Polytope of Type {188,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {188,4}*1504
Also Known As : {188,4|2}. if this polytope has another name.
Group : SmallGroup(1504,116)
Rank : 3
Schlafli Type : {188,4}
Number of vertices, edges, etc : 188, 376, 4
Order of s₀s₁s₂ : 188
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {188,2}*752, {94,4}*752
   4-fold quotients : {94,2}*376
   8-fold quotients : {47,2}*188
   47-fold quotients : {4,4}*32
   94-fold quotients : {2,4}*16, {4,2}*16
   188-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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