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# Polytope of Type {24,6,6}

Atlas Canonical Name : {24,6,6}*1728e
if this polytope has a name.
Group : SmallGroup(1728,36607)
Rank : 4
Schlafli Type : {24,6,6}
Number of vertices, edges, etc : 24, 72, 18, 6
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {24,6,3}*864b, {12,6,6}*864e
3-fold quotients : {24,2,6}*576, {8,6,6}*576c
4-fold quotients : {12,6,3}*432b, {6,6,6}*432c
6-fold quotients : {24,2,3}*288, {8,6,3}*288, {12,2,6}*288, {4,6,6}*288c
8-fold quotients : {6,6,3}*216b
9-fold quotients : {24,2,2}*192, {8,2,6}*192
12-fold quotients : {12,2,3}*144, {4,6,3}*144, {2,6,6}*144b, {6,2,6}*144
18-fold quotients : {8,2,3}*96, {12,2,2}*96, {4,2,6}*96
24-fold quotients : {2,6,3}*72, {3,2,6}*72, {6,2,3}*72
27-fold quotients : {8,2,2}*64
36-fold quotients : {4,2,3}*48, {2,2,6}*48, {6,2,2}*48
48-fold quotients : {3,2,3}*36
54-fold quotients : {4,2,2}*32
72-fold quotients : {2,2,3}*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 := (  4,  7)(  5,  8)(  6,  9)( 13, 16)( 14, 17)( 15, 18)( 22, 25)( 23, 26)
( 24, 27)( 31, 34)( 32, 35)( 33, 36)( 40, 43)( 41, 44)( 42, 45)( 49, 52)
( 50, 53)( 51, 54)( 55, 82)( 56, 83)( 57, 84)( 58, 88)( 59, 89)( 60, 90)
( 61, 85)( 62, 86)( 63, 87)( 64, 91)( 65, 92)( 66, 93)( 67, 97)( 68, 98)
( 69, 99)( 70, 94)( 71, 95)( 72, 96)( 73,100)( 74,101)( 75,102)( 76,106)
( 77,107)( 78,108)( 79,103)( 80,104)( 81,105)(112,115)(113,116)(114,117)
(121,124)(122,125)(123,126)(130,133)(131,134)(132,135)(139,142)(140,143)
(141,144)(148,151)(149,152)(150,153)(157,160)(158,161)(159,162)(163,190)
(164,191)(165,192)(166,196)(167,197)(168,198)(169,193)(170,194)(171,195)
(172,199)(173,200)(174,201)(175,205)(176,206)(177,207)(178,202)(179,203)
(180,204)(181,208)(182,209)(183,210)(184,214)(185,215)(186,216)(187,211)
(188,212)(189,213)(217,298)(218,299)(219,300)(220,304)(221,305)(222,306)
(223,301)(224,302)(225,303)(226,307)(227,308)(228,309)(229,313)(230,314)
(231,315)(232,310)(233,311)(234,312)(235,316)(236,317)(237,318)(238,322)
(239,323)(240,324)(241,319)(242,320)(243,321)(244,271)(245,272)(246,273)
(247,277)(248,278)(249,279)(250,274)(251,275)(252,276)(253,280)(254,281)
(255,282)(256,286)(257,287)(258,288)(259,283)(260,284)(261,285)(262,289)
(263,290)(264,291)(265,295)(266,296)(267,297)(268,292)(269,293)(270,294)
(325,406)(326,407)(327,408)(328,412)(329,413)(330,414)(331,409)(332,410)
(333,411)(334,415)(335,416)(336,417)(337,421)(338,422)(339,423)(340,418)
(341,419)(342,420)(343,424)(344,425)(345,426)(346,430)(347,431)(348,432)
(349,427)(350,428)(351,429)(352,379)(353,380)(354,381)(355,385)(356,386)
(357,387)(358,382)(359,383)(360,384)(361,388)(362,389)(363,390)(364,394)
(365,395)(366,396)(367,391)(368,392)(369,393)(370,397)(371,398)(372,399)
(373,403)(374,404)(375,405)(376,400)(377,401)(378,402)(433,487)(434,488)
(435,489)(436,493)(437,494)(438,495)(439,490)(440,491)(441,492)(442,496)
(443,497)(444,498)(445,502)(446,503)(447,504)(448,499)(449,500)(450,501)
(451,505)(452,506)(453,507)(454,511)(455,512)(456,513)(457,508)(458,509)
(459,510)(460,514)(461,515)(462,516)(463,520)(464,521)(465,522)(466,517)
(467,518)(468,519)(469,523)(470,524)(471,525)(472,529)(473,530)(474,531)
(475,526)(476,527)(477,528)(478,532)(479,533)(480,534)(481,538)(482,539)
(483,540)(484,535)(485,536)(486,537)(541,595)(542,596)(543,597)(544,601)
(545,602)(546,603)(547,598)(548,599)(549,600)(550,604)(551,605)(552,606)
(553,610)(554,611)(555,612)(556,607)(557,608)(558,609)(559,613)(560,614)
(561,615)(562,619)(563,620)(564,621)(565,616)(566,617)(567,618)(568,622)
(569,623)(570,624)(571,628)(572,629)(573,630)(574,625)(575,626)(576,627)
(577,631)(578,632)(579,633)(580,637)(581,638)(582,639)(583,634)(584,635)
(585,636)(586,640)(587,641)(588,642)(589,646)(590,647)(591,648)(592,643)
(593,644)(594,645)(652,655)(653,656)(654,657)(661,664)(662,665)(663,666)
(670,673)(671,674)(672,675)(679,682)(680,683)(681,684)(688,691)(689,692)
(690,693)(697,700)(698,701)(699,702)(703,730)(704,731)(705,732)(706,736)
(707,737)(708,738)(709,733)(710,734)(711,735)(712,739)(713,740)(714,741)
(715,745)(716,746)(717,747)(718,742)(719,743)(720,744)(721,748)(722,749)
(723,750)(724,754)(725,755)(726,756)(727,751)(728,752)(729,753)(760,763)
(761,764)(762,765)(769,772)(770,773)(771,774)(778,781)(779,782)(780,783)
(787,790)(788,791)(789,792)(796,799)(797,800)(798,801)(805,808)(806,809)
(807,810)(811,838)(812,839)(813,840)(814,844)(815,845)(816,846)(817,841)
(818,842)(819,843)(820,847)(821,848)(822,849)(823,853)(824,854)(825,855)
(826,850)(827,851)(828,852)(829,856)(830,857)(831,858)(832,862)(833,863)
(834,864)(835,859)(836,860)(837,861);;
s1 := (  1,436)(  2,437)(  3,438)(  4,433)(  5,434)(  6,435)(  7,439)(  8,440)
(  9,441)( 10,454)( 11,455)( 12,456)( 13,451)( 14,452)( 15,453)( 16,457)
( 17,458)( 18,459)( 19,445)( 20,446)( 21,447)( 22,442)( 23,443)( 24,444)
( 25,448)( 26,449)( 27,450)( 28,463)( 29,464)( 30,465)( 31,460)( 32,461)
( 33,462)( 34,466)( 35,467)( 36,468)( 37,481)( 38,482)( 39,483)( 40,478)
( 41,479)( 42,480)( 43,484)( 44,485)( 45,486)( 46,472)( 47,473)( 48,474)
( 49,469)( 50,470)( 51,471)( 52,475)( 53,476)( 54,477)( 55,517)( 56,518)
( 57,519)( 58,514)( 59,515)( 60,516)( 61,520)( 62,521)( 63,522)( 64,535)
( 65,536)( 66,537)( 67,532)( 68,533)( 69,534)( 70,538)( 71,539)( 72,540)
( 73,526)( 74,527)( 75,528)( 76,523)( 77,524)( 78,525)( 79,529)( 80,530)
( 81,531)( 82,490)( 83,491)( 84,492)( 85,487)( 86,488)( 87,489)( 88,493)
( 89,494)( 90,495)( 91,508)( 92,509)( 93,510)( 94,505)( 95,506)( 96,507)
( 97,511)( 98,512)( 99,513)(100,499)(101,500)(102,501)(103,496)(104,497)
(105,498)(106,502)(107,503)(108,504)(109,544)(110,545)(111,546)(112,541)
(113,542)(114,543)(115,547)(116,548)(117,549)(118,562)(119,563)(120,564)
(121,559)(122,560)(123,561)(124,565)(125,566)(126,567)(127,553)(128,554)
(129,555)(130,550)(131,551)(132,552)(133,556)(134,557)(135,558)(136,571)
(137,572)(138,573)(139,568)(140,569)(141,570)(142,574)(143,575)(144,576)
(145,589)(146,590)(147,591)(148,586)(149,587)(150,588)(151,592)(152,593)
(153,594)(154,580)(155,581)(156,582)(157,577)(158,578)(159,579)(160,583)
(161,584)(162,585)(163,625)(164,626)(165,627)(166,622)(167,623)(168,624)
(169,628)(170,629)(171,630)(172,643)(173,644)(174,645)(175,640)(176,641)
(177,642)(178,646)(179,647)(180,648)(181,634)(182,635)(183,636)(184,631)
(185,632)(186,633)(187,637)(188,638)(189,639)(190,598)(191,599)(192,600)
(193,595)(194,596)(195,597)(196,601)(197,602)(198,603)(199,616)(200,617)
(201,618)(202,613)(203,614)(204,615)(205,619)(206,620)(207,621)(208,607)
(209,608)(210,609)(211,604)(212,605)(213,606)(214,610)(215,611)(216,612)
(217,733)(218,734)(219,735)(220,730)(221,731)(222,732)(223,736)(224,737)
(225,738)(226,751)(227,752)(228,753)(229,748)(230,749)(231,750)(232,754)
(233,755)(234,756)(235,742)(236,743)(237,744)(238,739)(239,740)(240,741)
(241,745)(242,746)(243,747)(244,706)(245,707)(246,708)(247,703)(248,704)
(249,705)(250,709)(251,710)(252,711)(253,724)(254,725)(255,726)(256,721)
(257,722)(258,723)(259,727)(260,728)(261,729)(262,715)(263,716)(264,717)
(265,712)(266,713)(267,714)(268,718)(269,719)(270,720)(271,679)(272,680)
(273,681)(274,676)(275,677)(276,678)(277,682)(278,683)(279,684)(280,697)
(281,698)(282,699)(283,694)(284,695)(285,696)(286,700)(287,701)(288,702)
(289,688)(290,689)(291,690)(292,685)(293,686)(294,687)(295,691)(296,692)
(297,693)(298,652)(299,653)(300,654)(301,649)(302,650)(303,651)(304,655)
(305,656)(306,657)(307,670)(308,671)(309,672)(310,667)(311,668)(312,669)
(313,673)(314,674)(315,675)(316,661)(317,662)(318,663)(319,658)(320,659)
(321,660)(322,664)(323,665)(324,666)(325,841)(326,842)(327,843)(328,838)
(329,839)(330,840)(331,844)(332,845)(333,846)(334,859)(335,860)(336,861)
(337,856)(338,857)(339,858)(340,862)(341,863)(342,864)(343,850)(344,851)
(345,852)(346,847)(347,848)(348,849)(349,853)(350,854)(351,855)(352,814)
(353,815)(354,816)(355,811)(356,812)(357,813)(358,817)(359,818)(360,819)
(361,832)(362,833)(363,834)(364,829)(365,830)(366,831)(367,835)(368,836)
(369,837)(370,823)(371,824)(372,825)(373,820)(374,821)(375,822)(376,826)
(377,827)(378,828)(379,787)(380,788)(381,789)(382,784)(383,785)(384,786)
(385,790)(386,791)(387,792)(388,805)(389,806)(390,807)(391,802)(392,803)
(393,804)(394,808)(395,809)(396,810)(397,796)(398,797)(399,798)(400,793)
(401,794)(402,795)(403,799)(404,800)(405,801)(406,760)(407,761)(408,762)
(409,757)(410,758)(411,759)(412,763)(413,764)(414,765)(415,778)(416,779)
(417,780)(418,775)(419,776)(420,777)(421,781)(422,782)(423,783)(424,769)
(425,770)(426,771)(427,766)(428,767)(429,768)(430,772)(431,773)(432,774);;
s2 := (  1,658)(  2,660)(  3,659)(  4,661)(  5,663)(  6,662)(  7,664)(  8,666)
(  9,665)( 10,649)( 11,651)( 12,650)( 13,652)( 14,654)( 15,653)( 16,655)
( 17,657)( 18,656)( 19,667)( 20,669)( 21,668)( 22,670)( 23,672)( 24,671)
( 25,673)( 26,675)( 27,674)( 28,685)( 29,687)( 30,686)( 31,688)( 32,690)
( 33,689)( 34,691)( 35,693)( 36,692)( 37,676)( 38,678)( 39,677)( 40,679)
( 41,681)( 42,680)( 43,682)( 44,684)( 45,683)( 46,694)( 47,696)( 48,695)
( 49,697)( 50,699)( 51,698)( 52,700)( 53,702)( 54,701)( 55,712)( 56,714)
( 57,713)( 58,715)( 59,717)( 60,716)( 61,718)( 62,720)( 63,719)( 64,703)
( 65,705)( 66,704)( 67,706)( 68,708)( 69,707)( 70,709)( 71,711)( 72,710)
( 73,721)( 74,723)( 75,722)( 76,724)( 77,726)( 78,725)( 79,727)( 80,729)
( 81,728)( 82,739)( 83,741)( 84,740)( 85,742)( 86,744)( 87,743)( 88,745)
( 89,747)( 90,746)( 91,730)( 92,732)( 93,731)( 94,733)( 95,735)( 96,734)
( 97,736)( 98,738)( 99,737)(100,748)(101,750)(102,749)(103,751)(104,753)
(105,752)(106,754)(107,756)(108,755)(109,766)(110,768)(111,767)(112,769)
(113,771)(114,770)(115,772)(116,774)(117,773)(118,757)(119,759)(120,758)
(121,760)(122,762)(123,761)(124,763)(125,765)(126,764)(127,775)(128,777)
(129,776)(130,778)(131,780)(132,779)(133,781)(134,783)(135,782)(136,793)
(137,795)(138,794)(139,796)(140,798)(141,797)(142,799)(143,801)(144,800)
(145,784)(146,786)(147,785)(148,787)(149,789)(150,788)(151,790)(152,792)
(153,791)(154,802)(155,804)(156,803)(157,805)(158,807)(159,806)(160,808)
(161,810)(162,809)(163,820)(164,822)(165,821)(166,823)(167,825)(168,824)
(169,826)(170,828)(171,827)(172,811)(173,813)(174,812)(175,814)(176,816)
(177,815)(178,817)(179,819)(180,818)(181,829)(182,831)(183,830)(184,832)
(185,834)(186,833)(187,835)(188,837)(189,836)(190,847)(191,849)(192,848)
(193,850)(194,852)(195,851)(196,853)(197,855)(198,854)(199,838)(200,840)
(201,839)(202,841)(203,843)(204,842)(205,844)(206,846)(207,845)(208,856)
(209,858)(210,857)(211,859)(212,861)(213,860)(214,862)(215,864)(216,863)
(217,496)(218,498)(219,497)(220,499)(221,501)(222,500)(223,502)(224,504)
(225,503)(226,487)(227,489)(228,488)(229,490)(230,492)(231,491)(232,493)
(233,495)(234,494)(235,505)(236,507)(237,506)(238,508)(239,510)(240,509)
(241,511)(242,513)(243,512)(244,523)(245,525)(246,524)(247,526)(248,528)
(249,527)(250,529)(251,531)(252,530)(253,514)(254,516)(255,515)(256,517)
(257,519)(258,518)(259,520)(260,522)(261,521)(262,532)(263,534)(264,533)
(265,535)(266,537)(267,536)(268,538)(269,540)(270,539)(271,469)(272,471)
(273,470)(274,472)(275,474)(276,473)(277,475)(278,477)(279,476)(280,460)
(281,462)(282,461)(283,463)(284,465)(285,464)(286,466)(287,468)(288,467)
(289,478)(290,480)(291,479)(292,481)(293,483)(294,482)(295,484)(296,486)
(297,485)(298,442)(299,444)(300,443)(301,445)(302,447)(303,446)(304,448)
(305,450)(306,449)(307,433)(308,435)(309,434)(310,436)(311,438)(312,437)
(313,439)(314,441)(315,440)(316,451)(317,453)(318,452)(319,454)(320,456)
(321,455)(322,457)(323,459)(324,458)(325,604)(326,606)(327,605)(328,607)
(329,609)(330,608)(331,610)(332,612)(333,611)(334,595)(335,597)(336,596)
(337,598)(338,600)(339,599)(340,601)(341,603)(342,602)(343,613)(344,615)
(345,614)(346,616)(347,618)(348,617)(349,619)(350,621)(351,620)(352,631)
(353,633)(354,632)(355,634)(356,636)(357,635)(358,637)(359,639)(360,638)
(361,622)(362,624)(363,623)(364,625)(365,627)(366,626)(367,628)(368,630)
(369,629)(370,640)(371,642)(372,641)(373,643)(374,645)(375,644)(376,646)
(377,648)(378,647)(379,577)(380,579)(381,578)(382,580)(383,582)(384,581)
(385,583)(386,585)(387,584)(388,568)(389,570)(390,569)(391,571)(392,573)
(393,572)(394,574)(395,576)(396,575)(397,586)(398,588)(399,587)(400,589)
(401,591)(402,590)(403,592)(404,594)(405,593)(406,550)(407,552)(408,551)
(409,553)(410,555)(411,554)(412,556)(413,558)(414,557)(415,541)(416,543)
(417,542)(418,544)(419,546)(420,545)(421,547)(422,549)(423,548)(424,559)
(425,561)(426,560)(427,562)(428,564)(429,563)(430,565)(431,567)(432,566);;
s3 := (  1,758)(  2,757)(  3,759)(  4,761)(  5,760)(  6,762)(  7,764)(  8,763)
(  9,765)( 10,776)( 11,775)( 12,777)( 13,779)( 14,778)( 15,780)( 16,782)
( 17,781)( 18,783)( 19,767)( 20,766)( 21,768)( 22,770)( 23,769)( 24,771)
( 25,773)( 26,772)( 27,774)( 28,785)( 29,784)( 30,786)( 31,788)( 32,787)
( 33,789)( 34,791)( 35,790)( 36,792)( 37,803)( 38,802)( 39,804)( 40,806)
( 41,805)( 42,807)( 43,809)( 44,808)( 45,810)( 46,794)( 47,793)( 48,795)
( 49,797)( 50,796)( 51,798)( 52,800)( 53,799)( 54,801)( 55,812)( 56,811)
( 57,813)( 58,815)( 59,814)( 60,816)( 61,818)( 62,817)( 63,819)( 64,830)
( 65,829)( 66,831)( 67,833)( 68,832)( 69,834)( 70,836)( 71,835)( 72,837)
( 73,821)( 74,820)( 75,822)( 76,824)( 77,823)( 78,825)( 79,827)( 80,826)
( 81,828)( 82,839)( 83,838)( 84,840)( 85,842)( 86,841)( 87,843)( 88,845)
( 89,844)( 90,846)( 91,857)( 92,856)( 93,858)( 94,860)( 95,859)( 96,861)
( 97,863)( 98,862)( 99,864)(100,848)(101,847)(102,849)(103,851)(104,850)
(105,852)(106,854)(107,853)(108,855)(109,650)(110,649)(111,651)(112,653)
(113,652)(114,654)(115,656)(116,655)(117,657)(118,668)(119,667)(120,669)
(121,671)(122,670)(123,672)(124,674)(125,673)(126,675)(127,659)(128,658)
(129,660)(130,662)(131,661)(132,663)(133,665)(134,664)(135,666)(136,677)
(137,676)(138,678)(139,680)(140,679)(141,681)(142,683)(143,682)(144,684)
(145,695)(146,694)(147,696)(148,698)(149,697)(150,699)(151,701)(152,700)
(153,702)(154,686)(155,685)(156,687)(157,689)(158,688)(159,690)(160,692)
(161,691)(162,693)(163,704)(164,703)(165,705)(166,707)(167,706)(168,708)
(169,710)(170,709)(171,711)(172,722)(173,721)(174,723)(175,725)(176,724)
(177,726)(178,728)(179,727)(180,729)(181,713)(182,712)(183,714)(184,716)
(185,715)(186,717)(187,719)(188,718)(189,720)(190,731)(191,730)(192,732)
(193,734)(194,733)(195,735)(196,737)(197,736)(198,738)(199,749)(200,748)
(201,750)(202,752)(203,751)(204,753)(205,755)(206,754)(207,756)(208,740)
(209,739)(210,741)(211,743)(212,742)(213,744)(214,746)(215,745)(216,747)
(217,596)(218,595)(219,597)(220,599)(221,598)(222,600)(223,602)(224,601)
(225,603)(226,614)(227,613)(228,615)(229,617)(230,616)(231,618)(232,620)
(233,619)(234,621)(235,605)(236,604)(237,606)(238,608)(239,607)(240,609)
(241,611)(242,610)(243,612)(244,623)(245,622)(246,624)(247,626)(248,625)
(249,627)(250,629)(251,628)(252,630)(253,641)(254,640)(255,642)(256,644)
(257,643)(258,645)(259,647)(260,646)(261,648)(262,632)(263,631)(264,633)
(265,635)(266,634)(267,636)(268,638)(269,637)(270,639)(271,569)(272,568)
(273,570)(274,572)(275,571)(276,573)(277,575)(278,574)(279,576)(280,587)
(281,586)(282,588)(283,590)(284,589)(285,591)(286,593)(287,592)(288,594)
(289,578)(290,577)(291,579)(292,581)(293,580)(294,582)(295,584)(296,583)
(297,585)(298,542)(299,541)(300,543)(301,545)(302,544)(303,546)(304,548)
(305,547)(306,549)(307,560)(308,559)(309,561)(310,563)(311,562)(312,564)
(313,566)(314,565)(315,567)(316,551)(317,550)(318,552)(319,554)(320,553)
(321,555)(322,557)(323,556)(324,558)(325,488)(326,487)(327,489)(328,491)
(329,490)(330,492)(331,494)(332,493)(333,495)(334,506)(335,505)(336,507)
(337,509)(338,508)(339,510)(340,512)(341,511)(342,513)(343,497)(344,496)
(345,498)(346,500)(347,499)(348,501)(349,503)(350,502)(351,504)(352,515)
(353,514)(354,516)(355,518)(356,517)(357,519)(358,521)(359,520)(360,522)
(361,533)(362,532)(363,534)(364,536)(365,535)(366,537)(367,539)(368,538)
(369,540)(370,524)(371,523)(372,525)(373,527)(374,526)(375,528)(376,530)
(377,529)(378,531)(379,461)(380,460)(381,462)(382,464)(383,463)(384,465)
(385,467)(386,466)(387,468)(388,479)(389,478)(390,480)(391,482)(392,481)
(393,483)(394,485)(395,484)(396,486)(397,470)(398,469)(399,471)(400,473)
(401,472)(402,474)(403,476)(404,475)(405,477)(406,434)(407,433)(408,435)
(409,437)(410,436)(411,438)(412,440)(413,439)(414,441)(415,452)(416,451)
(417,453)(418,455)(419,454)(420,456)(421,458)(422,457)(423,459)(424,443)
(425,442)(426,444)(427,446)(428,445)(429,447)(430,449)(431,448)(432,450);;
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,
s3*s1*s2*s1*s2*s3*s1*s2*s1*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,
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)!(  4,  7)(  5,  8)(  6,  9)( 13, 16)( 14, 17)( 15, 18)( 22, 25)
( 23, 26)( 24, 27)( 31, 34)( 32, 35)( 33, 36)( 40, 43)( 41, 44)( 42, 45)
( 49, 52)( 50, 53)( 51, 54)( 55, 82)( 56, 83)( 57, 84)( 58, 88)( 59, 89)
( 60, 90)( 61, 85)( 62, 86)( 63, 87)( 64, 91)( 65, 92)( 66, 93)( 67, 97)
( 68, 98)( 69, 99)( 70, 94)( 71, 95)( 72, 96)( 73,100)( 74,101)( 75,102)
( 76,106)( 77,107)( 78,108)( 79,103)( 80,104)( 81,105)(112,115)(113,116)
(114,117)(121,124)(122,125)(123,126)(130,133)(131,134)(132,135)(139,142)
(140,143)(141,144)(148,151)(149,152)(150,153)(157,160)(158,161)(159,162)
(163,190)(164,191)(165,192)(166,196)(167,197)(168,198)(169,193)(170,194)
(171,195)(172,199)(173,200)(174,201)(175,205)(176,206)(177,207)(178,202)
(179,203)(180,204)(181,208)(182,209)(183,210)(184,214)(185,215)(186,216)
(187,211)(188,212)(189,213)(217,298)(218,299)(219,300)(220,304)(221,305)
(222,306)(223,301)(224,302)(225,303)(226,307)(227,308)(228,309)(229,313)
(230,314)(231,315)(232,310)(233,311)(234,312)(235,316)(236,317)(237,318)
(238,322)(239,323)(240,324)(241,319)(242,320)(243,321)(244,271)(245,272)
(246,273)(247,277)(248,278)(249,279)(250,274)(251,275)(252,276)(253,280)
(254,281)(255,282)(256,286)(257,287)(258,288)(259,283)(260,284)(261,285)
(262,289)(263,290)(264,291)(265,295)(266,296)(267,297)(268,292)(269,293)
(270,294)(325,406)(326,407)(327,408)(328,412)(329,413)(330,414)(331,409)
(332,410)(333,411)(334,415)(335,416)(336,417)(337,421)(338,422)(339,423)
(340,418)(341,419)(342,420)(343,424)(344,425)(345,426)(346,430)(347,431)
(348,432)(349,427)(350,428)(351,429)(352,379)(353,380)(354,381)(355,385)
(356,386)(357,387)(358,382)(359,383)(360,384)(361,388)(362,389)(363,390)
(364,394)(365,395)(366,396)(367,391)(368,392)(369,393)(370,397)(371,398)
(372,399)(373,403)(374,404)(375,405)(376,400)(377,401)(378,402)(433,487)
(434,488)(435,489)(436,493)(437,494)(438,495)(439,490)(440,491)(441,492)
(442,496)(443,497)(444,498)(445,502)(446,503)(447,504)(448,499)(449,500)
(450,501)(451,505)(452,506)(453,507)(454,511)(455,512)(456,513)(457,508)
(458,509)(459,510)(460,514)(461,515)(462,516)(463,520)(464,521)(465,522)
(466,517)(467,518)(468,519)(469,523)(470,524)(471,525)(472,529)(473,530)
(474,531)(475,526)(476,527)(477,528)(478,532)(479,533)(480,534)(481,538)
(482,539)(483,540)(484,535)(485,536)(486,537)(541,595)(542,596)(543,597)
(544,601)(545,602)(546,603)(547,598)(548,599)(549,600)(550,604)(551,605)
(552,606)(553,610)(554,611)(555,612)(556,607)(557,608)(558,609)(559,613)
(560,614)(561,615)(562,619)(563,620)(564,621)(565,616)(566,617)(567,618)
(568,622)(569,623)(570,624)(571,628)(572,629)(573,630)(574,625)(575,626)
(576,627)(577,631)(578,632)(579,633)(580,637)(581,638)(582,639)(583,634)
(584,635)(585,636)(586,640)(587,641)(588,642)(589,646)(590,647)(591,648)
(592,643)(593,644)(594,645)(652,655)(653,656)(654,657)(661,664)(662,665)
(663,666)(670,673)(671,674)(672,675)(679,682)(680,683)(681,684)(688,691)
(689,692)(690,693)(697,700)(698,701)(699,702)(703,730)(704,731)(705,732)
(706,736)(707,737)(708,738)(709,733)(710,734)(711,735)(712,739)(713,740)
(714,741)(715,745)(716,746)(717,747)(718,742)(719,743)(720,744)(721,748)
(722,749)(723,750)(724,754)(725,755)(726,756)(727,751)(728,752)(729,753)
(760,763)(761,764)(762,765)(769,772)(770,773)(771,774)(778,781)(779,782)
(780,783)(787,790)(788,791)(789,792)(796,799)(797,800)(798,801)(805,808)
(806,809)(807,810)(811,838)(812,839)(813,840)(814,844)(815,845)(816,846)
(817,841)(818,842)(819,843)(820,847)(821,848)(822,849)(823,853)(824,854)
(825,855)(826,850)(827,851)(828,852)(829,856)(830,857)(831,858)(832,862)
(833,863)(834,864)(835,859)(836,860)(837,861);
s1 := Sym(864)!(  1,436)(  2,437)(  3,438)(  4,433)(  5,434)(  6,435)(  7,439)
(  8,440)(  9,441)( 10,454)( 11,455)( 12,456)( 13,451)( 14,452)( 15,453)
( 16,457)( 17,458)( 18,459)( 19,445)( 20,446)( 21,447)( 22,442)( 23,443)
( 24,444)( 25,448)( 26,449)( 27,450)( 28,463)( 29,464)( 30,465)( 31,460)
( 32,461)( 33,462)( 34,466)( 35,467)( 36,468)( 37,481)( 38,482)( 39,483)
( 40,478)( 41,479)( 42,480)( 43,484)( 44,485)( 45,486)( 46,472)( 47,473)
( 48,474)( 49,469)( 50,470)( 51,471)( 52,475)( 53,476)( 54,477)( 55,517)
( 56,518)( 57,519)( 58,514)( 59,515)( 60,516)( 61,520)( 62,521)( 63,522)
( 64,535)( 65,536)( 66,537)( 67,532)( 68,533)( 69,534)( 70,538)( 71,539)
( 72,540)( 73,526)( 74,527)( 75,528)( 76,523)( 77,524)( 78,525)( 79,529)
( 80,530)( 81,531)( 82,490)( 83,491)( 84,492)( 85,487)( 86,488)( 87,489)
( 88,493)( 89,494)( 90,495)( 91,508)( 92,509)( 93,510)( 94,505)( 95,506)
( 96,507)( 97,511)( 98,512)( 99,513)(100,499)(101,500)(102,501)(103,496)
(104,497)(105,498)(106,502)(107,503)(108,504)(109,544)(110,545)(111,546)
(112,541)(113,542)(114,543)(115,547)(116,548)(117,549)(118,562)(119,563)
(120,564)(121,559)(122,560)(123,561)(124,565)(125,566)(126,567)(127,553)
(128,554)(129,555)(130,550)(131,551)(132,552)(133,556)(134,557)(135,558)
(136,571)(137,572)(138,573)(139,568)(140,569)(141,570)(142,574)(143,575)
(144,576)(145,589)(146,590)(147,591)(148,586)(149,587)(150,588)(151,592)
(152,593)(153,594)(154,580)(155,581)(156,582)(157,577)(158,578)(159,579)
(160,583)(161,584)(162,585)(163,625)(164,626)(165,627)(166,622)(167,623)
(168,624)(169,628)(170,629)(171,630)(172,643)(173,644)(174,645)(175,640)
(176,641)(177,642)(178,646)(179,647)(180,648)(181,634)(182,635)(183,636)
(184,631)(185,632)(186,633)(187,637)(188,638)(189,639)(190,598)(191,599)
(192,600)(193,595)(194,596)(195,597)(196,601)(197,602)(198,603)(199,616)
(200,617)(201,618)(202,613)(203,614)(204,615)(205,619)(206,620)(207,621)
(208,607)(209,608)(210,609)(211,604)(212,605)(213,606)(214,610)(215,611)
(216,612)(217,733)(218,734)(219,735)(220,730)(221,731)(222,732)(223,736)
(224,737)(225,738)(226,751)(227,752)(228,753)(229,748)(230,749)(231,750)
(232,754)(233,755)(234,756)(235,742)(236,743)(237,744)(238,739)(239,740)
(240,741)(241,745)(242,746)(243,747)(244,706)(245,707)(246,708)(247,703)
(248,704)(249,705)(250,709)(251,710)(252,711)(253,724)(254,725)(255,726)
(256,721)(257,722)(258,723)(259,727)(260,728)(261,729)(262,715)(263,716)
(264,717)(265,712)(266,713)(267,714)(268,718)(269,719)(270,720)(271,679)
(272,680)(273,681)(274,676)(275,677)(276,678)(277,682)(278,683)(279,684)
(280,697)(281,698)(282,699)(283,694)(284,695)(285,696)(286,700)(287,701)
(288,702)(289,688)(290,689)(291,690)(292,685)(293,686)(294,687)(295,691)
(296,692)(297,693)(298,652)(299,653)(300,654)(301,649)(302,650)(303,651)
(304,655)(305,656)(306,657)(307,670)(308,671)(309,672)(310,667)(311,668)
(312,669)(313,673)(314,674)(315,675)(316,661)(317,662)(318,663)(319,658)
(320,659)(321,660)(322,664)(323,665)(324,666)(325,841)(326,842)(327,843)
(328,838)(329,839)(330,840)(331,844)(332,845)(333,846)(334,859)(335,860)
(336,861)(337,856)(338,857)(339,858)(340,862)(341,863)(342,864)(343,850)
(344,851)(345,852)(346,847)(347,848)(348,849)(349,853)(350,854)(351,855)
(352,814)(353,815)(354,816)(355,811)(356,812)(357,813)(358,817)(359,818)
(360,819)(361,832)(362,833)(363,834)(364,829)(365,830)(366,831)(367,835)
(368,836)(369,837)(370,823)(371,824)(372,825)(373,820)(374,821)(375,822)
(376,826)(377,827)(378,828)(379,787)(380,788)(381,789)(382,784)(383,785)
(384,786)(385,790)(386,791)(387,792)(388,805)(389,806)(390,807)(391,802)
(392,803)(393,804)(394,808)(395,809)(396,810)(397,796)(398,797)(399,798)
(400,793)(401,794)(402,795)(403,799)(404,800)(405,801)(406,760)(407,761)
(408,762)(409,757)(410,758)(411,759)(412,763)(413,764)(414,765)(415,778)
(416,779)(417,780)(418,775)(419,776)(420,777)(421,781)(422,782)(423,783)
(424,769)(425,770)(426,771)(427,766)(428,767)(429,768)(430,772)(431,773)
(432,774);
s2 := Sym(864)!(  1,658)(  2,660)(  3,659)(  4,661)(  5,663)(  6,662)(  7,664)
(  8,666)(  9,665)( 10,649)( 11,651)( 12,650)( 13,652)( 14,654)( 15,653)
( 16,655)( 17,657)( 18,656)( 19,667)( 20,669)( 21,668)( 22,670)( 23,672)
( 24,671)( 25,673)( 26,675)( 27,674)( 28,685)( 29,687)( 30,686)( 31,688)
( 32,690)( 33,689)( 34,691)( 35,693)( 36,692)( 37,676)( 38,678)( 39,677)
( 40,679)( 41,681)( 42,680)( 43,682)( 44,684)( 45,683)( 46,694)( 47,696)
( 48,695)( 49,697)( 50,699)( 51,698)( 52,700)( 53,702)( 54,701)( 55,712)
( 56,714)( 57,713)( 58,715)( 59,717)( 60,716)( 61,718)( 62,720)( 63,719)
( 64,703)( 65,705)( 66,704)( 67,706)( 68,708)( 69,707)( 70,709)( 71,711)
( 72,710)( 73,721)( 74,723)( 75,722)( 76,724)( 77,726)( 78,725)( 79,727)
( 80,729)( 81,728)( 82,739)( 83,741)( 84,740)( 85,742)( 86,744)( 87,743)
( 88,745)( 89,747)( 90,746)( 91,730)( 92,732)( 93,731)( 94,733)( 95,735)
( 96,734)( 97,736)( 98,738)( 99,737)(100,748)(101,750)(102,749)(103,751)
(104,753)(105,752)(106,754)(107,756)(108,755)(109,766)(110,768)(111,767)
(112,769)(113,771)(114,770)(115,772)(116,774)(117,773)(118,757)(119,759)
(120,758)(121,760)(122,762)(123,761)(124,763)(125,765)(126,764)(127,775)
(128,777)(129,776)(130,778)(131,780)(132,779)(133,781)(134,783)(135,782)
(136,793)(137,795)(138,794)(139,796)(140,798)(141,797)(142,799)(143,801)
(144,800)(145,784)(146,786)(147,785)(148,787)(149,789)(150,788)(151,790)
(152,792)(153,791)(154,802)(155,804)(156,803)(157,805)(158,807)(159,806)
(160,808)(161,810)(162,809)(163,820)(164,822)(165,821)(166,823)(167,825)
(168,824)(169,826)(170,828)(171,827)(172,811)(173,813)(174,812)(175,814)
(176,816)(177,815)(178,817)(179,819)(180,818)(181,829)(182,831)(183,830)
(184,832)(185,834)(186,833)(187,835)(188,837)(189,836)(190,847)(191,849)
(192,848)(193,850)(194,852)(195,851)(196,853)(197,855)(198,854)(199,838)
(200,840)(201,839)(202,841)(203,843)(204,842)(205,844)(206,846)(207,845)
(208,856)(209,858)(210,857)(211,859)(212,861)(213,860)(214,862)(215,864)
(216,863)(217,496)(218,498)(219,497)(220,499)(221,501)(222,500)(223,502)
(224,504)(225,503)(226,487)(227,489)(228,488)(229,490)(230,492)(231,491)
(232,493)(233,495)(234,494)(235,505)(236,507)(237,506)(238,508)(239,510)
(240,509)(241,511)(242,513)(243,512)(244,523)(245,525)(246,524)(247,526)
(248,528)(249,527)(250,529)(251,531)(252,530)(253,514)(254,516)(255,515)
(256,517)(257,519)(258,518)(259,520)(260,522)(261,521)(262,532)(263,534)
(264,533)(265,535)(266,537)(267,536)(268,538)(269,540)(270,539)(271,469)
(272,471)(273,470)(274,472)(275,474)(276,473)(277,475)(278,477)(279,476)
(280,460)(281,462)(282,461)(283,463)(284,465)(285,464)(286,466)(287,468)
(288,467)(289,478)(290,480)(291,479)(292,481)(293,483)(294,482)(295,484)
(296,486)(297,485)(298,442)(299,444)(300,443)(301,445)(302,447)(303,446)
(304,448)(305,450)(306,449)(307,433)(308,435)(309,434)(310,436)(311,438)
(312,437)(313,439)(314,441)(315,440)(316,451)(317,453)(318,452)(319,454)
(320,456)(321,455)(322,457)(323,459)(324,458)(325,604)(326,606)(327,605)
(328,607)(329,609)(330,608)(331,610)(332,612)(333,611)(334,595)(335,597)
(336,596)(337,598)(338,600)(339,599)(340,601)(341,603)(342,602)(343,613)
(344,615)(345,614)(346,616)(347,618)(348,617)(349,619)(350,621)(351,620)
(352,631)(353,633)(354,632)(355,634)(356,636)(357,635)(358,637)(359,639)
(360,638)(361,622)(362,624)(363,623)(364,625)(365,627)(366,626)(367,628)
(368,630)(369,629)(370,640)(371,642)(372,641)(373,643)(374,645)(375,644)
(376,646)(377,648)(378,647)(379,577)(380,579)(381,578)(382,580)(383,582)
(384,581)(385,583)(386,585)(387,584)(388,568)(389,570)(390,569)(391,571)
(392,573)(393,572)(394,574)(395,576)(396,575)(397,586)(398,588)(399,587)
(400,589)(401,591)(402,590)(403,592)(404,594)(405,593)(406,550)(407,552)
(408,551)(409,553)(410,555)(411,554)(412,556)(413,558)(414,557)(415,541)
(416,543)(417,542)(418,544)(419,546)(420,545)(421,547)(422,549)(423,548)
(424,559)(425,561)(426,560)(427,562)(428,564)(429,563)(430,565)(431,567)
(432,566);
s3 := Sym(864)!(  1,758)(  2,757)(  3,759)(  4,761)(  5,760)(  6,762)(  7,764)
(  8,763)(  9,765)( 10,776)( 11,775)( 12,777)( 13,779)( 14,778)( 15,780)
( 16,782)( 17,781)( 18,783)( 19,767)( 20,766)( 21,768)( 22,770)( 23,769)
( 24,771)( 25,773)( 26,772)( 27,774)( 28,785)( 29,784)( 30,786)( 31,788)
( 32,787)( 33,789)( 34,791)( 35,790)( 36,792)( 37,803)( 38,802)( 39,804)
( 40,806)( 41,805)( 42,807)( 43,809)( 44,808)( 45,810)( 46,794)( 47,793)
( 48,795)( 49,797)( 50,796)( 51,798)( 52,800)( 53,799)( 54,801)( 55,812)
( 56,811)( 57,813)( 58,815)( 59,814)( 60,816)( 61,818)( 62,817)( 63,819)
( 64,830)( 65,829)( 66,831)( 67,833)( 68,832)( 69,834)( 70,836)( 71,835)
( 72,837)( 73,821)( 74,820)( 75,822)( 76,824)( 77,823)( 78,825)( 79,827)
( 80,826)( 81,828)( 82,839)( 83,838)( 84,840)( 85,842)( 86,841)( 87,843)
( 88,845)( 89,844)( 90,846)( 91,857)( 92,856)( 93,858)( 94,860)( 95,859)
( 96,861)( 97,863)( 98,862)( 99,864)(100,848)(101,847)(102,849)(103,851)
(104,850)(105,852)(106,854)(107,853)(108,855)(109,650)(110,649)(111,651)
(112,653)(113,652)(114,654)(115,656)(116,655)(117,657)(118,668)(119,667)
(120,669)(121,671)(122,670)(123,672)(124,674)(125,673)(126,675)(127,659)
(128,658)(129,660)(130,662)(131,661)(132,663)(133,665)(134,664)(135,666)
(136,677)(137,676)(138,678)(139,680)(140,679)(141,681)(142,683)(143,682)
(144,684)(145,695)(146,694)(147,696)(148,698)(149,697)(150,699)(151,701)
(152,700)(153,702)(154,686)(155,685)(156,687)(157,689)(158,688)(159,690)
(160,692)(161,691)(162,693)(163,704)(164,703)(165,705)(166,707)(167,706)
(168,708)(169,710)(170,709)(171,711)(172,722)(173,721)(174,723)(175,725)
(176,724)(177,726)(178,728)(179,727)(180,729)(181,713)(182,712)(183,714)
(184,716)(185,715)(186,717)(187,719)(188,718)(189,720)(190,731)(191,730)
(192,732)(193,734)(194,733)(195,735)(196,737)(197,736)(198,738)(199,749)
(200,748)(201,750)(202,752)(203,751)(204,753)(205,755)(206,754)(207,756)
(208,740)(209,739)(210,741)(211,743)(212,742)(213,744)(214,746)(215,745)
(216,747)(217,596)(218,595)(219,597)(220,599)(221,598)(222,600)(223,602)
(224,601)(225,603)(226,614)(227,613)(228,615)(229,617)(230,616)(231,618)
(232,620)(233,619)(234,621)(235,605)(236,604)(237,606)(238,608)(239,607)
(240,609)(241,611)(242,610)(243,612)(244,623)(245,622)(246,624)(247,626)
(248,625)(249,627)(250,629)(251,628)(252,630)(253,641)(254,640)(255,642)
(256,644)(257,643)(258,645)(259,647)(260,646)(261,648)(262,632)(263,631)
(264,633)(265,635)(266,634)(267,636)(268,638)(269,637)(270,639)(271,569)
(272,568)(273,570)(274,572)(275,571)(276,573)(277,575)(278,574)(279,576)
(280,587)(281,586)(282,588)(283,590)(284,589)(285,591)(286,593)(287,592)
(288,594)(289,578)(290,577)(291,579)(292,581)(293,580)(294,582)(295,584)
(296,583)(297,585)(298,542)(299,541)(300,543)(301,545)(302,544)(303,546)
(304,548)(305,547)(306,549)(307,560)(308,559)(309,561)(310,563)(311,562)
(312,564)(313,566)(314,565)(315,567)(316,551)(317,550)(318,552)(319,554)
(320,553)(321,555)(322,557)(323,556)(324,558)(325,488)(326,487)(327,489)
(328,491)(329,490)(330,492)(331,494)(332,493)(333,495)(334,506)(335,505)
(336,507)(337,509)(338,508)(339,510)(340,512)(341,511)(342,513)(343,497)
(344,496)(345,498)(346,500)(347,499)(348,501)(349,503)(350,502)(351,504)
(352,515)(353,514)(354,516)(355,518)(356,517)(357,519)(358,521)(359,520)
(360,522)(361,533)(362,532)(363,534)(364,536)(365,535)(366,537)(367,539)
(368,538)(369,540)(370,524)(371,523)(372,525)(373,527)(374,526)(375,528)
(376,530)(377,529)(378,531)(379,461)(380,460)(381,462)(382,464)(383,463)
(384,465)(385,467)(386,466)(387,468)(388,479)(389,478)(390,480)(391,482)
(392,481)(393,483)(394,485)(395,484)(396,486)(397,470)(398,469)(399,471)
(400,473)(401,472)(402,474)(403,476)(404,475)(405,477)(406,434)(407,433)
(408,435)(409,437)(410,436)(411,438)(412,440)(413,439)(414,441)(415,452)
(416,451)(417,453)(418,455)(419,454)(420,456)(421,458)(422,457)(423,459)
(424,443)(425,442)(426,444)(427,446)(428,445)(429,447)(430,449)(431,448)
(432,450);
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, s3*s1*s2*s1*s2*s3*s1*s2*s1*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,
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