Polytope of Type {4,188}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,188}*1504
Also Known As : {4,188|2}. if this polytope has another name.
Group : SmallGroup(1504,116)
Rank : 3
Schlafli Type : {4,188}
Number of vertices, edges, etc : 4, 376, 188
Order of s₀s₁s₂ : 188
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,188}*752, {4,94}*752
   4-fold quotients : {2,94}*376
   8-fold quotients : {2,47}*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 := (  1,377)(  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);;
s1 := (  2, 47)(  3, 46)(  4, 45)(  5, 44)(  6, 43)(  7, 42)(  8, 41)(  9, 40)
( 10, 39)( 11, 38)( 12, 37)( 13, 36)( 14, 35)( 15, 34)( 16, 33)( 17, 32)
( 18, 31)( 19, 30)( 20, 29)( 21, 28)( 22, 27)( 23, 26)( 24, 25)( 49, 94)
( 50, 93)( 51, 92)( 52, 91)( 53, 90)( 54, 89)( 55, 88)( 56, 87)( 57, 86)
( 58, 85)( 59, 84)( 60, 83)( 61, 82)( 62, 81)( 63, 80)( 64, 79)( 65, 78)
( 66, 77)( 67, 76)( 68, 75)( 69, 74)( 70, 73)( 71, 72)( 96,141)( 97,140)
( 98,139)( 99,138)(100,137)(101,136)(102,135)(103,134)(104,133)(105,132)
(106,131)(107,130)(108,129)(109,128)(110,127)(111,126)(112,125)(113,124)
(114,123)(115,122)(116,121)(117,120)(118,119)(143,188)(144,187)(145,186)
(146,185)(147,184)(148,183)(149,182)(150,181)(151,180)(152,179)(153,178)
(154,177)(155,176)(156,175)(157,174)(158,173)(159,172)(160,171)(161,170)
(162,169)(163,168)(164,167)(165,166)(189,236)(190,282)(191,281)(192,280)
(193,279)(194,278)(195,277)(196,276)(197,275)(198,274)(199,273)(200,272)
(201,271)(202,270)(203,269)(204,268)(205,267)(206,266)(207,265)(208,264)
(209,263)(210,262)(211,261)(212,260)(213,259)(214,258)(215,257)(216,256)
(217,255)(218,254)(219,253)(220,252)(221,251)(222,250)(223,249)(224,248)
(225,247)(226,246)(227,245)(228,244)(229,243)(230,242)(231,241)(232,240)
(233,239)(234,238)(235,237)(283,330)(284,376)(285,375)(286,374)(287,373)
(288,372)(289,371)(290,370)(291,369)(292,368)(293,367)(294,366)(295,365)
(296,364)(297,363)(298,362)(299,361)(300,360)(301,359)(302,358)(303,357)
(304,356)(305,355)(306,354)(307,353)(308,352)(309,351)(310,350)(311,349)
(312,348)(313,347)(314,346)(315,345)(316,344)(317,343)(318,342)(319,341)
(320,340)(321,339)(322,338)(323,337)(324,336)(325,335)(326,334)(327,333)
(328,332)(329,331)(377,471)(378,517)(379,516)(380,515)(381,514)(382,513)
(383,512)(384,511)(385,510)(386,509)(387,508)(388,507)(389,506)(390,505)
(391,504)(392,503)(393,502)(394,501)(395,500)(396,499)(397,498)(398,497)
(399,496)(400,495)(401,494)(402,493)(403,492)(404,491)(405,490)(406,489)
(407,488)(408,487)(409,486)(410,485)(411,484)(412,483)(413,482)(414,481)
(415,480)(416,479)(417,478)(418,477)(419,476)(420,475)(421,474)(422,473)
(423,472)(424,518)(425,564)(426,563)(427,562)(428,561)(429,560)(430,559)
(431,558)(432,557)(433,556)(434,555)(435,554)(436,553)(437,552)(438,551)
(439,550)(440,549)(441,548)(442,547)(443,546)(444,545)(445,544)(446,543)
(447,542)(448,541)(449,540)(450,539)(451,538)(452,537)(453,536)(454,535)
(455,534)(456,533)(457,532)(458,531)(459,530)(460,529)(461,528)(462,527)
(463,526)(464,525)(465,524)(466,523)(467,522)(468,521)(469,520)(470,519)
(565,706)(566,752)(567,751)(568,750)(569,749)(570,748)(571,747)(572,746)
(573,745)(574,744)(575,743)(576,742)(577,741)(578,740)(579,739)(580,738)
(581,737)(582,736)(583,735)(584,734)(585,733)(586,732)(587,731)(588,730)
(589,729)(590,728)(591,727)(592,726)(593,725)(594,724)(595,723)(596,722)
(597,721)(598,720)(599,719)(600,718)(601,717)(602,716)(603,715)(604,714)
(605,713)(606,712)(607,711)(608,710)(609,709)(610,708)(611,707)(612,659)
(613,705)(614,704)(615,703)(616,702)(617,701)(618,700)(619,699)(620,698)
(621,697)(622,696)(623,695)(624,694)(625,693)(626,692)(627,691)(628,690)
(629,689)(630,688)(631,687)(632,686)(633,685)(634,684)(635,683)(636,682)
(637,681)(638,680)(639,679)(640,678)(641,677)(642,676)(643,675)(644,674)
(645,673)(646,672)(647,671)(648,670)(649,669)(650,668)(651,667)(652,666)
(653,665)(654,664)(655,663)(656,662)(657,661)(658,660);;
s2 := (  1,190)(  2,189)(  3,235)(  4,234)(  5,233)(  6,232)(  7,231)(  8,230)
(  9,229)( 10,228)( 11,227)( 12,226)( 13,225)( 14,224)( 15,223)( 16,222)
( 17,221)( 18,220)( 19,219)( 20,218)( 21,217)( 22,216)( 23,215)( 24,214)
( 25,213)( 26,212)( 27,211)( 28,210)( 29,209)( 30,208)( 31,207)( 32,206)
( 33,205)( 34,204)( 35,203)( 36,202)( 37,201)( 38,200)( 39,199)( 40,198)
( 41,197)( 42,196)( 43,195)( 44,194)( 45,193)( 46,192)( 47,191)( 48,237)
( 49,236)( 50,282)( 51,281)( 52,280)( 53,279)( 54,278)( 55,277)( 56,276)
( 57,275)( 58,274)( 59,273)( 60,272)( 61,271)( 62,270)( 63,269)( 64,268)
( 65,267)( 66,266)( 67,265)( 68,264)( 69,263)( 70,262)( 71,261)( 72,260)
( 73,259)( 74,258)( 75,257)( 76,256)( 77,255)( 78,254)( 79,253)( 80,252)
( 81,251)( 82,250)( 83,249)( 84,248)( 85,247)( 86,246)( 87,245)( 88,244)
( 89,243)( 90,242)( 91,241)( 92,240)( 93,239)( 94,238)( 95,284)( 96,283)
( 97,329)( 98,328)( 99,327)(100,326)(101,325)(102,324)(103,323)(104,322)
(105,321)(106,320)(107,319)(108,318)(109,317)(110,316)(111,315)(112,314)
(113,313)(114,312)(115,311)(116,310)(117,309)(118,308)(119,307)(120,306)
(121,305)(122,304)(123,303)(124,302)(125,301)(126,300)(127,299)(128,298)
(129,297)(130,296)(131,295)(132,294)(133,293)(134,292)(135,291)(136,290)
(137,289)(138,288)(139,287)(140,286)(141,285)(142,331)(143,330)(144,376)
(145,375)(146,374)(147,373)(148,372)(149,371)(150,370)(151,369)(152,368)
(153,367)(154,366)(155,365)(156,364)(157,363)(158,362)(159,361)(160,360)
(161,359)(162,358)(163,357)(164,356)(165,355)(166,354)(167,353)(168,352)
(169,351)(170,350)(171,349)(172,348)(173,347)(174,346)(175,345)(176,344)
(177,343)(178,342)(179,341)(180,340)(181,339)(182,338)(183,337)(184,336)
(185,335)(186,334)(187,333)(188,332)(377,566)(378,565)(379,611)(380,610)
(381,609)(382,608)(383,607)(384,606)(385,605)(386,604)(387,603)(388,602)
(389,601)(390,600)(391,599)(392,598)(393,597)(394,596)(395,595)(396,594)
(397,593)(398,592)(399,591)(400,590)(401,589)(402,588)(403,587)(404,586)
(405,585)(406,584)(407,583)(408,582)(409,581)(410,580)(411,579)(412,578)
(413,577)(414,576)(415,575)(416,574)(417,573)(418,572)(419,571)(420,570)
(421,569)(422,568)(423,567)(424,613)(425,612)(426,658)(427,657)(428,656)
(429,655)(430,654)(431,653)(432,652)(433,651)(434,650)(435,649)(436,648)
(437,647)(438,646)(439,645)(440,644)(441,643)(442,642)(443,641)(444,640)
(445,639)(446,638)(447,637)(448,636)(449,635)(450,634)(451,633)(452,632)
(453,631)(454,630)(455,629)(456,628)(457,627)(458,626)(459,625)(460,624)
(461,623)(462,622)(463,621)(464,620)(465,619)(466,618)(467,617)(468,616)
(469,615)(470,614)(471,660)(472,659)(473,705)(474,704)(475,703)(476,702)
(477,701)(478,700)(479,699)(480,698)(481,697)(482,696)(483,695)(484,694)
(485,693)(486,692)(487,691)(488,690)(489,689)(490,688)(491,687)(492,686)
(493,685)(494,684)(495,683)(496,682)(497,681)(498,680)(499,679)(500,678)
(501,677)(502,676)(503,675)(504,674)(505,673)(506,672)(507,671)(508,670)
(509,669)(510,668)(511,667)(512,666)(513,665)(514,664)(515,663)(516,662)
(517,661)(518,707)(519,706)(520,752)(521,751)(522,750)(523,749)(524,748)
(525,747)(526,746)(527,745)(528,744)(529,743)(530,742)(531,741)(532,740)
(533,739)(534,738)(535,737)(536,736)(537,735)(538,734)(539,733)(540,732)
(541,731)(542,730)(543,729)(544,728)(545,727)(546,726)(547,725)(548,724)
(549,723)(550,722)(551,721)(552,720)(553,719)(554,718)(555,717)(556,716)
(557,715)(558,714)(559,713)(560,712)(561,711)(562,710)(563,709)(564,708);;
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*s0*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*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*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope