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Polytope of Type {4,93}

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