Polytope of Type {189,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {189,4}*1512
if this polytope has a name.
Group : SmallGroup(1512,85)
Rank : 3
Schlafli Type : {189,4}
Number of vertices, edges, etc : 189, 378, 4
Order of s₀s₁s₂ : 189
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) :
   3-fold quotients : {63,4}*504
   7-fold quotients : {27,4}*216
   9-fold quotients : {21,4}*168
   21-fold quotients : {9,4}*72
   63-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 13, 33)( 14, 34)( 15, 36)
( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)( 23, 28)
( 24, 27)( 37,217)( 38,218)( 39,220)( 40,219)( 41,225)( 42,226)( 43,228)
( 44,227)( 45,221)( 46,222)( 47,224)( 48,223)( 49,249)( 50,250)( 51,252)
( 52,251)( 53,245)( 54,246)( 55,248)( 56,247)( 57,241)( 58,242)( 59,244)
( 60,243)( 61,237)( 62,238)( 63,240)( 64,239)( 65,233)( 66,234)( 67,236)
( 68,235)( 69,229)( 70,230)( 71,232)( 72,231)( 73,181)( 74,182)( 75,184)
( 76,183)( 77,189)( 78,190)( 79,192)( 80,191)( 81,185)( 82,186)( 83,188)
( 84,187)( 85,213)( 86,214)( 87,216)( 88,215)( 89,209)( 90,210)( 91,212)
( 92,211)( 93,205)( 94,206)( 95,208)( 96,207)( 97,201)( 98,202)( 99,204)
(100,203)(101,197)(102,198)(103,200)(104,199)(105,193)(106,194)(107,196)
(108,195)(109,145)(110,146)(111,148)(112,147)(113,153)(114,154)(115,156)
(116,155)(117,149)(118,150)(119,152)(120,151)(121,177)(122,178)(123,180)
(124,179)(125,173)(126,174)(127,176)(128,175)(129,169)(130,170)(131,172)
(132,171)(133,165)(134,166)(135,168)(136,167)(137,161)(138,162)(139,164)
(140,163)(141,157)(142,158)(143,160)(144,159)(253,537)(254,538)(255,540)
(256,539)(257,533)(258,534)(259,536)(260,535)(261,529)(262,530)(263,532)
(264,531)(265,525)(266,526)(267,528)(268,527)(269,521)(270,522)(271,524)
(272,523)(273,517)(274,518)(275,520)(276,519)(277,513)(278,514)(279,516)
(280,515)(281,509)(282,510)(283,512)(284,511)(285,505)(286,506)(287,508)
(288,507)(289,753)(290,754)(291,756)(292,755)(293,749)(294,750)(295,752)
(296,751)(297,745)(298,746)(299,748)(300,747)(301,741)(302,742)(303,744)
(304,743)(305,737)(306,738)(307,740)(308,739)(309,733)(310,734)(311,736)
(312,735)(313,729)(314,730)(315,732)(316,731)(317,725)(318,726)(319,728)
(320,727)(321,721)(322,722)(323,724)(324,723)(325,717)(326,718)(327,720)
(328,719)(329,713)(330,714)(331,716)(332,715)(333,709)(334,710)(335,712)
(336,711)(337,705)(338,706)(339,708)(340,707)(341,701)(342,702)(343,704)
(344,703)(345,697)(346,698)(347,700)(348,699)(349,693)(350,694)(351,696)
(352,695)(353,689)(354,690)(355,692)(356,691)(357,685)(358,686)(359,688)
(360,687)(361,681)(362,682)(363,684)(364,683)(365,677)(366,678)(367,680)
(368,679)(369,673)(370,674)(371,676)(372,675)(373,669)(374,670)(375,672)
(376,671)(377,665)(378,666)(379,668)(380,667)(381,661)(382,662)(383,664)
(384,663)(385,657)(386,658)(387,660)(388,659)(389,653)(390,654)(391,656)
(392,655)(393,649)(394,650)(395,652)(396,651)(397,645)(398,646)(399,648)
(400,647)(401,641)(402,642)(403,644)(404,643)(405,637)(406,638)(407,640)
(408,639)(409,633)(410,634)(411,636)(412,635)(413,629)(414,630)(415,632)
(416,631)(417,625)(418,626)(419,628)(420,627)(421,621)(422,622)(423,624)
(424,623)(425,617)(426,618)(427,620)(428,619)(429,613)(430,614)(431,616)
(432,615)(433,609)(434,610)(435,612)(436,611)(437,605)(438,606)(439,608)
(440,607)(441,601)(442,602)(443,604)(444,603)(445,597)(446,598)(447,600)
(448,599)(449,593)(450,594)(451,596)(452,595)(453,589)(454,590)(455,592)
(456,591)(457,585)(458,586)(459,588)(460,587)(461,581)(462,582)(463,584)
(464,583)(465,577)(466,578)(467,580)(468,579)(469,573)(470,574)(471,576)
(472,575)(473,569)(474,570)(475,572)(476,571)(477,565)(478,566)(479,568)
(480,567)(481,561)(482,562)(483,564)(484,563)(485,557)(486,558)(487,560)
(488,559)(489,553)(490,554)(491,556)(492,555)(493,549)(494,550)(495,552)
(496,551)(497,545)(498,546)(499,548)(500,547)(501,541)(502,542)(503,544)
(504,543);;
s1 := (  1,289)(  2,292)(  3,291)(  4,290)(  5,297)(  6,300)(  7,299)(  8,298)
(  9,293)( 10,296)( 11,295)( 12,294)( 13,321)( 14,324)( 15,323)( 16,322)
( 17,317)( 18,320)( 19,319)( 20,318)( 21,313)( 22,316)( 23,315)( 24,314)
( 25,309)( 26,312)( 27,311)( 28,310)( 29,305)( 30,308)( 31,307)( 32,306)
( 33,301)( 34,304)( 35,303)( 36,302)( 37,253)( 38,256)( 39,255)( 40,254)
( 41,261)( 42,264)( 43,263)( 44,262)( 45,257)( 46,260)( 47,259)( 48,258)
( 49,285)( 50,288)( 51,287)( 52,286)( 53,281)( 54,284)( 55,283)( 56,282)
( 57,277)( 58,280)( 59,279)( 60,278)( 61,273)( 62,276)( 63,275)( 64,274)
( 65,269)( 66,272)( 67,271)( 68,270)( 69,265)( 70,268)( 71,267)( 72,266)
( 73,469)( 74,472)( 75,471)( 76,470)( 77,477)( 78,480)( 79,479)( 80,478)
( 81,473)( 82,476)( 83,475)( 84,474)( 85,501)( 86,504)( 87,503)( 88,502)
( 89,497)( 90,500)( 91,499)( 92,498)( 93,493)( 94,496)( 95,495)( 96,494)
( 97,489)( 98,492)( 99,491)(100,490)(101,485)(102,488)(103,487)(104,486)
(105,481)(106,484)(107,483)(108,482)(109,433)(110,436)(111,435)(112,434)
(113,441)(114,444)(115,443)(116,442)(117,437)(118,440)(119,439)(120,438)
(121,465)(122,468)(123,467)(124,466)(125,461)(126,464)(127,463)(128,462)
(129,457)(130,460)(131,459)(132,458)(133,453)(134,456)(135,455)(136,454)
(137,449)(138,452)(139,451)(140,450)(141,445)(142,448)(143,447)(144,446)
(145,397)(146,400)(147,399)(148,398)(149,405)(150,408)(151,407)(152,406)
(153,401)(154,404)(155,403)(156,402)(157,429)(158,432)(159,431)(160,430)
(161,425)(162,428)(163,427)(164,426)(165,421)(166,424)(167,423)(168,422)
(169,417)(170,420)(171,419)(172,418)(173,413)(174,416)(175,415)(176,414)
(177,409)(178,412)(179,411)(180,410)(181,361)(182,364)(183,363)(184,362)
(185,369)(186,372)(187,371)(188,370)(189,365)(190,368)(191,367)(192,366)
(193,393)(194,396)(195,395)(196,394)(197,389)(198,392)(199,391)(200,390)
(201,385)(202,388)(203,387)(204,386)(205,381)(206,384)(207,383)(208,382)
(209,377)(210,380)(211,379)(212,378)(213,373)(214,376)(215,375)(216,374)
(217,325)(218,328)(219,327)(220,326)(221,333)(222,336)(223,335)(224,334)
(225,329)(226,332)(227,331)(228,330)(229,357)(230,360)(231,359)(232,358)
(233,353)(234,356)(235,355)(236,354)(237,349)(238,352)(239,351)(240,350)
(241,345)(242,348)(243,347)(244,346)(245,341)(246,344)(247,343)(248,342)
(249,337)(250,340)(251,339)(252,338)(505,573)(506,576)(507,575)(508,574)
(509,569)(510,572)(511,571)(512,570)(513,565)(514,568)(515,567)(516,566)
(517,561)(518,564)(519,563)(520,562)(521,557)(522,560)(523,559)(524,558)
(525,553)(526,556)(527,555)(528,554)(529,549)(530,552)(531,551)(532,550)
(533,545)(534,548)(535,547)(536,546)(537,541)(538,544)(539,543)(540,542)
(577,753)(578,756)(579,755)(580,754)(581,749)(582,752)(583,751)(584,750)
(585,745)(586,748)(587,747)(588,746)(589,741)(590,744)(591,743)(592,742)
(593,737)(594,740)(595,739)(596,738)(597,733)(598,736)(599,735)(600,734)
(601,729)(602,732)(603,731)(604,730)(605,725)(606,728)(607,727)(608,726)
(609,721)(610,724)(611,723)(612,722)(613,717)(614,720)(615,719)(616,718)
(617,713)(618,716)(619,715)(620,714)(621,709)(622,712)(623,711)(624,710)
(625,705)(626,708)(627,707)(628,706)(629,701)(630,704)(631,703)(632,702)
(633,697)(634,700)(635,699)(636,698)(637,693)(638,696)(639,695)(640,694)
(641,689)(642,692)(643,691)(644,690)(645,685)(646,688)(647,687)(648,686)
(649,681)(650,684)(651,683)(652,682)(653,677)(654,680)(655,679)(656,678)
(657,673)(658,676)(659,675)(660,674)(661,669)(662,672)(663,671)(664,670)
(666,668);;
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)(745,746)(747,748)(749,750)(751,752)
(753,754)(755,756);;
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*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(756)!(  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 13, 33)( 14, 34)
( 15, 36)( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)
( 23, 28)( 24, 27)( 37,217)( 38,218)( 39,220)( 40,219)( 41,225)( 42,226)
( 43,228)( 44,227)( 45,221)( 46,222)( 47,224)( 48,223)( 49,249)( 50,250)
( 51,252)( 52,251)( 53,245)( 54,246)( 55,248)( 56,247)( 57,241)( 58,242)
( 59,244)( 60,243)( 61,237)( 62,238)( 63,240)( 64,239)( 65,233)( 66,234)
( 67,236)( 68,235)( 69,229)( 70,230)( 71,232)( 72,231)( 73,181)( 74,182)
( 75,184)( 76,183)( 77,189)( 78,190)( 79,192)( 80,191)( 81,185)( 82,186)
( 83,188)( 84,187)( 85,213)( 86,214)( 87,216)( 88,215)( 89,209)( 90,210)
( 91,212)( 92,211)( 93,205)( 94,206)( 95,208)( 96,207)( 97,201)( 98,202)
( 99,204)(100,203)(101,197)(102,198)(103,200)(104,199)(105,193)(106,194)
(107,196)(108,195)(109,145)(110,146)(111,148)(112,147)(113,153)(114,154)
(115,156)(116,155)(117,149)(118,150)(119,152)(120,151)(121,177)(122,178)
(123,180)(124,179)(125,173)(126,174)(127,176)(128,175)(129,169)(130,170)
(131,172)(132,171)(133,165)(134,166)(135,168)(136,167)(137,161)(138,162)
(139,164)(140,163)(141,157)(142,158)(143,160)(144,159)(253,537)(254,538)
(255,540)(256,539)(257,533)(258,534)(259,536)(260,535)(261,529)(262,530)
(263,532)(264,531)(265,525)(266,526)(267,528)(268,527)(269,521)(270,522)
(271,524)(272,523)(273,517)(274,518)(275,520)(276,519)(277,513)(278,514)
(279,516)(280,515)(281,509)(282,510)(283,512)(284,511)(285,505)(286,506)
(287,508)(288,507)(289,753)(290,754)(291,756)(292,755)(293,749)(294,750)
(295,752)(296,751)(297,745)(298,746)(299,748)(300,747)(301,741)(302,742)
(303,744)(304,743)(305,737)(306,738)(307,740)(308,739)(309,733)(310,734)
(311,736)(312,735)(313,729)(314,730)(315,732)(316,731)(317,725)(318,726)
(319,728)(320,727)(321,721)(322,722)(323,724)(324,723)(325,717)(326,718)
(327,720)(328,719)(329,713)(330,714)(331,716)(332,715)(333,709)(334,710)
(335,712)(336,711)(337,705)(338,706)(339,708)(340,707)(341,701)(342,702)
(343,704)(344,703)(345,697)(346,698)(347,700)(348,699)(349,693)(350,694)
(351,696)(352,695)(353,689)(354,690)(355,692)(356,691)(357,685)(358,686)
(359,688)(360,687)(361,681)(362,682)(363,684)(364,683)(365,677)(366,678)
(367,680)(368,679)(369,673)(370,674)(371,676)(372,675)(373,669)(374,670)
(375,672)(376,671)(377,665)(378,666)(379,668)(380,667)(381,661)(382,662)
(383,664)(384,663)(385,657)(386,658)(387,660)(388,659)(389,653)(390,654)
(391,656)(392,655)(393,649)(394,650)(395,652)(396,651)(397,645)(398,646)
(399,648)(400,647)(401,641)(402,642)(403,644)(404,643)(405,637)(406,638)
(407,640)(408,639)(409,633)(410,634)(411,636)(412,635)(413,629)(414,630)
(415,632)(416,631)(417,625)(418,626)(419,628)(420,627)(421,621)(422,622)
(423,624)(424,623)(425,617)(426,618)(427,620)(428,619)(429,613)(430,614)
(431,616)(432,615)(433,609)(434,610)(435,612)(436,611)(437,605)(438,606)
(439,608)(440,607)(441,601)(442,602)(443,604)(444,603)(445,597)(446,598)
(447,600)(448,599)(449,593)(450,594)(451,596)(452,595)(453,589)(454,590)
(455,592)(456,591)(457,585)(458,586)(459,588)(460,587)(461,581)(462,582)
(463,584)(464,583)(465,577)(466,578)(467,580)(468,579)(469,573)(470,574)
(471,576)(472,575)(473,569)(474,570)(475,572)(476,571)(477,565)(478,566)
(479,568)(480,567)(481,561)(482,562)(483,564)(484,563)(485,557)(486,558)
(487,560)(488,559)(489,553)(490,554)(491,556)(492,555)(493,549)(494,550)
(495,552)(496,551)(497,545)(498,546)(499,548)(500,547)(501,541)(502,542)
(503,544)(504,543);
s1 := Sym(756)!(  1,289)(  2,292)(  3,291)(  4,290)(  5,297)(  6,300)(  7,299)
(  8,298)(  9,293)( 10,296)( 11,295)( 12,294)( 13,321)( 14,324)( 15,323)
( 16,322)( 17,317)( 18,320)( 19,319)( 20,318)( 21,313)( 22,316)( 23,315)
( 24,314)( 25,309)( 26,312)( 27,311)( 28,310)( 29,305)( 30,308)( 31,307)
( 32,306)( 33,301)( 34,304)( 35,303)( 36,302)( 37,253)( 38,256)( 39,255)
( 40,254)( 41,261)( 42,264)( 43,263)( 44,262)( 45,257)( 46,260)( 47,259)
( 48,258)( 49,285)( 50,288)( 51,287)( 52,286)( 53,281)( 54,284)( 55,283)
( 56,282)( 57,277)( 58,280)( 59,279)( 60,278)( 61,273)( 62,276)( 63,275)
( 64,274)( 65,269)( 66,272)( 67,271)( 68,270)( 69,265)( 70,268)( 71,267)
( 72,266)( 73,469)( 74,472)( 75,471)( 76,470)( 77,477)( 78,480)( 79,479)
( 80,478)( 81,473)( 82,476)( 83,475)( 84,474)( 85,501)( 86,504)( 87,503)
( 88,502)( 89,497)( 90,500)( 91,499)( 92,498)( 93,493)( 94,496)( 95,495)
( 96,494)( 97,489)( 98,492)( 99,491)(100,490)(101,485)(102,488)(103,487)
(104,486)(105,481)(106,484)(107,483)(108,482)(109,433)(110,436)(111,435)
(112,434)(113,441)(114,444)(115,443)(116,442)(117,437)(118,440)(119,439)
(120,438)(121,465)(122,468)(123,467)(124,466)(125,461)(126,464)(127,463)
(128,462)(129,457)(130,460)(131,459)(132,458)(133,453)(134,456)(135,455)
(136,454)(137,449)(138,452)(139,451)(140,450)(141,445)(142,448)(143,447)
(144,446)(145,397)(146,400)(147,399)(148,398)(149,405)(150,408)(151,407)
(152,406)(153,401)(154,404)(155,403)(156,402)(157,429)(158,432)(159,431)
(160,430)(161,425)(162,428)(163,427)(164,426)(165,421)(166,424)(167,423)
(168,422)(169,417)(170,420)(171,419)(172,418)(173,413)(174,416)(175,415)
(176,414)(177,409)(178,412)(179,411)(180,410)(181,361)(182,364)(183,363)
(184,362)(185,369)(186,372)(187,371)(188,370)(189,365)(190,368)(191,367)
(192,366)(193,393)(194,396)(195,395)(196,394)(197,389)(198,392)(199,391)
(200,390)(201,385)(202,388)(203,387)(204,386)(205,381)(206,384)(207,383)
(208,382)(209,377)(210,380)(211,379)(212,378)(213,373)(214,376)(215,375)
(216,374)(217,325)(218,328)(219,327)(220,326)(221,333)(222,336)(223,335)
(224,334)(225,329)(226,332)(227,331)(228,330)(229,357)(230,360)(231,359)
(232,358)(233,353)(234,356)(235,355)(236,354)(237,349)(238,352)(239,351)
(240,350)(241,345)(242,348)(243,347)(244,346)(245,341)(246,344)(247,343)
(248,342)(249,337)(250,340)(251,339)(252,338)(505,573)(506,576)(507,575)
(508,574)(509,569)(510,572)(511,571)(512,570)(513,565)(514,568)(515,567)
(516,566)(517,561)(518,564)(519,563)(520,562)(521,557)(522,560)(523,559)
(524,558)(525,553)(526,556)(527,555)(528,554)(529,549)(530,552)(531,551)
(532,550)(533,545)(534,548)(535,547)(536,546)(537,541)(538,544)(539,543)
(540,542)(577,753)(578,756)(579,755)(580,754)(581,749)(582,752)(583,751)
(584,750)(585,745)(586,748)(587,747)(588,746)(589,741)(590,744)(591,743)
(592,742)(593,737)(594,740)(595,739)(596,738)(597,733)(598,736)(599,735)
(600,734)(601,729)(602,732)(603,731)(604,730)(605,725)(606,728)(607,727)
(608,726)(609,721)(610,724)(611,723)(612,722)(613,717)(614,720)(615,719)
(616,718)(617,713)(618,716)(619,715)(620,714)(621,709)(622,712)(623,711)
(624,710)(625,705)(626,708)(627,707)(628,706)(629,701)(630,704)(631,703)
(632,702)(633,697)(634,700)(635,699)(636,698)(637,693)(638,696)(639,695)
(640,694)(641,689)(642,692)(643,691)(644,690)(645,685)(646,688)(647,687)
(648,686)(649,681)(650,684)(651,683)(652,682)(653,677)(654,680)(655,679)
(656,678)(657,673)(658,676)(659,675)(660,674)(661,669)(662,672)(663,671)
(664,670)(666,668);
s2 := Sym(756)!(  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)(745,746)(747,748)(749,750)
(751,752)(753,754)(755,756);
poly := sub<Sym(756)|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*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope