Polytope of Type {12,6,3,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6,3,4}*1728b
if this polytope has a name.
Group : SmallGroup(1728,46356)
Rank : 5
Schlafli Type : {12,6,3,4}
Number of vertices, edges, etc : 12, 36, 9, 6, 4
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Universal
Non-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 : {6,6,3,4}*864b
3-fold quotients : {12,2,3,4}*576, {4,6,3,4}*576
6-fold quotients : {2,6,3,4}*288, {6,2,3,4}*288
9-fold quotients : {4,2,3,4}*192
12-fold quotients : {3,2,3,4}*144
18-fold quotients : {2,2,3,4}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Irregular Quotients (of which this is a minimal cover):
None.
Permutation Representation (GAP) :
s0 := ( 13, 25)( 14, 26)( 15, 27)( 16, 28)( 17, 29)( 18, 30)( 19, 31)( 20, 32)( 21, 33)( 22, 34)( 23, 35)( 24, 36)( 49, 61)( 50, 62)( 51, 63)( 52, 64)( 53, 65)( 54, 66)( 55, 67)( 56, 68)( 57, 69)( 58, 70)( 59, 71)( 60, 72)( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89,101)( 90,102)( 91,103)( 92,104)( 93,105)( 94,106)( 95,107)( 96,108)(121,133)(122,134)(123,135)(124,136)(125,137)(126,138)(127,139)(128,140)(129,141)(130,142)(131,143)(132,144)(157,169)(158,170)(159,171)(160,172)(161,173)(162,174)(163,175)(164,176)(165,177)(166,178)(167,179)(168,180)(193,205)(194,206)(195,207)(196,208)(197,209)(198,210)(199,211)(200,212)(201,213)(202,214)(203,215)(204,216)(217,325)(218,326)(219,327)(220,328)(221,329)(222,330)(223,331)(224,332)(225,333)(226,334)(227,335)(228,336)(229,349)(230,350)(231,351)(232,352)(233,353)(234,354)(235,355)(236,356)(237,357)(238,358)(239,359)(240,360)(241,337)(242,338)(243,339)(244,340)(245,341)(246,342)(247,343)(248,344)(249,345)(250,346)(251,347)(252,348)(253,361)(254,362)(255,363)(256,364)(257,365)(258,366)(259,367)(260,368)(261,369)(262,370)(263,371)(264,372)(265,385)(266,386)(267,387)(268,388)(269,389)(270,390)(271,391)(272,392)(273,393)(274,394)(275,395)(276,396)(277,373)(278,374)(279,375)(280,376)(281,377)(282,378)(283,379)(284,380)(285,381)(286,382)(287,383)(288,384)(289,397)(290,398)(291,399)(292,400)(293,401)(294,402)(295,403)(296,404)(297,405)(298,406)(299,407)(300,408)(301,421)(302,422)(303,423)(304,424)(305,425)(306,426)(307,427)(308,428)(309,429)(310,430)(311,431)(312,432)(313,409)(314,410)(315,411)(316,412)(317,413)(318,414)(319,415)(320,416)(321,417)(322,418)(323,419)(324,420)(433,541)(434,542)(435,543)(436,544)(437,545)(438,546)(439,547)(440,548)(441,549)(442,550)(443,551)(444,552)(445,565)(446,566)(447,567)(448,568)(449,569)(450,570)(451,571)(452,572)(453,573)(454,574)(455,575)(456,576)(457,553)(458,554)(459,555)(460,556)(461,557)(462,558)(463,559)(464,560)(465,561)(466,562)(467,563)(468,564)(469,577)(470,578)(471,579)(472,580)(473,581)(474,582)(475,583)(476,584)(477,585)(478,586)(479,587)(480,588)(481,601)(482,602)(483,603)(484,604)(485,605)(486,606)(487,607)(488,608)(489,609)(490,610)(491,611)(492,612)(493,589)(494,590)(495,591)(496,592)(497,593)(498,594)(499,595)(500,596)(501,597)(502,598)(503,599)(504,600)(505,613)(506,614)(507,615)(508,616)(509,617)(510,618)(511,619)(512,620)(513,621)(514,622)(515,623)(516,624)(517,637)(518,638)(519,639)(520,640)(521,641)(522,642)(523,643)(524,644)(525,645)(526,646)(527,647)(528,648)(529,625)(530,626)(531,627)(532,628)(533,629)(534,630)(535,631)(536,632)(537,633)(538,634)(539,635)(540,636)(661,673)(662,674)(663,675)(664,676)(665,677)(666,678)(667,679)(668,680)(669,681)(670,682)(671,683)(672,684)(697,709)(698,710)(699,711)(700,712)(701,713)(702,714)(703,715)(704,716)(705,717)(706,718)(707,719)(708,720)(733,745)(734,746)(735,747)(736,748)(737,749)(738,750)(739,751)(740,752)(741,753)(742,754)(743,755)(744,756)(769,781)(770,782)(771,783)(772,784)(773,785)(774,786)(775,787)(776,788)(777,789)(778,790)(779,791)(780,792)(805,817)(806,818)(807,819)(808,820)(809,821)(810,822)(811,823)(812,824)(813,825)(814,826)(815,827)(816,828)(841,853)(842,854)(843,855)(844,856)(845,857)(846,858)(847,859)(848,860)(849,861)(850,862)(851,863)(852,864);;
s1 := ( 1,445)( 2,446)( 3,447)( 4,448)( 5,453)( 6,454)( 7,455)( 8,456)( 9,449)( 10,450)( 11,451)( 12,452)( 13,433)( 14,434)( 15,435)( 16,436)( 17,441)( 18,442)( 19,443)( 20,444)( 21,437)( 22,438)( 23,439)( 24,440)( 25,457)( 26,458)( 27,459)( 28,460)( 29,465)( 30,466)( 31,467)( 32,468)( 33,461)( 34,462)( 35,463)( 36,464)( 37,481)( 38,482)( 39,483)( 40,484)( 41,489)( 42,490)( 43,491)( 44,492)( 45,485)( 46,486)( 47,487)( 48,488)( 49,469)( 50,470)( 51,471)( 52,472)( 53,477)( 54,478)( 55,479)( 56,480)( 57,473)( 58,474)( 59,475)( 60,476)( 61,493)( 62,494)( 63,495)( 64,496)( 65,501)( 66,502)( 67,503)( 68,504)( 69,497)( 70,498)( 71,499)( 72,500)( 73,517)( 74,518)( 75,519)( 76,520)( 77,525)( 78,526)( 79,527)( 80,528)( 81,521)( 82,522)( 83,523)( 84,524)( 85,505)( 86,506)( 87,507)( 88,508)( 89,513)( 90,514)( 91,515)( 92,516)( 93,509)( 94,510)( 95,511)( 96,512)( 97,529)( 98,530)( 99,531)(100,532)(101,537)(102,538)(103,539)(104,540)(105,533)(106,534)(107,535)(108,536)(109,553)(110,554)(111,555)(112,556)(113,561)(114,562)(115,563)(116,564)(117,557)(118,558)(119,559)(120,560)(121,541)(122,542)(123,543)(124,544)(125,549)(126,550)(127,551)(128,552)(129,545)(130,546)(131,547)(132,548)(133,565)(134,566)(135,567)(136,568)(137,573)(138,574)(139,575)(140,576)(141,569)(142,570)(143,571)(144,572)(145,589)(146,590)(147,591)(148,592)(149,597)(150,598)(151,599)(152,600)(153,593)(154,594)(155,595)(156,596)(157,577)(158,578)(159,579)(160,580)(161,585)(162,586)(163,587)(164,588)(165,581)(166,582)(167,583)(168,584)(169,601)(170,602)(171,603)(172,604)(173,609)(174,610)(175,611)(176,612)(177,605)(178,606)(179,607)(180,608)(181,625)(182,626)(183,627)(184,628)(185,633)(186,634)(187,635)(188,636)(189,629)(190,630)(191,631)(192,632)(193,613)(194,614)(195,615)(196,616)(197,621)(198,622)(199,623)(200,624)(201,617)(202,618)(203,619)(204,620)(205,637)(206,638)(207,639)(208,640)(209,645)(210,646)(211,647)(212,648)(213,641)(214,642)(215,643)(216,644)(217,769)(218,770)(219,771)(220,772)(221,777)(222,778)(223,779)(224,780)(225,773)(226,774)(227,775)(228,776)(229,757)(230,758)(231,759)(232,760)(233,765)(234,766)(235,767)(236,768)(237,761)(238,762)(239,763)(240,764)(241,781)(242,782)(243,783)(244,784)(245,789)(246,790)(247,791)(248,792)(249,785)(250,786)(251,787)(252,788)(253,805)(254,806)(255,807)(256,808)(257,813)(258,814)(259,815)(260,816)(261,809)(262,810)(263,811)(264,812)(265,793)(266,794)(267,795)(268,796)(269,801)(270,802)(271,803)(272,804)(273,797)(274,798)(275,799)(276,800)(277,817)(278,818)(279,819)(280,820)(281,825)(282,826)(283,827)(284,828)(285,821)(286,822)(287,823)(288,824)(289,841)(290,842)(291,843)(292,844)(293,849)(294,850)(295,851)(296,852)(297,845)(298,846)(299,847)(300,848)(301,829)(302,830)(303,831)(304,832)(305,837)(306,838)(307,839)(308,840)(309,833)(310,834)(311,835)(312,836)(313,853)(314,854)(315,855)(316,856)(317,861)(318,862)(319,863)(320,864)(321,857)(322,858)(323,859)(324,860)(325,661)(326,662)(327,663)(328,664)(329,669)(330,670)(331,671)(332,672)(333,665)(334,666)(335,667)(336,668)(337,649)(338,650)(339,651)(340,652)(341,657)(342,658)(343,659)(344,660)(345,653)(346,654)(347,655)(348,656)(349,673)(350,674)(351,675)(352,676)(353,681)(354,682)(355,683)(356,684)(357,677)(358,678)(359,679)(360,680)(361,697)(362,698)(363,699)(364,700)(365,705)(366,706)(367,707)(368,708)(369,701)(370,702)(371,703)(372,704)(373,685)(374,686)(375,687)(376,688)(377,693)(378,694)(379,695)(380,696)(381,689)(382,690)(383,691)(384,692)(385,709)(386,710)(387,711)(388,712)(389,717)(390,718)(391,719)(392,720)(393,713)(394,714)(395,715)(396,716)(397,733)(398,734)(399,735)(400,736)(401,741)(402,742)(403,743)(404,744)(405,737)(406,738)(407,739)(408,740)(409,721)(410,722)(411,723)(412,724)(413,729)(414,730)(415,731)(416,732)(417,725)(418,726)(419,727)(420,728)(421,745)(422,746)(423,747)(424,748)(425,753)(426,754)(427,755)(428,756)(429,749)(430,750)(431,751)(432,752);;
s2 := ( 1,653)( 2,654)( 3,656)( 4,655)( 5,649)( 6,650)( 7,652)( 8,651)( 9,657)( 10,658)( 11,660)( 12,659)( 13,665)( 14,666)( 15,668)( 16,667)( 17,661)( 18,662)( 19,664)( 20,663)( 21,669)( 22,670)( 23,672)( 24,671)( 25,677)( 26,678)( 27,680)( 28,679)( 29,673)( 30,674)( 31,676)( 32,675)( 33,681)( 34,682)( 35,684)( 36,683)( 37,725)( 38,726)( 39,728)( 40,727)( 41,721)( 42,722)( 43,724)( 44,723)( 45,729)( 46,730)( 47,732)( 48,731)( 49,737)( 50,738)( 51,740)( 52,739)( 53,733)( 54,734)( 55,736)( 56,735)( 57,741)( 58,742)( 59,744)( 60,743)( 61,749)( 62,750)( 63,752)( 64,751)( 65,745)( 66,746)( 67,748)( 68,747)( 69,753)( 70,754)( 71,756)( 72,755)( 73,689)( 74,690)( 75,692)( 76,691)( 77,685)( 78,686)( 79,688)( 80,687)( 81,693)( 82,694)( 83,696)( 84,695)( 85,701)( 86,702)( 87,704)( 88,703)( 89,697)( 90,698)( 91,700)( 92,699)( 93,705)( 94,706)( 95,708)( 96,707)( 97,713)( 98,714)( 99,716)(100,715)(101,709)(102,710)(103,712)(104,711)(105,717)(106,718)(107,720)(108,719)(109,761)(110,762)(111,764)(112,763)(113,757)(114,758)(115,760)(116,759)(117,765)(118,766)(119,768)(120,767)(121,773)(122,774)(123,776)(124,775)(125,769)(126,770)(127,772)(128,771)(129,777)(130,778)(131,780)(132,779)(133,785)(134,786)(135,788)(136,787)(137,781)(138,782)(139,784)(140,783)(141,789)(142,790)(143,792)(144,791)(145,833)(146,834)(147,836)(148,835)(149,829)(150,830)(151,832)(152,831)(153,837)(154,838)(155,840)(156,839)(157,845)(158,846)(159,848)(160,847)(161,841)(162,842)(163,844)(164,843)(165,849)(166,850)(167,852)(168,851)(169,857)(170,858)(171,860)(172,859)(173,853)(174,854)(175,856)(176,855)(177,861)(178,862)(179,864)(180,863)(181,797)(182,798)(183,800)(184,799)(185,793)(186,794)(187,796)(188,795)(189,801)(190,802)(191,804)(192,803)(193,809)(194,810)(195,812)(196,811)(197,805)(198,806)(199,808)(200,807)(201,813)(202,814)(203,816)(204,815)(205,821)(206,822)(207,824)(208,823)(209,817)(210,818)(211,820)(212,819)(213,825)(214,826)(215,828)(216,827)(217,545)(218,546)(219,548)(220,547)(221,541)(222,542)(223,544)(224,543)(225,549)(226,550)(227,552)(228,551)(229,557)(230,558)(231,560)(232,559)(233,553)(234,554)(235,556)(236,555)(237,561)(238,562)(239,564)(240,563)(241,569)(242,570)(243,572)(244,571)(245,565)(246,566)(247,568)(248,567)(249,573)(250,574)(251,576)(252,575)(253,617)(254,618)(255,620)(256,619)(257,613)(258,614)(259,616)(260,615)(261,621)(262,622)(263,624)(264,623)(265,629)(266,630)(267,632)(268,631)(269,625)(270,626)(271,628)(272,627)(273,633)(274,634)(275,636)(276,635)(277,641)(278,642)(279,644)(280,643)(281,637)(282,638)(283,640)(284,639)(285,645)(286,646)(287,648)(288,647)(289,581)(290,582)(291,584)(292,583)(293,577)(294,578)(295,580)(296,579)(297,585)(298,586)(299,588)(300,587)(301,593)(302,594)(303,596)(304,595)(305,589)(306,590)(307,592)(308,591)(309,597)(310,598)(311,600)(312,599)(313,605)(314,606)(315,608)(316,607)(317,601)(318,602)(319,604)(320,603)(321,609)(322,610)(323,612)(324,611)(325,437)(326,438)(327,440)(328,439)(329,433)(330,434)(331,436)(332,435)(333,441)(334,442)(335,444)(336,443)(337,449)(338,450)(339,452)(340,451)(341,445)(342,446)(343,448)(344,447)(345,453)(346,454)(347,456)(348,455)(349,461)(350,462)(351,464)(352,463)(353,457)(354,458)(355,460)(356,459)(357,465)(358,466)(359,468)(360,467)(361,509)(362,510)(363,512)(364,511)(365,505)(366,506)(367,508)(368,507)(369,513)(370,514)(371,516)(372,515)(373,521)(374,522)(375,524)(376,523)(377,517)(378,518)(379,520)(380,519)(381,525)(382,526)(383,528)(384,527)(385,533)(386,534)(387,536)(388,535)(389,529)(390,530)(391,532)(392,531)(393,537)(394,538)(395,540)(396,539)(397,473)(398,474)(399,476)(400,475)(401,469)(402,470)(403,472)(404,471)(405,477)(406,478)(407,480)(408,479)(409,485)(410,486)(411,488)(412,487)(413,481)(414,482)(415,484)(416,483)(417,489)(418,490)(419,492)(420,491)(421,497)(422,498)(423,500)(424,499)(425,493)(426,494)(427,496)(428,495)(429,501)(430,502)(431,504)(432,503);;
s3 := ( 1,685)( 2,688)( 3,687)( 4,686)( 5,693)( 6,696)( 7,695)( 8,694)( 9,689)( 10,692)( 11,691)( 12,690)( 13,697)( 14,700)( 15,699)( 16,698)( 17,705)( 18,708)( 19,707)( 20,706)( 21,701)( 22,704)( 23,703)( 24,702)( 25,709)( 26,712)( 27,711)( 28,710)( 29,717)( 30,720)( 31,719)( 32,718)( 33,713)( 34,716)( 35,715)( 36,714)( 37,649)( 38,652)( 39,651)( 40,650)( 41,657)( 42,660)( 43,659)( 44,658)( 45,653)( 46,656)( 47,655)( 48,654)( 49,661)( 50,664)( 51,663)( 52,662)( 53,669)( 54,672)( 55,671)( 56,670)( 57,665)( 58,668)( 59,667)( 60,666)( 61,673)( 62,676)( 63,675)( 64,674)( 65,681)( 66,684)( 67,683)( 68,682)( 69,677)( 70,680)( 71,679)( 72,678)( 73,721)( 74,724)( 75,723)( 76,722)( 77,729)( 78,732)( 79,731)( 80,730)( 81,725)( 82,728)( 83,727)( 84,726)( 85,733)( 86,736)( 87,735)( 88,734)( 89,741)( 90,744)( 91,743)( 92,742)( 93,737)( 94,740)( 95,739)( 96,738)( 97,745)( 98,748)( 99,747)(100,746)(101,753)(102,756)(103,755)(104,754)(105,749)(106,752)(107,751)(108,750)(109,793)(110,796)(111,795)(112,794)(113,801)(114,804)(115,803)(116,802)(117,797)(118,800)(119,799)(120,798)(121,805)(122,808)(123,807)(124,806)(125,813)(126,816)(127,815)(128,814)(129,809)(130,812)(131,811)(132,810)(133,817)(134,820)(135,819)(136,818)(137,825)(138,828)(139,827)(140,826)(141,821)(142,824)(143,823)(144,822)(145,757)(146,760)(147,759)(148,758)(149,765)(150,768)(151,767)(152,766)(153,761)(154,764)(155,763)(156,762)(157,769)(158,772)(159,771)(160,770)(161,777)(162,780)(163,779)(164,778)(165,773)(166,776)(167,775)(168,774)(169,781)(170,784)(171,783)(172,782)(173,789)(174,792)(175,791)(176,790)(177,785)(178,788)(179,787)(180,786)(181,829)(182,832)(183,831)(184,830)(185,837)(186,840)(187,839)(188,838)(189,833)(190,836)(191,835)(192,834)(193,841)(194,844)(195,843)(196,842)(197,849)(198,852)(199,851)(200,850)(201,845)(202,848)(203,847)(204,846)(205,853)(206,856)(207,855)(208,854)(209,861)(210,864)(211,863)(212,862)(213,857)(214,860)(215,859)(216,858)(217,577)(218,580)(219,579)(220,578)(221,585)(222,588)(223,587)(224,586)(225,581)(226,584)(227,583)(228,582)(229,589)(230,592)(231,591)(232,590)(233,597)(234,600)(235,599)(236,598)(237,593)(238,596)(239,595)(240,594)(241,601)(242,604)(243,603)(244,602)(245,609)(246,612)(247,611)(248,610)(249,605)(250,608)(251,607)(252,606)(253,541)(254,544)(255,543)(256,542)(257,549)(258,552)(259,551)(260,550)(261,545)(262,548)(263,547)(264,546)(265,553)(266,556)(267,555)(268,554)(269,561)(270,564)(271,563)(272,562)(273,557)(274,560)(275,559)(276,558)(277,565)(278,568)(279,567)(280,566)(281,573)(282,576)(283,575)(284,574)(285,569)(286,572)(287,571)(288,570)(289,613)(290,616)(291,615)(292,614)(293,621)(294,624)(295,623)(296,622)(297,617)(298,620)(299,619)(300,618)(301,625)(302,628)(303,627)(304,626)(305,633)(306,636)(307,635)(308,634)(309,629)(310,632)(311,631)(312,630)(313,637)(314,640)(315,639)(316,638)(317,645)(318,648)(319,647)(320,646)(321,641)(322,644)(323,643)(324,642)(325,469)(326,472)(327,471)(328,470)(329,477)(330,480)(331,479)(332,478)(333,473)(334,476)(335,475)(336,474)(337,481)(338,484)(339,483)(340,482)(341,489)(342,492)(343,491)(344,490)(345,485)(346,488)(347,487)(348,486)(349,493)(350,496)(351,495)(352,494)(353,501)(354,504)(355,503)(356,502)(357,497)(358,500)(359,499)(360,498)(361,433)(362,436)(363,435)(364,434)(365,441)(366,444)(367,443)(368,442)(369,437)(370,440)(371,439)(372,438)(373,445)(374,448)(375,447)(376,446)(377,453)(378,456)(379,455)(380,454)(381,449)(382,452)(383,451)(384,450)(385,457)(386,460)(387,459)(388,458)(389,465)(390,468)(391,467)(392,466)(393,461)(394,464)(395,463)(396,462)(397,505)(398,508)(399,507)(400,506)(401,513)(402,516)(403,515)(404,514)(405,509)(406,512)(407,511)(408,510)(409,517)(410,520)(411,519)(412,518)(413,525)(414,528)(415,527)(416,526)(417,521)(418,524)(419,523)(420,522)(421,529)(422,532)(423,531)(424,530)(425,537)(426,540)(427,539)(428,538)(429,533)(430,536)(431,535)(432,534);;
s4 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272)(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)(287,288)(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)(303,304)(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)(319,320)(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)(335,336)(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)(351,352)(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)(367,368)(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)(383,384)(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)(399,400)(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)(415,416)(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)(431,432)(433,434)(435,436)(437,438)(439,440)(441,442)(443,444)(445,446)(447,448)(449,450)(451,452)(453,454)(455,456)(457,458)(459,460)(461,462)(463,464)(465,466)(467,468)(469,470)(471,472)(473,474)(475,476)(477,478)(479,480)(481,482)(483,484)(485,486)(487,488)(489,490)(491,492)(493,494)(495,496)(497,498)(499,500)(501,502)(503,504)(505,506)(507,508)(509,510)(511,512)(513,514)(515,516)(517,518)(519,520)(521,522)(523,524)(525,526)(527,528)(529,530)(531,532)(533,534)(535,536)(537,538)(539,540)(541,542)(543,544)(545,546)(547,548)(549,550)(551,552)(553,554)(555,556)(557,558)(559,560)(561,562)(563,564)(565,566)(567,568)(569,570)(571,572)(573,574)(575,576)(577,578)(579,580)(581,582)(583,584)(585,586)(587,588)(589,590)(591,592)(593,594)(595,596)(597,598)(599,600)(601,602)(603,604)(605,606)(607,608)(609,610)(611,612)(613,614)(615,616)(617,618)(619,620)(621,622)(623,624)(625,626)(627,628)(629,630)(631,632)(633,634)(635,636)(637,638)(639,640)(641,642)(643,644)(645,646)(647,648)(649,650)(651,652)(653,654)(655,656)(657,658)(659,660)(661,662)(663,664)(665,666)(667,668)(669,670)(671,672)(673,674)(675,676)(677,678)(679,680)(681,682)(683,684)(685,686)(687,688)(689,690)(691,692)(693,694)(695,696)(697,698)(699,700)(701,702)(703,704)(705,706)(707,708)(709,710)(711,712)(713,714)(715,716)(717,718)(719,720)(721,722)(723,724)(725,726)(727,728)(729,730)(731,732)(733,734)(735,736)(737,738)(739,740)(741,742)(743,744)(745,746)(747,748)(749,750)(751,752)(753,754)(755,756)(757,758)(759,760)(761,762)(763,764)(765,766)(767,768)(769,770)(771,772)(773,774)(775,776)(777,778)(779,780)(781,782)(783,784)(785,786)(787,788)(789,790)(791,792)(793,794)(795,796)(797,798)(799,800)(801,802)(803,804)(805,806)(807,808)(809,810)(811,812)(813,814)(815,816)(817,818)(819,820)(821,822)(823,824)(825,826)(827,828)(829,830)(831,832)(833,834)(835,836)(837,838)(839,840)(841,842)(843,844)(845,846)(847,848)(849,850)(851,852)(853,854)(855,856)(857,858)(859,860)(861,862)(863,864);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s4*s3*s2*s4*s3*s2*s4*s3, s1*s2*s3*s1*s2*s1*s2*s3*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(864)!( 13, 25)( 14, 26)( 15, 27)( 16, 28)( 17, 29)( 18, 30)( 19, 31)( 20, 32)( 21, 33)( 22, 34)( 23, 35)( 24, 36)( 49, 61)( 50, 62)( 51, 63)( 52, 64)( 53, 65)( 54, 66)( 55, 67)( 56, 68)( 57, 69)( 58, 70)( 59, 71)( 60, 72)( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89,101)( 90,102)( 91,103)( 92,104)( 93,105)( 94,106)( 95,107)( 96,108)(121,133)(122,134)(123,135)(124,136)(125,137)(126,138)(127,139)(128,140)(129,141)(130,142)(131,143)(132,144)(157,169)(158,170)(159,171)(160,172)(161,173)(162,174)(163,175)(164,176)(165,177)(166,178)(167,179)(168,180)(193,205)(194,206)(195,207)(196,208)(197,209)(198,210)(199,211)(200,212)(201,213)(202,214)(203,215)(204,216)(217,325)(218,326)(219,327)(220,328)(221,329)(222,330)(223,331)(224,332)(225,333)(226,334)(227,335)(228,336)(229,349)(230,350)(231,351)(232,352)(233,353)(234,354)(235,355)(236,356)(237,357)(238,358)(239,359)(240,360)(241,337)(242,338)(243,339)(244,340)(245,341)(246,342)(247,343)(248,344)(249,345)(250,346)(251,347)(252,348)(253,361)(254,362)(255,363)(256,364)(257,365)(258,366)(259,367)(260,368)(261,369)(262,370)(263,371)(264,372)(265,385)(266,386)(267,387)(268,388)(269,389)(270,390)(271,391)(272,392)(273,393)(274,394)(275,395)(276,396)(277,373)(278,374)(279,375)(280,376)(281,377)(282,378)(283,379)(284,380)(285,381)(286,382)(287,383)(288,384)(289,397)(290,398)(291,399)(292,400)(293,401)(294,402)(295,403)(296,404)(297,405)(298,406)(299,407)(300,408)(301,421)(302,422)(303,423)(304,424)(305,425)(306,426)(307,427)(308,428)(309,429)(310,430)(311,431)(312,432)(313,409)(314,410)(315,411)(316,412)(317,413)(318,414)(319,415)(320,416)(321,417)(322,418)(323,419)(324,420)(433,541)(434,542)(435,543)(436,544)(437,545)(438,546)(439,547)(440,548)(441,549)(442,550)(443,551)(444,552)(445,565)(446,566)(447,567)(448,568)(449,569)(450,570)(451,571)(452,572)(453,573)(454,574)(455,575)(456,576)(457,553)(458,554)(459,555)(460,556)(461,557)(462,558)(463,559)(464,560)(465,561)(466,562)(467,563)(468,564)(469,577)(470,578)(471,579)(472,580)(473,581)(474,582)(475,583)(476,584)(477,585)(478,586)(479,587)(480,588)(481,601)(482,602)(483,603)(484,604)(485,605)(486,606)(487,607)(488,608)(489,609)(490,610)(491,611)(492,612)(493,589)(494,590)(495,591)(496,592)(497,593)(498,594)(499,595)(500,596)(501,597)(502,598)(503,599)(504,600)(505,613)(506,614)(507,615)(508,616)(509,617)(510,618)(511,619)(512,620)(513,621)(514,622)(515,623)(516,624)(517,637)(518,638)(519,639)(520,640)(521,641)(522,642)(523,643)(524,644)(525,645)(526,646)(527,647)(528,648)(529,625)(530,626)(531,627)(532,628)(533,629)(534,630)(535,631)(536,632)(537,633)(538,634)(539,635)(540,636)(661,673)(662,674)(663,675)(664,676)(665,677)(666,678)(667,679)(668,680)(669,681)(670,682)(671,683)(672,684)(697,709)(698,710)(699,711)(700,712)(701,713)(702,714)(703,715)(704,716)(705,717)(706,718)(707,719)(708,720)(733,745)(734,746)(735,747)(736,748)(737,749)(738,750)(739,751)(740,752)(741,753)(742,754)(743,755)(744,756)(769,781)(770,782)(771,783)(772,784)(773,785)(774,786)(775,787)(776,788)(777,789)(778,790)(779,791)(780,792)(805,817)(806,818)(807,819)(808,820)(809,821)(810,822)(811,823)(812,824)(813,825)(814,826)(815,827)(816,828)(841,853)(842,854)(843,855)(844,856)(845,857)(846,858)(847,859)(848,860)(849,861)(850,862)(851,863)(852,864);
s1 := Sym(864)!( 1,445)( 2,446)( 3,447)( 4,448)( 5,453)( 6,454)( 7,455)( 8,456)( 9,449)( 10,450)( 11,451)( 12,452)( 13,433)( 14,434)( 15,435)( 16,436)( 17,441)( 18,442)( 19,443)( 20,444)( 21,437)( 22,438)( 23,439)( 24,440)( 25,457)( 26,458)( 27,459)( 28,460)( 29,465)( 30,466)( 31,467)( 32,468)( 33,461)( 34,462)( 35,463)( 36,464)( 37,481)( 38,482)( 39,483)( 40,484)( 41,489)( 42,490)( 43,491)( 44,492)( 45,485)( 46,486)( 47,487)( 48,488)( 49,469)( 50,470)( 51,471)( 52,472)( 53,477)( 54,478)( 55,479)( 56,480)( 57,473)( 58,474)( 59,475)( 60,476)( 61,493)( 62,494)( 63,495)( 64,496)( 65,501)( 66,502)( 67,503)( 68,504)( 69,497)( 70,498)( 71,499)( 72,500)( 73,517)( 74,518)( 75,519)( 76,520)( 77,525)( 78,526)( 79,527)( 80,528)( 81,521)( 82,522)( 83,523)( 84,524)( 85,505)( 86,506)( 87,507)( 88,508)( 89,513)( 90,514)( 91,515)( 92,516)( 93,509)( 94,510)( 95,511)( 96,512)( 97,529)( 98,530)( 99,531)(100,532)(101,537)(102,538)(103,539)(104,540)(105,533)(106,534)(107,535)(108,536)(109,553)(110,554)(111,555)(112,556)(113,561)(114,562)(115,563)(116,564)(117,557)(118,558)(119,559)(120,560)(121,541)(122,542)(123,543)(124,544)(125,549)(126,550)(127,551)(128,552)(129,545)(130,546)(131,547)(132,548)(133,565)(134,566)(135,567)(136,568)(137,573)(138,574)(139,575)(140,576)(141,569)(142,570)(143,571)(144,572)(145,589)(146,590)(147,591)(148,592)(149,597)(150,598)(151,599)(152,600)(153,593)(154,594)(155,595)(156,596)(157,577)(158,578)(159,579)(160,580)(161,585)(162,586)(163,587)(164,588)(165,581)(166,582)(167,583)(168,584)(169,601)(170,602)(171,603)(172,604)(173,609)(174,610)(175,611)(176,612)(177,605)(178,606)(179,607)(180,608)(181,625)(182,626)(183,627)(184,628)(185,633)(186,634)(187,635)(188,636)(189,629)(190,630)(191,631)(192,632)(193,613)(194,614)(195,615)(196,616)(197,621)(198,622)(199,623)(200,624)(201,617)(202,618)(203,619)(204,620)(205,637)(206,638)(207,639)(208,640)(209,645)(210,646)(211,647)(212,648)(213,641)(214,642)(215,643)(216,644)(217,769)(218,770)(219,771)(220,772)(221,777)(222,778)(223,779)(224,780)(225,773)(226,774)(227,775)(228,776)(229,757)(230,758)(231,759)(232,760)(233,765)(234,766)(235,767)(236,768)(237,761)(238,762)(239,763)(240,764)(241,781)(242,782)(243,783)(244,784)(245,789)(246,790)(247,791)(248,792)(249,785)(250,786)(251,787)(252,788)(253,805)(254,806)(255,807)(256,808)(257,813)(258,814)(259,815)(260,816)(261,809)(262,810)(263,811)(264,812)(265,793)(266,794)(267,795)(268,796)(269,801)(270,802)(271,803)(272,804)(273,797)(274,798)(275,799)(276,800)(277,817)(278,818)(279,819)(280,820)(281,825)(282,826)(283,827)(284,828)(285,821)(286,822)(287,823)(288,824)(289,841)(290,842)(291,843)(292,844)(293,849)(294,850)(295,851)(296,852)(297,845)(298,846)(299,847)(300,848)(301,829)(302,830)(303,831)(304,832)(305,837)(306,838)(307,839)(308,840)(309,833)(310,834)(311,835)(312,836)(313,853)(314,854)(315,855)(316,856)(317,861)(318,862)(319,863)(320,864)(321,857)(322,858)(323,859)(324,860)(325,661)(326,662)(327,663)(328,664)(329,669)(330,670)(331,671)(332,672)(333,665)(334,666)(335,667)(336,668)(337,649)(338,650)(339,651)(340,652)(341,657)(342,658)(343,659)(344,660)(345,653)(346,654)(347,655)(348,656)(349,673)(350,674)(351,675)(352,676)(353,681)(354,682)(355,683)(356,684)(357,677)(358,678)(359,679)(360,680)(361,697)(362,698)(363,699)(364,700)(365,705)(366,706)(367,707)(368,708)(369,701)(370,702)(371,703)(372,704)(373,685)(374,686)(375,687)(376,688)(377,693)(378,694)(379,695)(380,696)(381,689)(382,690)(383,691)(384,692)(385,709)(386,710)(387,711)(388,712)(389,717)(390,718)(391,719)(392,720)(393,713)(394,714)(395,715)(396,716)(397,733)(398,734)(399,735)(400,736)(401,741)(402,742)(403,743)(404,744)(405,737)(406,738)(407,739)(408,740)(409,721)(410,722)(411,723)(412,724)(413,729)(414,730)(415,731)(416,732)(417,725)(418,726)(419,727)(420,728)(421,745)(422,746)(423,747)(424,748)(425,753)(426,754)(427,755)(428,756)(429,749)(430,750)(431,751)(432,752);
s2 := Sym(864)!( 1,653)( 2,654)( 3,656)( 4,655)( 5,649)( 6,650)( 7,652)( 8,651)( 9,657)( 10,658)( 11,660)( 12,659)( 13,665)( 14,666)( 15,668)( 16,667)( 17,661)( 18,662)( 19,664)( 20,663)( 21,669)( 22,670)( 23,672)( 24,671)( 25,677)( 26,678)( 27,680)( 28,679)( 29,673)( 30,674)( 31,676)( 32,675)( 33,681)( 34,682)( 35,684)( 36,683)( 37,725)( 38,726)( 39,728)( 40,727)( 41,721)( 42,722)( 43,724)( 44,723)( 45,729)( 46,730)( 47,732)( 48,731)( 49,737)( 50,738)( 51,740)( 52,739)( 53,733)( 54,734)( 55,736)( 56,735)( 57,741)( 58,742)( 59,744)( 60,743)( 61,749)( 62,750)( 63,752)( 64,751)( 65,745)( 66,746)( 67,748)( 68,747)( 69,753)( 70,754)( 71,756)( 72,755)( 73,689)( 74,690)( 75,692)( 76,691)( 77,685)( 78,686)( 79,688)( 80,687)( 81,693)( 82,694)( 83,696)( 84,695)( 85,701)( 86,702)( 87,704)( 88,703)( 89,697)( 90,698)( 91,700)( 92,699)( 93,705)( 94,706)( 95,708)( 96,707)( 97,713)( 98,714)( 99,716)(100,715)(101,709)(102,710)(103,712)(104,711)(105,717)(106,718)(107,720)(108,719)(109,761)(110,762)(111,764)(112,763)(113,757)(114,758)(115,760)(116,759)(117,765)(118,766)(119,768)(120,767)(121,773)(122,774)(123,776)(124,775)(125,769)(126,770)(127,772)(128,771)(129,777)(130,778)(131,780)(132,779)(133,785)(134,786)(135,788)(136,787)(137,781)(138,782)(139,784)(140,783)(141,789)(142,790)(143,792)(144,791)(145,833)(146,834)(147,836)(148,835)(149,829)(150,830)(151,832)(152,831)(153,837)(154,838)(155,840)(156,839)(157,845)(158,846)(159,848)(160,847)(161,841)(162,842)(163,844)(164,843)(165,849)(166,850)(167,852)(168,851)(169,857)(170,858)(171,860)(172,859)(173,853)(174,854)(175,856)(176,855)(177,861)(178,862)(179,864)(180,863)(181,797)(182,798)(183,800)(184,799)(185,793)(186,794)(187,796)(188,795)(189,801)(190,802)(191,804)(192,803)(193,809)(194,810)(195,812)(196,811)(197,805)(198,806)(199,808)(200,807)(201,813)(202,814)(203,816)(204,815)(205,821)(206,822)(207,824)(208,823)(209,817)(210,818)(211,820)(212,819)(213,825)(214,826)(215,828)(216,827)(217,545)(218,546)(219,548)(220,547)(221,541)(222,542)(223,544)(224,543)(225,549)(226,550)(227,552)(228,551)(229,557)(230,558)(231,560)(232,559)(233,553)(234,554)(235,556)(236,555)(237,561)(238,562)(239,564)(240,563)(241,569)(242,570)(243,572)(244,571)(245,565)(246,566)(247,568)(248,567)(249,573)(250,574)(251,576)(252,575)(253,617)(254,618)(255,620)(256,619)(257,613)(258,614)(259,616)(260,615)(261,621)(262,622)(263,624)(264,623)(265,629)(266,630)(267,632)(268,631)(269,625)(270,626)(271,628)(272,627)(273,633)(274,634)(275,636)(276,635)(277,641)(278,642)(279,644)(280,643)(281,637)(282,638)(283,640)(284,639)(285,645)(286,646)(287,648)(288,647)(289,581)(290,582)(291,584)(292,583)(293,577)(294,578)(295,580)(296,579)(297,585)(298,586)(299,588)(300,587)(301,593)(302,594)(303,596)(304,595)(305,589)(306,590)(307,592)(308,591)(309,597)(310,598)(311,600)(312,599)(313,605)(314,606)(315,608)(316,607)(317,601)(318,602)(319,604)(320,603)(321,609)(322,610)(323,612)(324,611)(325,437)(326,438)(327,440)(328,439)(329,433)(330,434)(331,436)(332,435)(333,441)(334,442)(335,444)(336,443)(337,449)(338,450)(339,452)(340,451)(341,445)(342,446)(343,448)(344,447)(345,453)(346,454)(347,456)(348,455)(349,461)(350,462)(351,464)(352,463)(353,457)(354,458)(355,460)(356,459)(357,465)(358,466)(359,468)(360,467)(361,509)(362,510)(363,512)(364,511)(365,505)(366,506)(367,508)(368,507)(369,513)(370,514)(371,516)(372,515)(373,521)(374,522)(375,524)(376,523)(377,517)(378,518)(379,520)(380,519)(381,525)(382,526)(383,528)(384,527)(385,533)(386,534)(387,536)(388,535)(389,529)(390,530)(391,532)(392,531)(393,537)(394,538)(395,540)(396,539)(397,473)(398,474)(399,476)(400,475)(401,469)(402,470)(403,472)(404,471)(405,477)(406,478)(407,480)(408,479)(409,485)(410,486)(411,488)(412,487)(413,481)(414,482)(415,484)(416,483)(417,489)(418,490)(419,492)(420,491)(421,497)(422,498)(423,500)(424,499)(425,493)(426,494)(427,496)(428,495)(429,501)(430,502)(431,504)(432,503);
s3 := Sym(864)!( 1,685)( 2,688)( 3,687)( 4,686)( 5,693)( 6,696)( 7,695)( 8,694)( 9,689)( 10,692)( 11,691)( 12,690)( 13,697)( 14,700)( 15,699)( 16,698)( 17,705)( 18,708)( 19,707)( 20,706)( 21,701)( 22,704)( 23,703)( 24,702)( 25,709)( 26,712)( 27,711)( 28,710)( 29,717)( 30,720)( 31,719)( 32,718)( 33,713)( 34,716)( 35,715)( 36,714)( 37,649)( 38,652)( 39,651)( 40,650)( 41,657)( 42,660)( 43,659)( 44,658)( 45,653)( 46,656)( 47,655)( 48,654)( 49,661)( 50,664)( 51,663)( 52,662)( 53,669)( 54,672)( 55,671)( 56,670)( 57,665)( 58,668)( 59,667)( 60,666)( 61,673)( 62,676)( 63,675)( 64,674)( 65,681)( 66,684)( 67,683)( 68,682)( 69,677)( 70,680)( 71,679)( 72,678)( 73,721)( 74,724)( 75,723)( 76,722)( 77,729)( 78,732)( 79,731)( 80,730)( 81,725)( 82,728)( 83,727)( 84,726)( 85,733)( 86,736)( 87,735)( 88,734)( 89,741)( 90,744)( 91,743)( 92,742)( 93,737)( 94,740)( 95,739)( 96,738)( 97,745)( 98,748)( 99,747)(100,746)(101,753)(102,756)(103,755)(104,754)(105,749)(106,752)(107,751)(108,750)(109,793)(110,796)(111,795)(112,794)(113,801)(114,804)(115,803)(116,802)(117,797)(118,800)(119,799)(120,798)(121,805)(122,808)(123,807)(124,806)(125,813)(126,816)(127,815)(128,814)(129,809)(130,812)(131,811)(132,810)(133,817)(134,820)(135,819)(136,818)(137,825)(138,828)(139,827)(140,826)(141,821)(142,824)(143,823)(144,822)(145,757)(146,760)(147,759)(148,758)(149,765)(150,768)(151,767)(152,766)(153,761)(154,764)(155,763)(156,762)(157,769)(158,772)(159,771)(160,770)(161,777)(162,780)(163,779)(164,778)(165,773)(166,776)(167,775)(168,774)(169,781)(170,784)(171,783)(172,782)(173,789)(174,792)(175,791)(176,790)(177,785)(178,788)(179,787)(180,786)(181,829)(182,832)(183,831)(184,830)(185,837)(186,840)(187,839)(188,838)(189,833)(190,836)(191,835)(192,834)(193,841)(194,844)(195,843)(196,842)(197,849)(198,852)(199,851)(200,850)(201,845)(202,848)(203,847)(204,846)(205,853)(206,856)(207,855)(208,854)(209,861)(210,864)(211,863)(212,862)(213,857)(214,860)(215,859)(216,858)(217,577)(218,580)(219,579)(220,578)(221,585)(222,588)(223,587)(224,586)(225,581)(226,584)(227,583)(228,582)(229,589)(230,592)(231,591)(232,590)(233,597)(234,600)(235,599)(236,598)(237,593)(238,596)(239,595)(240,594)(241,601)(242,604)(243,603)(244,602)(245,609)(246,612)(247,611)(248,610)(249,605)(250,608)(251,607)(252,606)(253,541)(254,544)(255,543)(256,542)(257,549)(258,552)(259,551)(260,550)(261,545)(262,548)(263,547)(264,546)(265,553)(266,556)(267,555)(268,554)(269,561)(270,564)(271,563)(272,562)(273,557)(274,560)(275,559)(276,558)(277,565)(278,568)(279,567)(280,566)(281,573)(282,576)(283,575)(284,574)(285,569)(286,572)(287,571)(288,570)(289,613)(290,616)(291,615)(292,614)(293,621)(294,624)(295,623)(296,622)(297,617)(298,620)(299,619)(300,618)(301,625)(302,628)(303,627)(304,626)(305,633)(306,636)(307,635)(308,634)(309,629)(310,632)(311,631)(312,630)(313,637)(314,640)(315,639)(316,638)(317,645)(318,648)(319,647)(320,646)(321,641)(322,644)(323,643)(324,642)(325,469)(326,472)(327,471)(328,470)(329,477)(330,480)(331,479)(332,478)(333,473)(334,476)(335,475)(336,474)(337,481)(338,484)(339,483)(340,482)(341,489)(342,492)(343,491)(344,490)(345,485)(346,488)(347,487)(348,486)(349,493)(350,496)(351,495)(352,494)(353,501)(354,504)(355,503)(356,502)(357,497)(358,500)(359,499)(360,498)(361,433)(362,436)(363,435)(364,434)(365,441)(366,444)(367,443)(368,442)(369,437)(370,440)(371,439)(372,438)(373,445)(374,448)(375,447)(376,446)(377,453)(378,456)(379,455)(380,454)(381,449)(382,452)(383,451)(384,450)(385,457)(386,460)(387,459)(388,458)(389,465)(390,468)(391,467)(392,466)(393,461)(394,464)(395,463)(396,462)(397,505)(398,508)(399,507)(400,506)(401,513)(402,516)(403,515)(404,514)(405,509)(406,512)(407,511)(408,510)(409,517)(410,520)(411,519)(412,518)(413,525)(414,528)(415,527)(416,526)(417,521)(418,524)(419,523)(420,522)(421,529)(422,532)(423,531)(424,530)(425,537)(426,540)(427,539)(428,538)(429,533)(430,536)(431,535)(432,534);
s4 := Sym(864)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272)(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)(287,288)(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)(303,304)(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)(319,320)(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)(335,336)(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)(351,352)(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)(367,368)(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)(383,384)(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)(399,400)(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)(415,416)(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)(431,432)(433,434)(435,436)(437,438)(439,440)(441,442)(443,444)(445,446)(447,448)(449,450)(451,452)(453,454)(455,456)(457,458)(459,460)(461,462)(463,464)(465,466)(467,468)(469,470)(471,472)(473,474)(475,476)(477,478)(479,480)(481,482)(483,484)(485,486)(487,488)(489,490)(491,492)(493,494)(495,496)(497,498)(499,500)(501,502)(503,504)(505,506)(507,508)(509,510)(511,512)(513,514)(515,516)(517,518)(519,520)(521,522)(523,524)(525,526)(527,528)(529,530)(531,532)(533,534)(535,536)(537,538)(539,540)(541,542)(543,544)(545,546)(547,548)(549,550)(551,552)(553,554)(555,556)(557,558)(559,560)(561,562)(563,564)(565,566)(567,568)(569,570)(571,572)(573,574)(575,576)(577,578)(579,580)(581,582)(583,584)(585,586)(587,588)(589,590)(591,592)(593,594)(595,596)(597,598)(599,600)(601,602)(603,604)(605,606)(607,608)(609,610)(611,612)(613,614)(615,616)(617,618)(619,620)(621,622)(623,624)(625,626)(627,628)(629,630)(631,632)(633,634)(635,636)(637,638)(639,640)(641,642)(643,644)(645,646)(647,648)(649,650)(651,652)(653,654)(655,656)(657,658)(659,660)(661,662)(663,664)(665,666)(667,668)(669,670)(671,672)(673,674)(675,676)(677,678)(679,680)(681,682)(683,684)(685,686)(687,688)(689,690)(691,692)(693,694)(695,696)(697,698)(699,700)(701,702)(703,704)(705,706)(707,708)(709,710)(711,712)(713,714)(715,716)(717,718)(719,720)(721,722)(723,724)(725,726)(727,728)(729,730)(731,732)(733,734)(735,736)(737,738)(739,740)(741,742)(743,744)(745,746)(747,748)(749,750)(751,752)(753,754)(755,756)(757,758)(759,760)(761,762)(763,764)(765,766)(767,768)(769,770)(771,772)(773,774)(775,776)(777,778)(779,780)(781,782)(783,784)(785,786)(787,788)(789,790)(791,792)(793,794)(795,796)(797,798)(799,800)(801,802)(803,804)(805,806)(807,808)(809,810)(811,812)(813,814)(815,816)(817,818)(819,820)(821,822)(823,824)(825,826)(827,828)(829,830)(831,832)(833,834)(835,836)(837,838)(839,840)(841,842)(843,844)(845,846)(847,848)(849,850)(851,852)(853,854)(855,856)(857,858)(859,860)(861,862)(863,864);
poly := sub<Sym(864)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s4*s3*s2*s4*s3*s2*s4*s3,
s1*s2*s3*s1*s2*s1*s2*s3*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 >;
References : None.
to this polytope