Polytope of Type {186,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {186,4}*1488b
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 : 186
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Flat
Self-Petrie
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}*48c
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, 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);;
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,
s2*s1*s0*s2*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*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*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*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, 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);
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,
s2*s1*s0*s2*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*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*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*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