189,837)(190,850)(191,851)
(192,852)(193,847)(194,848)(195,849)(196,853)(197,854)(198,855)(199,841)
(200,842)(201,843)(202,838)(203,839)(204,840)(205,844)(206,845)(207,846)
(208,859)(209,860)(210,861)(211,856)(212,857)(213,858)(214,862)(215,863)
(216,864)(217,553)(218,554)(219,555)(220,550)(221,551)(222,552)(223,556)
(224,557)(225,558)(226,544)(227,545)(228,546)(229,541)(230,542)(231,543)
(232,547)(233,548)(234,549)(235,562)(236,563)(237,564)(238,559)(239,560)
(240,561)(241,565)(242,566)(243,567)(244,580)(245,581)(246,582)(247,577)
(248,578)(249,579)(250,583)(251,584)(252,585)(253,571)(254,572)(255,573)
(256,568)(257,569)(258,570)(259,574)(260,575)(261,576)(262,589)(263,590)
(264,591)(265,586)(266,587)(267,588)(268,592)(269,593)(270,594)(271,607)
(272,608)(273,609)(274,604)(275,605)(276,606)(277,610)(278,611)(279,612)
(280,598)(281,599)(282,600)(283,595)(284,596)(285,597)(286,601)(287,602)
(288,603)(289,616)(290,617)(291,618)(292,613)(293,614)(294,615)(295,619)
(296,620)(297,621)(298,634)(299,635)(300,636)(301,631)(302,632)(303,633)
(304,637)(305,638)(306,639)(307,625)(308,626)(309,627)(310,622)(311,623)
(312,624)(313,628)(314,629)(315,630)(316,643)(317,644)(318,645)(319,640)
(320,641)(321,642)(322,646)(323,647)(324,648)(325,526)(326,527)(327,528)
(328,523)(329,524)(330,525)(331,529)(332,530)(333,531)(334,517)(335,518)
(336,519)(337,514)(338,515)(339,516)(340,520)(341,521)(342,522)(343,535)
(344,536)(345,537)(346,532)(347,533)(348,534)(349,538)(350,539)(351,540)
(352,499)(353,500)(354,501)(355,496)(356,497)(357,498)(358,502)(359,503)
(360,504)(361,490)(362,491)(363,492)(364,487)(365,488)(366,489)(367,493)
(368,494)(369,495)(370,508)(371,509)(372,510)(373,505)(374,506)(375,507)
(376,511)(377,512)(378,513)(379,445)(380,446)(381,447)(382,442)(383,443)
(384,444)(385,448)(386,449)(387,450)(388,436)(389,437)(390,438)(391,433)
(392,434)(393,435)(394,439)(395,440)(396,441)(397,454)(398,455)(399,456)
(400,451)(401,452)(402,453)(403,457)(404,458)(405,459)(406,472)(407,473)
(408,474)(409,469)(410,470)(411,471)(412,475)(413,476)(414,477)(415,463)
(416,464)(417,465)(418,460)(419,461)(420,462)(421,466)(422,467)(423,468)
(424,481)(425,482)(426,483)(427,478)(428,479)(429,480)(430,484)(431,485)
(432,486);
s2 := Sym(864)!(  1,433)(  2,435)(  3,434)(  4,436)(  5,438)(  6,437)(  7,439)
(  8,441)(  9,440)( 10,451)( 11,453)( 12,452)( 13,454)( 14,456)( 15,455)
( 16,457)( 17,459)( 18,458)( 19,442)( 20,444)( 21,443)( 22,445)( 23,447)
( 24,446)( 25,448)( 26,450)( 27,449)( 28,460)( 29,462)( 30,461)( 31,463)
( 32,465)( 33,464)( 34,466)( 35,468)( 36,467)( 37,478)( 38,480)( 39,479)
( 40,481)( 41,483)( 42,482)( 43,484)( 44,486)( 45,485)( 46,469)( 47,471)
( 48,470)( 49,472)( 50,474)( 51,473)( 52,475)( 53,477)( 54,476)( 55,514)
( 56,516)( 57,515)( 58,517)( 59,519)( 60,518)( 61,520)( 62,522)( 63,521)
( 64,532)( 65,534)( 66,533)( 67,535)( 68,537)( 69,536)( 70,538)( 71,540)
( 72,539)( 73,523)( 74,525)( 75,524)( 76,526)( 77,528)( 78,527)( 79,529)
( 80,531)( 81,530)( 82,487)( 83,489)( 84,488)( 85,490)( 86,492)( 87,491)
( 88,493)( 89,495)( 90,494)( 91,505)( 92,507)( 93,506)( 94,508)( 95,510)
( 96,509)( 97,511)( 98,513)( 99,512)(100,496)(101,498)(102,497)(103,499)
(104,501)(105,500)(106,502)(107,504)(108,503)(109,595)(110,597)(111,596)
(112,598)(113,600)(114,599)(115,601)(116,603)(117,602)(118,613)(119,615)
(120,614)(121,616)(122,618)(123,617)(124,619)(125,621)(126,620)(127,604)
(128,606)(129,605)(130,607)(131,609)(132,608)(133,610)(134,612)(135,611)
(136,622)(137,624)(138,623)(139,625)(140,627)(141,626)(142,628)(143,630)
(144,629)(145,640)(146,642)(147,641)(148,643)(149,645)(150,644)(151,646)
(152,648)(153,647)(154,631)(155,633)(156,632)(157,634)(158,636)(159,635)
(160,637)(161,639)(162,638)(163,541)(164,543)(165,542)(166,544)(167,546)
(168,545)(169,547)(170,549)(171,548)(172,559)(173,561)(174,560)(175,562)
(176,564)(177,563)(178,565)(179,567)(180,566)(181,550)(182,552)(183,551)
(184,553)(185,555)(186,554)(187,556)(188,558)(189,557)(190,568)(191,570)
(192,569)(193,571)(194,573)(195,572)(196,574)(197,576)(198,575)(199,586)
(200,588)(201,587)(202,589)(203,591)(204,590)(205,592)(206,594)(207,593)
(208,577)(209,579)(210,578)(211,580)(212,582)(213,581)(214,583)(215,585)
(216,584)(217,811)(218,813)(219,812)(220,814)(221,816)(222,815)(223,817)
(224,819)(225,818)(226,829)(227,831)(228,830)(229,832)(230,834)(231,833)
(232,835)(233,837)(234,836)(235,820)(236,822)(237,821)(238,823)(239,825)
(240,824)(241,826)(242,828)(243,827)(244,838)(245,840)(246,839)(247,841)
(248,843)(249,842)(250,844)(251,846)(252,845)(253,856)(254,858)(255,857)
(256,859)(257,861)(258,860)(259,862)(260,864)(261,863)(262,847)(263,849)
(264,848)(265,850)(266,852)(267,851)(268,853)(269,855)(270,854)(271,757)
(272,759)(273,758)(274,760)(275,762)(276,761)(277,763)(278,765)(279,764)
(280,775)(281,777)(282,776)(283,778)(284,780)(285,779)(286,781)(287,783)
(288,782)(289,766)(290,768)(291,767)(292,769)(293,771)(294,770)(295,772)
(296,774)(297,773)(298,784)(299,786)(300,785)(301,787)(302,789)(303,788)
(304,790)(305,792)(306,791)(307,802)(308,804)(309,803)(310,805)(311,807)
(312,806)(313,808)(314,810)(315,809)(316,793)(317,795)(318,794)(319,796)
(320,798)(321,797)(322,799)(323,801)(324,800)(325,703)(326,705)(327,704)
(328,706)(329,708)(330,707)(331,709)(332,711)(333,710)(334,721)(335,723)
(336,722)(337,724)(338,726)(339,725)(340,727)(341,729)(342,728)(343,712)
(344,714)(345,713)(346,715)(347,717)(348,716)(349,718)(350,720)(351,719)
(352,730)(353,732)(354,731)(355,733)(356,735)(357,734)(358,736)(359,738)
(360,737)(361,748)(362,750)(363,749)(364,751)(365,753)(366,752)(367,754)
(368,756)(369,755)(370,739)(371,741)(372,740)(373,742)(374,744)(375,743)
(376,745)(377,747)(378,746)(379,649)(380,651)(381,650)(382,652)(383,654)
(384,653)(385,655)(386,657)(387,656)(388,667)(389,669)(390,668)(391,670)
(392,672)(393,671)(394,673)(395,675)(396,674)(397,658)(398,660)(399,659)
(400,661)(401,663)(402,662)(403,664)(404,666)(405,665)(406,676)(407,678)
(408,677)(409,679)(410,681)(411,680)(412,682)(413,684)(414,683)(415,694)
(416,696)(417,695)(418,697)(419,699)(420,698)(421,700)(422,702)(423,701)
(424,685)(425,687)(426,686)(427,688)(428,690)(429,689)(430,691)(431,693)
(432,692);
s3 := Sym(864)!(  1,  2)(  4,  5)(  7,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)
( 22, 23)( 25, 26)( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 40, 41)( 43, 44)
( 46, 47)( 49, 50)( 52, 53)( 55, 83)( 56, 82)( 57, 84)( 58, 86)( 59, 85)
( 60, 87)( 61, 89)( 62, 88)( 63, 90)( 64, 92)( 65, 91)( 66, 93)( 67, 95)
( 68, 94)( 69, 96)( 70, 98)( 71, 97)( 72, 99)( 73,101)( 74,100)( 75,102)
( 76,104)( 77,103)( 78,105)( 79,107)( 80,106)( 81,108)(109,164)(110,163)
(111,165)(112,167)(113,166)(114,168)(115,170)(116,169)(117,171)(118,173)
(119,172)(120,174)(121,176)(122,175)(123,177)(124,179)(125,178)(126,180)
(127,182)(128,181)(129,183)(130,185)(131,184)(132,186)(133,188)(134,187)
(135,189)(136,191)(137,190)(138,192)(139,194)(140,193)(141,195)(142,197)
(143,196)(144,198)(145,200)(146,199)(147,201)(148,203)(149,202)(150,204)
(151,206)(152,205)(153,207)(154,209)(155,208)(156,210)(157,212)(158,211)
(159,213)(160,215)(161,214)(162,216)(217,380)(218,379)(219,381)(220,383)
(221,382)(222,384)(223,386)(224,385)(225,387)(226,389)(227,388)(228,390)
(229,392)(230,391)(231,393)(232,395)(233,394)(234,396)(235,398)(236,397)
(237,399)(238,401)(239,400)(240,402)(241,404)(242,403)(243,405)(244,407)
(245,406)(246,408)(247,410)(248,409)(249,411)(250,413)(251,412)(252,414)
(253,416)(254,415)(255,417)(256,419)(257,418)(258,420)(259,422)(260,421)
(261,423)(262,425)(263,424)(264,426)(265,428)(266,427)(267,429)(268,431)
(269,430)(270,432)(271,326)(272,325)(273,327)(274,329)(275,328)(276,330)
(277,332)(278,331)(279,333)(280,335)(281,334)(282,336)(283,338)(284,337)
(285,339)(286,341)(287,340)(288,342)(289,344)(290,343)(291,345)(292,347)
(293,346)(294,348)(295,350)(296,349)(297,351)(298,353)(299,352)(300,354)
(301,356)(302,355)(303,357)(304,359)(305,358)(306,360)(307,362)(308,361)
(309,363)(310,365)(311,364)(312,366)(313,368)(314,367)(315,369)(316,371)
(317,370)(318,372)(319,374)(320,373)(321,375)(322,377)(323,376)(324,378)
(433,542)(434,541)(435,543)(436,545)(437,544)(438,546)(439,548)(440,547)
(441,549)(442,551)(443,550)(444,552)(445,554)(446,553)(447,555)(448,557)
(449,556)(450,558)(451,560)(452,559)(453,561)(454,563)(455,562)(456,564)
(457,566)(458,565)(459,567)(460,569)(461,568)(462,570)(463,572)(464,571)
(465,573)(466,575)(467,574)(468,576)(469,578)(470,577)(471,579)(472,581)
(473,580)(474,582)(475,584)(476,583)(477,585)(478,587)(479,586)(480,588)
(481,590)(482,589)(483,591)(484,593)(485,592)(486,594)(487,623)(488,622)
(489,624)(490,626)(491,625)(492,627)(493,629)(494,628)(495,630)(496,632)
(497,631)(498,633)(499,635)(500,634)(501,636)(502,638)(503,637)(504,639)
(505,641)(506,640)(507,642)(508,644)(509,643)(510,645)(511,647)(512,646)
(513,648)(514,596)(515,595)(516,597)(517,599)(518,598)(519,600)(520,602)
(521,601)(522,603)(523,605)(524,604)(525,606)(526,608)(527,607)(528,609)
(529,611)(530,610)(531,612)(532,614)(533,613)(534,615)(535,617)(536,616)
(537,618)(538,620)(539,619)(540,621)(649,650)(652,653)(655,656)(658,659)
(661,662)(664,665)(667,668)(670,671)(673,674)(676,677)(679,680)(682,683)
(685,686)(688,689)(691,692)(694,695)(697,698)(700,701)(703,731)(704,730)
(705,732)(706,734)(707,733)(708,735)(709,737)(710,736)(711,738)(712,740)
(713,739)(714,741)(715,743)(716,742)(717,744)(718,746)(719,745)(720,747)
(721,749)(722,748)(723,750)(724,752)(725,751)(726,753)(727,755)(728,754)
(729,756)(757,812)(758,811)(759,813)(760,815)(761,814)(762,816)(763,818)
(764,817)(765,819)(766,821)(767,820)(768,822)(769,824)(770,823)(771,825)
(772,827)(773,826)(774,828)(775,830)(776,829)(777,831)(778,833)(779,832)
(780,834)(781,836)(782,835)(783,837)(784,839)(785,838)(786,840)(787,842)
(788,841)(789,843)(790,845)(791,844)(792,846)(793,848)(794,847)(795,849)
(796,851)(797,850)(798,852)(799,854)(800,853)(801,855)(802,857)(803,856)
(804,858)(805,860)(806,859)(807,861)(808,863)(809,862)(810,864);
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, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 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*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