Polytope of Type {186,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {186,4}*1488c
if this polytope has a name.
Group : SmallGroup(1488,209)
Rank : 3
Schlafli Type : {186,4}
Number of vertices, edges, etc : 186, 372, 4
Order of s0s1s2 : 93
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {93,4}*744
31-fold quotients : {6,4}*48b
62-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5,121)( 6,122)( 7,124)( 8,123)( 9,117)( 10,118)( 11,120)
( 12,119)( 13,113)( 14,114)( 15,116)( 16,115)( 17,109)( 18,110)( 19,112)
( 20,111)( 21,105)( 22,106)( 23,108)( 24,107)( 25,101)( 26,102)( 27,104)
( 28,103)( 29, 97)( 30, 98)( 31,100)( 32, 99)( 33, 93)( 34, 94)( 35, 96)
( 36, 95)( 37, 89)( 38, 90)( 39, 92)( 40, 91)( 41, 85)( 42, 86)( 43, 88)
( 44, 87)( 45, 81)( 46, 82)( 47, 84)( 48, 83)( 49, 77)( 50, 78)( 51, 80)
( 52, 79)( 53, 73)( 54, 74)( 55, 76)( 56, 75)( 57, 69)( 58, 70)( 59, 72)
( 60, 71)( 61, 65)( 62, 66)( 63, 68)( 64, 67)(125,249)(126,250)(127,252)
(128,251)(129,369)(130,370)(131,372)(132,371)(133,365)(134,366)(135,368)
(136,367)(137,361)(138,362)(139,364)(140,363)(141,357)(142,358)(143,360)
(144,359)(145,353)(146,354)(147,356)(148,355)(149,349)(150,350)(151,352)
(152,351)(153,345)(154,346)(155,348)(156,347)(157,341)(158,342)(159,344)
(160,343)(161,337)(162,338)(163,340)(164,339)(165,333)(166,334)(167,336)
(168,335)(169,329)(170,330)(171,332)(172,331)(173,325)(174,326)(175,328)
(176,327)(177,321)(178,322)(179,324)(180,323)(181,317)(182,318)(183,320)
(184,319)(185,313)(186,314)(187,316)(188,315)(189,309)(190,310)(191,312)
(192,311)(193,305)(194,306)(195,308)(196,307)(197,301)(198,302)(199,304)
(200,303)(201,297)(202,298)(203,300)(204,299)(205,293)(206,294)(207,296)
(208,295)(209,289)(210,290)(211,292)(212,291)(213,285)(214,286)(215,288)
(216,287)(217,281)(218,282)(219,284)(220,283)(221,277)(222,278)(223,280)
(224,279)(225,273)(226,274)(227,276)(228,275)(229,269)(230,270)(231,272)
(232,271)(233,265)(234,266)(235,268)(236,267)(237,261)(238,262)(239,264)
(240,263)(241,257)(242,258)(243,260)(244,259)(245,253)(246,254)(247,256)
(248,255)(375,376)(377,493)(378,494)(379,496)(380,495)(381,489)(382,490)
(383,492)(384,491)(385,485)(386,486)(387,488)(388,487)(389,481)(390,482)
(391,484)(392,483)(393,477)(394,478)(395,480)(396,479)(397,473)(398,474)
(399,476)(400,475)(401,469)(402,470)(403,472)(404,471)(405,465)(406,466)
(407,468)(408,467)(409,461)(410,462)(411,464)(412,463)(413,457)(414,458)
(415,460)(416,459)(417,453)(418,454)(419,456)(420,455)(421,449)(422,450)
(423,452)(424,451)(425,445)(426,446)(427,448)(428,447)(429,441)(430,442)
(431,444)(432,443)(433,437)(434,438)(435,440)(436,439)(497,621)(498,622)
(499,624)(500,623)(501,741)(502,742)(503,744)(504,743)(505,737)(506,738)
(507,740)(508,739)(509,733)(510,734)(511,736)(512,735)(513,729)(514,730)
(515,732)(516,731)(517,725)(518,726)(519,728)(520,727)(521,721)(522,722)
(523,724)(524,723)(525,717)(526,718)(527,720)(528,719)(529,713)(530,714)
(531,716)(532,715)(533,709)(534,710)(535,712)(536,711)(537,705)(538,706)
(539,708)(540,707)(541,701)(542,702)(543,704)(544,703)(545,697)(546,698)
(547,700)(548,699)(549,693)(550,694)(551,696)(552,695)(553,689)(554,690)
(555,692)(556,691)(557,685)(558,686)(559,688)(560,687)(561,681)(562,682)
(563,684)(564,683)(565,677)(566,678)(567,680)(568,679)(569,673)(570,674)
(571,676)(572,675)(573,669)(574,670)(575,672)(576,671)(577,665)(578,666)
(579,668)(580,667)(581,661)(582,662)(583,664)(584,663)(585,657)(586,658)
(587,660)(588,659)(589,653)(590,654)(591,656)(592,655)(593,649)(594,650)
(595,652)(596,651)(597,645)(598,646)(599,648)(600,647)(601,641)(602,642)
(603,644)(604,643)(605,637)(606,638)(607,640)(608,639)(609,633)(610,634)
(611,636)(612,635)(613,629)(614,630)(615,632)(616,631)(617,625)(618,626)
(619,628)(620,627);;
s1 := ( 1,501)( 2,504)( 3,503)( 4,502)( 5,497)( 6,500)( 7,499)( 8,498)
( 9,617)( 10,620)( 11,619)( 12,618)( 13,613)( 14,616)( 15,615)( 16,614)
( 17,609)( 18,612)( 19,611)( 20,610)( 21,605)( 22,608)( 23,607)( 24,606)
( 25,601)( 26,604)( 27,603)( 28,602)( 29,597)( 30,600)( 31,599)( 32,598)
( 33,593)( 34,596)( 35,595)( 36,594)( 37,589)( 38,592)( 39,591)( 40,590)
( 41,585)( 42,588)( 43,587)( 44,586)( 45,581)( 46,584)( 47,583)( 48,582)
( 49,577)( 50,580)( 51,579)( 52,578)( 53,573)( 54,576)( 55,575)( 56,574)
( 57,569)( 58,572)( 59,571)( 60,570)( 61,565)( 62,568)( 63,567)( 64,566)
( 65,561)( 66,564)( 67,563)( 68,562)( 69,557)( 70,560)( 71,559)( 72,558)
( 73,553)( 74,556)( 75,555)( 76,554)( 77,549)( 78,552)( 79,551)( 80,550)
( 81,545)( 82,548)( 83,547)( 84,546)( 85,541)( 86,544)( 87,543)( 88,542)
( 89,537)( 90,540)( 91,539)( 92,538)( 93,533)( 94,536)( 95,535)( 96,534)
( 97,529)( 98,532)( 99,531)(100,530)(101,525)(102,528)(103,527)(104,526)
(105,521)(106,524)(107,523)(108,522)(109,517)(110,520)(111,519)(112,518)
(113,513)(114,516)(115,515)(116,514)(117,509)(118,512)(119,511)(120,510)
(121,505)(122,508)(123,507)(124,506)(125,377)(126,380)(127,379)(128,378)
(129,373)(130,376)(131,375)(132,374)(133,493)(134,496)(135,495)(136,494)
(137,489)(138,492)(139,491)(140,490)(141,485)(142,488)(143,487)(144,486)
(145,481)(146,484)(147,483)(148,482)(149,477)(150,480)(151,479)(152,478)
(153,473)(154,476)(155,475)(156,474)(157,469)(158,472)(159,471)(160,470)
(161,465)(162,468)(163,467)(164,466)(165,461)(166,464)(167,463)(168,462)
(169,457)(170,460)(171,459)(172,458)(173,453)(174,456)(175,455)(176,454)
(177,449)(178,452)(179,451)(180,450)(181,445)(182,448)(183,447)(184,446)
(185,441)(186,444)(187,443)(188,442)(189,437)(190,440)(191,439)(192,438)
(193,433)(194,436)(195,435)(196,434)(197,429)(198,432)(199,431)(200,430)
(201,425)(202,428)(203,427)(204,426)(205,421)(206,424)(207,423)(208,422)
(209,417)(210,420)(211,419)(212,418)(213,413)(214,416)(215,415)(216,414)
(217,409)(218,412)(219,411)(220,410)(221,405)(222,408)(223,407)(224,406)
(225,401)(226,404)(227,403)(228,402)(229,397)(230,400)(231,399)(232,398)
(233,393)(234,396)(235,395)(236,394)(237,389)(238,392)(239,391)(240,390)
(241,385)(242,388)(243,387)(244,386)(245,381)(246,384)(247,383)(248,382)
(249,625)(250,628)(251,627)(252,626)(253,621)(254,624)(255,623)(256,622)
(257,741)(258,744)(259,743)(260,742)(261,737)(262,740)(263,739)(264,738)
(265,733)(266,736)(267,735)(268,734)(269,729)(270,732)(271,731)(272,730)
(273,725)(274,728)(275,727)(276,726)(277,721)(278,724)(279,723)(280,722)
(281,717)(282,720)(283,719)(284,718)(285,713)(286,716)(287,715)(288,714)
(289,709)(290,712)(291,711)(292,710)(293,705)(294,708)(295,707)(296,706)
(297,701)(298,704)(299,703)(300,702)(301,697)(302,700)(303,699)(304,698)
(305,693)(306,696)(307,695)(308,694)(309,689)(310,692)(311,691)(312,690)
(313,685)(314,688)(315,687)(316,686)(317,681)(318,684)(319,683)(320,682)
(321,677)(322,680)(323,679)(324,678)(325,673)(326,676)(327,675)(328,674)
(329,669)(330,672)(331,671)(332,670)(333,665)(334,668)(335,667)(336,666)
(337,661)(338,664)(339,663)(340,662)(341,657)(342,660)(343,659)(344,658)
(345,653)(346,656)(347,655)(348,654)(349,649)(350,652)(351,651)(352,650)
(353,645)(354,648)(355,647)(356,646)(357,641)(358,644)(359,643)(360,642)
(361,637)(362,640)(363,639)(364,638)(365,633)(366,636)(367,635)(368,634)
(369,629)(370,632)(371,631)(372,630);;
s2 := ( 1,374)( 2,373)( 3,376)( 4,375)( 5,378)( 6,377)( 7,380)( 8,379)
( 9,382)( 10,381)( 11,384)( 12,383)( 13,386)( 14,385)( 15,388)( 16,387)
( 17,390)( 18,389)( 19,392)( 20,391)( 21,394)( 22,393)( 23,396)( 24,395)
( 25,398)( 26,397)( 27,400)( 28,399)( 29,402)( 30,401)( 31,404)( 32,403)
( 33,406)( 34,405)( 35,408)( 36,407)( 37,410)( 38,409)( 39,412)( 40,411)
( 41,414)( 42,413)( 43,416)( 44,415)( 45,418)( 46,417)( 47,420)( 48,419)
( 49,422)( 50,421)( 51,424)( 52,423)( 53,426)( 54,425)( 55,428)( 56,427)
( 57,430)( 58,429)( 59,432)( 60,431)( 61,434)( 62,433)( 63,436)( 64,435)
( 65,438)( 66,437)( 67,440)( 68,439)( 69,442)( 70,441)( 71,444)( 72,443)
( 73,446)( 74,445)( 75,448)( 76,447)( 77,450)( 78,449)( 79,452)( 80,451)
( 81,454)( 82,453)( 83,456)( 84,455)( 85,458)( 86,457)( 87,460)( 88,459)
( 89,462)( 90,461)( 91,464)( 92,463)( 93,466)( 94,465)( 95,468)( 96,467)
( 97,470)( 98,469)( 99,472)(100,471)(101,474)(102,473)(103,476)(104,475)
(105,478)(106,477)(107,480)(108,479)(109,482)(110,481)(111,484)(112,483)
(113,486)(114,485)(115,488)(116,487)(117,490)(118,489)(119,492)(120,491)
(121,494)(122,493)(123,496)(124,495)(125,498)(126,497)(127,500)(128,499)
(129,502)(130,501)(131,504)(132,503)(133,506)(134,505)(135,508)(136,507)
(137,510)(138,509)(139,512)(140,511)(141,514)(142,513)(143,516)(144,515)
(145,518)(146,517)(147,520)(148,519)(149,522)(150,521)(151,524)(152,523)
(153,526)(154,525)(155,528)(156,527)(157,530)(158,529)(159,532)(160,531)
(161,534)(162,533)(163,536)(164,535)(165,538)(166,537)(167,540)(168,539)
(169,542)(170,541)(171,544)(172,543)(173,546)(174,545)(175,548)(176,547)
(177,550)(178,549)(179,552)(180,551)(181,554)(182,553)(183,556)(184,555)
(185,558)(186,557)(187,560)(188,559)(189,562)(190,561)(191,564)(192,563)
(193,566)(194,565)(195,568)(196,567)(197,570)(198,569)(199,572)(200,571)
(201,574)(202,573)(203,576)(204,575)(205,578)(206,577)(207,580)(208,579)
(209,582)(210,581)(211,584)(212,583)(213,586)(214,585)(215,588)(216,587)
(217,590)(218,589)(219,592)(220,591)(221,594)(222,593)(223,596)(224,595)
(225,598)(226,597)(227,600)(228,599)(229,602)(230,601)(231,604)(232,603)
(233,606)(234,605)(235,608)(236,607)(237,610)(238,609)(239,612)(240,611)
(241,614)(242,613)(243,616)(244,615)(245,618)(246,617)(247,620)(248,619)
(249,622)(250,621)(251,624)(252,623)(253,626)(254,625)(255,628)(256,627)
(257,630)(258,629)(259,632)(260,631)(261,634)(262,633)(263,636)(264,635)
(265,638)(266,637)(267,640)(268,639)(269,642)(270,641)(271,644)(272,643)
(273,646)(274,645)(275,648)(276,647)(277,650)(278,649)(279,652)(280,651)
(281,654)(282,653)(283,656)(284,655)(285,658)(286,657)(287,660)(288,659)
(289,662)(290,661)(291,664)(292,663)(293,666)(294,665)(295,668)(296,667)
(297,670)(298,669)(299,672)(300,671)(301,674)(302,673)(303,676)(304,675)
(305,678)(306,677)(307,680)(308,679)(309,682)(310,681)(311,684)(312,683)
(313,686)(314,685)(315,688)(316,687)(317,690)(318,689)(319,692)(320,691)
(321,694)(322,693)(323,696)(324,695)(325,698)(326,697)(327,700)(328,699)
(329,702)(330,701)(331,704)(332,703)(333,706)(334,705)(335,708)(336,707)
(337,710)(338,709)(339,712)(340,711)(341,714)(342,713)(343,716)(344,715)
(345,718)(346,717)(347,720)(348,719)(349,722)(350,721)(351,724)(352,723)
(353,726)(354,725)(355,728)(356,727)(357,730)(358,729)(359,732)(360,731)
(361,734)(362,733)(363,736)(364,735)(365,738)(366,737)(367,740)(368,739)
(369,742)(370,741)(371,744)(372,743);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(744)!( 3, 4)( 5,121)( 6,122)( 7,124)( 8,123)( 9,117)( 10,118)
( 11,120)( 12,119)( 13,113)( 14,114)( 15,116)( 16,115)( 17,109)( 18,110)
( 19,112)( 20,111)( 21,105)( 22,106)( 23,108)( 24,107)( 25,101)( 26,102)
( 27,104)( 28,103)( 29, 97)( 30, 98)( 31,100)( 32, 99)( 33, 93)( 34, 94)
( 35, 96)( 36, 95)( 37, 89)( 38, 90)( 39, 92)( 40, 91)( 41, 85)( 42, 86)
( 43, 88)( 44, 87)( 45, 81)( 46, 82)( 47, 84)( 48, 83)( 49, 77)( 50, 78)
( 51, 80)( 52, 79)( 53, 73)( 54, 74)( 55, 76)( 56, 75)( 57, 69)( 58, 70)
( 59, 72)( 60, 71)( 61, 65)( 62, 66)( 63, 68)( 64, 67)(125,249)(126,250)
(127,252)(128,251)(129,369)(130,370)(131,372)(132,371)(133,365)(134,366)
(135,368)(136,367)(137,361)(138,362)(139,364)(140,363)(141,357)(142,358)
(143,360)(144,359)(145,353)(146,354)(147,356)(148,355)(149,349)(150,350)
(151,352)(152,351)(153,345)(154,346)(155,348)(156,347)(157,341)(158,342)
(159,344)(160,343)(161,337)(162,338)(163,340)(164,339)(165,333)(166,334)
(167,336)(168,335)(169,329)(170,330)(171,332)(172,331)(173,325)(174,326)
(175,328)(176,327)(177,321)(178,322)(179,324)(180,323)(181,317)(182,318)
(183,320)(184,319)(185,313)(186,314)(187,316)(188,315)(189,309)(190,310)
(191,312)(192,311)(193,305)(194,306)(195,308)(196,307)(197,301)(198,302)
(199,304)(200,303)(201,297)(202,298)(203,300)(204,299)(205,293)(206,294)
(207,296)(208,295)(209,289)(210,290)(211,292)(212,291)(213,285)(214,286)
(215,288)(216,287)(217,281)(218,282)(219,284)(220,283)(221,277)(222,278)
(223,280)(224,279)(225,273)(226,274)(227,276)(228,275)(229,269)(230,270)
(231,272)(232,271)(233,265)(234,266)(235,268)(236,267)(237,261)(238,262)
(239,264)(240,263)(241,257)(242,258)(243,260)(244,259)(245,253)(246,254)
(247,256)(248,255)(375,376)(377,493)(378,494)(379,496)(380,495)(381,489)
(382,490)(383,492)(384,491)(385,485)(386,486)(387,488)(388,487)(389,481)
(390,482)(391,484)(392,483)(393,477)(394,478)(395,480)(396,479)(397,473)
(398,474)(399,476)(400,475)(401,469)(402,470)(403,472)(404,471)(405,465)
(406,466)(407,468)(408,467)(409,461)(410,462)(411,464)(412,463)(413,457)
(414,458)(415,460)(416,459)(417,453)(418,454)(419,456)(420,455)(421,449)
(422,450)(423,452)(424,451)(425,445)(426,446)(427,448)(428,447)(429,441)
(430,442)(431,444)(432,443)(433,437)(434,438)(435,440)(436,439)(497,621)
(498,622)(499,624)(500,623)(501,741)(502,742)(503,744)(504,743)(505,737)
(506,738)(507,740)(508,739)(509,733)(510,734)(511,736)(512,735)(513,729)
(514,730)(515,732)(516,731)(517,725)(518,726)(519,728)(520,727)(521,721)
(522,722)(523,724)(524,723)(525,717)(526,718)(527,720)(528,719)(529,713)
(530,714)(531,716)(532,715)(533,709)(534,710)(535,712)(536,711)(537,705)
(538,706)(539,708)(540,707)(541,701)(542,702)(543,704)(544,703)(545,697)
(546,698)(547,700)(548,699)(549,693)(550,694)(551,696)(552,695)(553,689)
(554,690)(555,692)(556,691)(557,685)(558,686)(559,688)(560,687)(561,681)
(562,682)(563,684)(564,683)(565,677)(566,678)(567,680)(568,679)(569,673)
(570,674)(571,676)(572,675)(573,669)(574,670)(575,672)(576,671)(577,665)
(578,666)(579,668)(580,667)(581,661)(582,662)(583,664)(584,663)(585,657)
(586,658)(587,660)(588,659)(589,653)(590,654)(591,656)(592,655)(593,649)
(594,650)(595,652)(596,651)(597,645)(598,646)(599,648)(600,647)(601,641)
(602,642)(603,644)(604,643)(605,637)(606,638)(607,640)(608,639)(609,633)
(610,634)(611,636)(612,635)(613,629)(614,630)(615,632)(616,631)(617,625)
(618,626)(619,628)(620,627);
s1 := Sym(744)!( 1,501)( 2,504)( 3,503)( 4,502)( 5,497)( 6,500)( 7,499)
( 8,498)( 9,617)( 10,620)( 11,619)( 12,618)( 13,613)( 14,616)( 15,615)
( 16,614)( 17,609)( 18,612)( 19,611)( 20,610)( 21,605)( 22,608)( 23,607)
( 24,606)( 25,601)( 26,604)( 27,603)( 28,602)( 29,597)( 30,600)( 31,599)
( 32,598)( 33,593)( 34,596)( 35,595)( 36,594)( 37,589)( 38,592)( 39,591)
( 40,590)( 41,585)( 42,588)( 43,587)( 44,586)( 45,581)( 46,584)( 47,583)
( 48,582)( 49,577)( 50,580)( 51,579)( 52,578)( 53,573)( 54,576)( 55,575)
( 56,574)( 57,569)( 58,572)( 59,571)( 60,570)( 61,565)( 62,568)( 63,567)
( 64,566)( 65,561)( 66,564)( 67,563)( 68,562)( 69,557)( 70,560)( 71,559)
( 72,558)( 73,553)( 74,556)( 75,555)( 76,554)( 77,549)( 78,552)( 79,551)
( 80,550)( 81,545)( 82,548)( 83,547)( 84,546)( 85,541)( 86,544)( 87,543)
( 88,542)( 89,537)( 90,540)( 91,539)( 92,538)( 93,533)( 94,536)( 95,535)
( 96,534)( 97,529)( 98,532)( 99,531)(100,530)(101,525)(102,528)(103,527)
(104,526)(105,521)(106,524)(107,523)(108,522)(109,517)(110,520)(111,519)
(112,518)(113,513)(114,516)(115,515)(116,514)(117,509)(118,512)(119,511)
(120,510)(121,505)(122,508)(123,507)(124,506)(125,377)(126,380)(127,379)
(128,378)(129,373)(130,376)(131,375)(132,374)(133,493)(134,496)(135,495)
(136,494)(137,489)(138,492)(139,491)(140,490)(141,485)(142,488)(143,487)
(144,486)(145,481)(146,484)(147,483)(148,482)(149,477)(150,480)(151,479)
(152,478)(153,473)(154,476)(155,475)(156,474)(157,469)(158,472)(159,471)
(160,470)(161,465)(162,468)(163,467)(164,466)(165,461)(166,464)(167,463)
(168,462)(169,457)(170,460)(171,459)(172,458)(173,453)(174,456)(175,455)
(176,454)(177,449)(178,452)(179,451)(180,450)(181,445)(182,448)(183,447)
(184,446)(185,441)(186,444)(187,443)(188,442)(189,437)(190,440)(191,439)
(192,438)(193,433)(194,436)(195,435)(196,434)(197,429)(198,432)(199,431)
(200,430)(201,425)(202,428)(203,427)(204,426)(205,421)(206,424)(207,423)
(208,422)(209,417)(210,420)(211,419)(212,418)(213,413)(214,416)(215,415)
(216,414)(217,409)(218,412)(219,411)(220,410)(221,405)(222,408)(223,407)
(224,406)(225,401)(226,404)(227,403)(228,402)(229,397)(230,400)(231,399)
(232,398)(233,393)(234,396)(235,395)(236,394)(237,389)(238,392)(239,391)
(240,390)(241,385)(242,388)(243,387)(244,386)(245,381)(246,384)(247,383)
(248,382)(249,625)(250,628)(251,627)(252,626)(253,621)(254,624)(255,623)
(256,622)(257,741)(258,744)(259,743)(260,742)(261,737)(262,740)(263,739)
(264,738)(265,733)(266,736)(267,735)(268,734)(269,729)(270,732)(271,731)
(272,730)(273,725)(274,728)(275,727)(276,726)(277,721)(278,724)(279,723)
(280,722)(281,717)(282,720)(283,719)(284,718)(285,713)(286,716)(287,715)
(288,714)(289,709)(290,712)(291,711)(292,710)(293,705)(294,708)(295,707)
(296,706)(297,701)(298,704)(299,703)(300,702)(301,697)(302,700)(303,699)
(304,698)(305,693)(306,696)(307,695)(308,694)(309,689)(310,692)(311,691)
(312,690)(313,685)(314,688)(315,687)(316,686)(317,681)(318,684)(319,683)
(320,682)(321,677)(322,680)(323,679)(324,678)(325,673)(326,676)(327,675)
(328,674)(329,669)(330,672)(331,671)(332,670)(333,665)(334,668)(335,667)
(336,666)(337,661)(338,664)(339,663)(340,662)(341,657)(342,660)(343,659)
(344,658)(345,653)(346,656)(347,655)(348,654)(349,649)(350,652)(351,651)
(352,650)(353,645)(354,648)(355,647)(356,646)(357,641)(358,644)(359,643)
(360,642)(361,637)(362,640)(363,639)(364,638)(365,633)(366,636)(367,635)
(368,634)(369,629)(370,632)(371,631)(372,630);
s2 := Sym(744)!( 1,374)( 2,373)( 3,376)( 4,375)( 5,378)( 6,377)( 7,380)
( 8,379)( 9,382)( 10,381)( 11,384)( 12,383)( 13,386)( 14,385)( 15,388)
( 16,387)( 17,390)( 18,389)( 19,392)( 20,391)( 21,394)( 22,393)( 23,396)
( 24,395)( 25,398)( 26,397)( 27,400)( 28,399)( 29,402)( 30,401)( 31,404)
( 32,403)( 33,406)( 34,405)( 35,408)( 36,407)( 37,410)( 38,409)( 39,412)
( 40,411)( 41,414)( 42,413)( 43,416)( 44,415)( 45,418)( 46,417)( 47,420)
( 48,419)( 49,422)( 50,421)( 51,424)( 52,423)( 53,426)( 54,425)( 55,428)
( 56,427)( 57,430)( 58,429)( 59,432)( 60,431)( 61,434)( 62,433)( 63,436)
( 64,435)( 65,438)( 66,437)( 67,440)( 68,439)( 69,442)( 70,441)( 71,444)
( 72,443)( 73,446)( 74,445)( 75,448)( 76,447)( 77,450)( 78,449)( 79,452)
( 80,451)( 81,454)( 82,453)( 83,456)( 84,455)( 85,458)( 86,457)( 87,460)
( 88,459)( 89,462)( 90,461)( 91,464)( 92,463)( 93,466)( 94,465)( 95,468)
( 96,467)( 97,470)( 98,469)( 99,472)(100,471)(101,474)(102,473)(103,476)
(104,475)(105,478)(106,477)(107,480)(108,479)(109,482)(110,481)(111,484)
(112,483)(113,486)(114,485)(115,488)(116,487)(117,490)(118,489)(119,492)
(120,491)(121,494)(122,493)(123,496)(124,495)(125,498)(126,497)(127,500)
(128,499)(129,502)(130,501)(131,504)(132,503)(133,506)(134,505)(135,508)
(136,507)(137,510)(138,509)(139,512)(140,511)(141,514)(142,513)(143,516)
(144,515)(145,518)(146,517)(147,520)(148,519)(149,522)(150,521)(151,524)
(152,523)(153,526)(154,525)(155,528)(156,527)(157,530)(158,529)(159,532)
(160,531)(161,534)(162,533)(163,536)(164,535)(165,538)(166,537)(167,540)
(168,539)(169,542)(170,541)(171,544)(172,543)(173,546)(174,545)(175,548)
(176,547)(177,550)(178,549)(179,552)(180,551)(181,554)(182,553)(183,556)
(184,555)(185,558)(186,557)(187,560)(188,559)(189,562)(190,561)(191,564)
(192,563)(193,566)(194,565)(195,568)(196,567)(197,570)(198,569)(199,572)
(200,571)(201,574)(202,573)(203,576)(204,575)(205,578)(206,577)(207,580)
(208,579)(209,582)(210,581)(211,584)(212,583)(213,586)(214,585)(215,588)
(216,587)(217,590)(218,589)(219,592)(220,591)(221,594)(222,593)(223,596)
(224,595)(225,598)(226,597)(227,600)(228,599)(229,602)(230,601)(231,604)
(232,603)(233,606)(234,605)(235,608)(236,607)(237,610)(238,609)(239,612)
(240,611)(241,614)(242,613)(243,616)(244,615)(245,618)(246,617)(247,620)
(248,619)(249,622)(250,621)(251,624)(252,623)(253,626)(254,625)(255,628)
(256,627)(257,630)(258,629)(259,632)(260,631)(261,634)(262,633)(263,636)
(264,635)(265,638)(266,637)(267,640)(268,639)(269,642)(270,641)(271,644)
(272,643)(273,646)(274,645)(275,648)(276,647)(277,650)(278,649)(279,652)
(280,651)(281,654)(282,653)(283,656)(284,655)(285,658)(286,657)(287,660)
(288,659)(289,662)(290,661)(291,664)(292,663)(293,666)(294,665)(295,668)
(296,667)(297,670)(298,669)(299,672)(300,671)(301,674)(302,673)(303,676)
(304,675)(305,678)(306,677)(307,680)(308,679)(309,682)(310,681)(311,684)
(312,683)(313,686)(314,685)(315,688)(316,687)(317,690)(318,689)(319,692)
(320,691)(321,694)(322,693)(323,696)(324,695)(325,698)(326,697)(327,700)
(328,699)(329,702)(330,701)(331,704)(332,703)(333,706)(334,705)(335,708)
(336,707)(337,710)(338,709)(339,712)(340,711)(341,714)(342,713)(343,716)
(344,715)(345,718)(346,717)(347,720)(348,719)(349,722)(350,721)(351,724)
(352,723)(353,726)(354,725)(355,728)(356,727)(357,730)(358,729)(359,732)
(360,731)(361,734)(362,733)(363,736)(364,735)(365,738)(366,737)(367,740)
(368,739)(369,742)(370,741)(371,744)(372,743);
poly := sub<Sym(744)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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