Polytope of Type {4,194}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,194}*1552
Also Known As : {4,194|2}. if this polytope has another name.
Group : SmallGroup(1552,34)
Rank : 3
Schlafli Type : {4,194}
Number of vertices, edges, etc : 4, 388, 194
Order of s₀s₁s₂ : 388
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 : {2,194}*776
   4-fold quotients : {2,97}*388
   97-fold quotients : {4,2}*16
   194-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (389,486)(390,487)(391,488)(392,489)(393,490)(394,491)(395,492)(396,493)
(397,494)(398,495)(399,496)(400,497)(401,498)(402,499)(403,500)(404,501)
(405,502)(406,503)(407,504)(408,505)(409,506)(410,507)(411,508)(412,509)
(413,510)(414,511)(415,512)(416,513)(417,514)(418,515)(419,516)(420,517)
(421,518)(422,519)(423,520)(424,521)(425,522)(426,523)(427,524)(428,525)
(429,526)(430,527)(431,528)(432,529)(433,530)(434,531)(435,532)(436,533)
(437,534)(438,535)(439,536)(440,537)(441,538)(442,539)(443,540)(444,541)
(445,542)(446,543)(447,544)(448,545)(449,546)(450,547)(451,548)(452,549)
(453,550)(454,551)(455,552)(456,553)(457,554)(458,555)(459,556)(460,557)
(461,558)(462,559)(463,560)(464,561)(465,562)(466,563)(467,564)(468,565)
(469,566)(470,567)(471,568)(472,569)(473,570)(474,571)(475,572)(476,573)
(477,574)(478,575)(479,576)(480,577)(481,578)(482,579)(483,580)(484,581)
(485,582)(583,680)(584,681)(585,682)(586,683)(587,684)(588,685)(589,686)
(590,687)(591,688)(592,689)(593,690)(594,691)(595,692)(596,693)(597,694)
(598,695)(599,696)(600,697)(601,698)(602,699)(603,700)(604,701)(605,702)
(606,703)(607,704)(608,705)(609,706)(610,707)(611,708)(612,709)(613,710)
(614,711)(615,712)(616,713)(617,714)(618,715)(619,716)(620,717)(621,718)
(622,719)(623,720)(624,721)(625,722)(626,723)(627,724)(628,725)(629,726)
(630,727)(631,728)(632,729)(633,730)(634,731)(635,732)(636,733)(637,734)
(638,735)(639,736)(640,737)(641,738)(642,739)(643,740)(644,741)(645,742)
(646,743)(647,744)(648,745)(649,746)(650,747)(651,748)(652,749)(653,750)
(654,751)(655,752)(656,753)(657,754)(658,755)(659,756)(660,757)(661,758)
(662,759)(663,760)(664,761)(665,762)(666,763)(667,764)(668,765)(669,766)
(670,767)(671,768)(672,769)(673,770)(674,771)(675,772)(676,773)(677,774)
(678,775)(679,776);;
s1 := (  1,583)(  2,679)(  3,678)(  4,677)(  5,676)(  6,675)(  7,674)(  8,673)
(  9,672)( 10,671)( 11,670)( 12,669)( 13,668)( 14,667)( 15,666)( 16,665)
( 17,664)( 18,663)( 19,662)( 20,661)( 21,660)( 22,659)( 23,658)( 24,657)
( 25,656)( 26,655)( 27,654)( 28,653)( 29,652)( 30,651)( 31,650)( 32,649)
( 33,648)( 34,647)( 35,646)( 36,645)( 37,644)( 38,643)( 39,642)( 40,641)
( 41,640)( 42,639)( 43,638)( 44,637)( 45,636)( 46,635)( 47,634)( 48,633)
( 49,632)( 50,631)( 51,630)( 52,629)( 53,628)( 54,627)( 55,626)( 56,625)
( 57,624)( 58,623)( 59,622)( 60,621)( 61,620)( 62,619)( 63,618)( 64,617)
( 65,616)( 66,615)( 67,614)( 68,613)( 69,612)( 70,611)( 71,610)( 72,609)
( 73,608)( 74,607)( 75,606)( 76,605)( 77,604)( 78,603)( 79,602)( 80,601)
( 81,600)( 82,599)( 83,598)( 84,597)( 85,596)( 86,595)( 87,594)( 88,593)
( 89,592)( 90,591)( 91,590)( 92,589)( 93,588)( 94,587)( 95,586)( 96,585)
( 97,584)( 98,680)( 99,776)(100,775)(101,774)(102,773)(103,772)(104,771)
(105,770)(106,769)(107,768)(108,767)(109,766)(110,765)(111,764)(112,763)
(113,762)(114,761)(115,760)(116,759)(117,758)(118,757)(119,756)(120,755)
(121,754)(122,753)(123,752)(124,751)(125,750)(126,749)(127,748)(128,747)
(129,746)(130,745)(131,744)(132,743)(133,742)(134,741)(135,740)(136,739)
(137,738)(138,737)(139,736)(140,735)(141,734)(142,733)(143,732)(144,731)
(145,730)(146,729)(147,728)(148,727)(149,726)(150,725)(151,724)(152,723)
(153,722)(154,721)(155,720)(156,719)(157,718)(158,717)(159,716)(160,715)
(161,714)(162,713)(163,712)(164,711)(165,710)(166,709)(167,708)(168,707)
(169,706)(170,705)(171,704)(172,703)(173,702)(174,701)(175,700)(176,699)
(177,698)(178,697)(179,696)(180,695)(181,694)(182,693)(183,692)(184,691)
(185,690)(186,689)(187,688)(188,687)(189,686)(190,685)(191,684)(192,683)
(193,682)(194,681)(195,389)(196,485)(197,484)(198,483)(199,482)(200,481)
(201,480)(202,479)(203,478)(204,477)(205,476)(206,475)(207,474)(208,473)
(209,472)(210,471)(211,470)(212,469)(213,468)(214,467)(215,466)(216,465)
(217,464)(218,463)(219,462)(220,461)(221,460)(222,459)(223,458)(224,457)
(225,456)(226,455)(227,454)(228,453)(229,452)(230,451)(231,450)(232,449)
(233,448)(234,447)(235,446)(236,445)(237,444)(238,443)(239,442)(240,441)
(241,440)(242,439)(243,438)(244,437)(245,436)(246,435)(247,434)(248,433)
(249,432)(250,431)(251,430)(252,429)(253,428)(254,427)(255,426)(256,425)
(257,424)(258,423)(259,422)(260,421)(261,420)(262,419)(263,418)(264,417)
(265,416)(266,415)(267,414)(268,413)(269,412)(270,411)(271,410)(272,409)
(273,408)(274,407)(275,406)(276,405)(277,404)(278,403)(279,402)(280,401)
(281,400)(282,399)(283,398)(284,397)(285,396)(286,395)(287,394)(288,393)
(289,392)(290,391)(291,390)(292,486)(293,582)(294,581)(295,580)(296,579)
(297,578)(298,577)(299,576)(300,575)(301,574)(302,573)(303,572)(304,571)
(305,570)(306,569)(307,568)(308,567)(309,566)(310,565)(311,564)(312,563)
(313,562)(314,561)(315,560)(316,559)(317,558)(318,557)(319,556)(320,555)
(321,554)(322,553)(323,552)(324,551)(325,550)(326,549)(327,548)(328,547)
(329,546)(330,545)(331,544)(332,543)(333,542)(334,541)(335,540)(336,539)
(337,538)(338,537)(339,536)(340,535)(341,534)(342,533)(343,532)(344,531)
(345,530)(346,529)(347,528)(348,527)(349,526)(350,525)(351,524)(352,523)
(353,522)(354,521)(355,520)(356,519)(357,518)(358,517)(359,516)(360,515)
(361,514)(362,513)(363,512)(364,511)(365,510)(366,509)(367,508)(368,507)
(369,506)(370,505)(371,504)(372,503)(373,502)(374,501)(375,500)(376,499)
(377,498)(378,497)(379,496)(380,495)(381,494)(382,493)(383,492)(384,491)
(385,490)(386,489)(387,488)(388,487);;
s2 := (  1,196)(  2,195)(  3,291)(  4,290)(  5,289)(  6,288)(  7,287)(  8,286)
(  9,285)( 10,284)( 11,283)( 12,282)( 13,281)( 14,280)( 15,279)( 16,278)
( 17,277)( 18,276)( 19,275)( 20,274)( 21,273)( 22,272)( 23,271)( 24,270)
( 25,269)( 26,268)( 27,267)( 28,266)( 29,265)( 30,264)( 31,263)( 32,262)
( 33,261)( 34,260)( 35,259)( 36,258)( 37,257)( 38,256)( 39,255)( 40,254)
( 41,253)( 42,252)( 43,251)( 44,250)( 45,249)( 46,248)( 47,247)( 48,246)
( 49,245)( 50,244)( 51,243)( 52,242)( 53,241)( 54,240)( 55,239)( 56,238)
( 57,237)( 58,236)( 59,235)( 60,234)( 61,233)( 62,232)( 63,231)( 64,230)
( 65,229)( 66,228)( 67,227)( 68,226)( 69,225)( 70,224)( 71,223)( 72,222)
( 73,221)( 74,220)( 75,219)( 76,218)( 77,217)( 78,216)( 79,215)( 80,214)
( 81,213)( 82,212)( 83,211)( 84,210)( 85,209)( 86,208)( 87,207)( 88,206)
( 89,205)( 90,204)( 91,203)( 92,202)( 93,201)( 94,200)( 95,199)( 96,198)
( 97,197)( 98,293)( 99,292)(100,388)(101,387)(102,386)(103,385)(104,384)
(105,383)(106,382)(107,381)(108,380)(109,379)(110,378)(111,377)(112,376)
(113,375)(114,374)(115,373)(116,372)(117,371)(118,370)(119,369)(120,368)
(121,367)(122,366)(123,365)(124,364)(125,363)(126,362)(127,361)(128,360)
(129,359)(130,358)(131,357)(132,356)(133,355)(134,354)(135,353)(136,352)
(137,351)(138,350)(139,349)(140,348)(141,347)(142,346)(143,345)(144,344)
(145,343)(146,342)(147,341)(148,340)(149,339)(150,338)(151,337)(152,336)
(153,335)(154,334)(155,333)(156,332)(157,331)(158,330)(159,329)(160,328)
(161,327)(162,326)(163,325)(164,324)(165,323)(166,322)(167,321)(168,320)
(169,319)(170,318)(171,317)(172,316)(173,315)(174,314)(175,313)(176,312)
(177,311)(178,310)(179,309)(180,308)(181,307)(182,306)(183,305)(184,304)
(185,303)(186,302)(187,301)(188,300)(189,299)(190,298)(191,297)(192,296)
(193,295)(194,294)(389,584)(390,583)(391,679)(392,678)(393,677)(394,676)
(395,675)(396,674)(397,673)(398,672)(399,671)(400,670)(401,669)(402,668)
(403,667)(404,666)(405,665)(406,664)(407,663)(408,662)(409,661)(410,660)
(411,659)(412,658)(413,657)(414,656)(415,655)(416,654)(417,653)(418,652)
(419,651)(420,650)(421,649)(422,648)(423,647)(424,646)(425,645)(426,644)
(427,643)(428,642)(429,641)(430,640)(431,639)(432,638)(433,637)(434,636)
(435,635)(436,634)(437,633)(438,632)(439,631)(440,630)(441,629)(442,628)
(443,627)(444,626)(445,625)(446,624)(447,623)(448,622)(449,621)(450,620)
(451,619)(452,618)(453,617)(454,616)(455,615)(456,614)(457,613)(458,612)
(459,611)(460,610)(461,609)(462,608)(463,607)(464,606)(465,605)(466,604)
(467,603)(468,602)(469,601)(470,600)(471,599)(472,598)(473,597)(474,596)
(475,595)(476,594)(477,593)(478,592)(479,591)(480,590)(481,589)(482,588)
(483,587)(484,586)(485,585)(486,681)(487,680)(488,776)(489,775)(490,774)
(491,773)(492,772)(493,771)(494,770)(495,769)(496,768)(497,767)(498,766)
(499,765)(500,764)(501,763)(502,762)(503,761)(504,760)(505,759)(506,758)
(507,757)(508,756)(509,755)(510,754)(511,753)(512,752)(513,751)(514,750)
(515,749)(516,748)(517,747)(518,746)(519,745)(520,744)(521,743)(522,742)
(523,741)(524,740)(525,739)(526,738)(527,737)(528,736)(529,735)(530,734)
(531,733)(532,732)(533,731)(534,730)(535,729)(536,728)(537,727)(538,726)
(539,725)(540,724)(541,723)(542,722)(543,721)(544,720)(545,719)(546,718)
(547,717)(548,716)(549,715)(550,714)(551,713)(552,712)(553,711)(554,710)
(555,709)(556,708)(557,707)(558,706)(559,705)(560,704)(561,703)(562,702)
(563,701)(564,700)(565,699)(566,698)(567,697)(568,696)(569,695)(570,694)
(571,693)(572,692)(573,691)(574,690)(575,689)(576,688)(577,687)(578,686)
(579,685)(580,684)(581,683)(582,682);;
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(776)!(389,486)(390,487)(391,488)(392,489)(393,490)(394,491)(395,492)
(396,493)(397,494)(398,495)(399,496)(400,497)(401,498)(402,499)(403,500)
(404,501)(405,502)(406,503)(407,504)(408,505)(409,506)(410,507)(411,508)
(412,509)(413,510)(414,511)(415,512)(416,513)(417,514)(418,515)(419,516)
(420,517)(421,518)(422,519)(423,520)(424,521)(425,522)(426,523)(427,524)
(428,525)(429,526)(430,527)(431,528)(432,529)(433,530)(434,531)(435,532)
(436,533)(437,534)(438,535)(439,536)(440,537)(441,538)(442,539)(443,540)
(444,541)(445,542)(446,543)(447,544)(448,545)(449,546)(450,547)(451,548)
(452,549)(453,550)(454,551)(455,552)(456,553)(457,554)(458,555)(459,556)
(460,557)(461,558)(462,559)(463,560)(464,561)(465,562)(466,563)(467,564)
(468,565)(469,566)(470,567)(471,568)(472,569)(473,570)(474,571)(475,572)
(476,573)(477,574)(478,575)(479,576)(480,577)(481,578)(482,579)(483,580)
(484,581)(485,582)(583,680)(584,681)(585,682)(586,683)(587,684)(588,685)
(589,686)(590,687)(591,688)(592,689)(593,690)(594,691)(595,692)(596,693)
(597,694)(598,695)(599,696)(600,697)(601,698)(602,699)(603,700)(604,701)
(605,702)(606,703)(607,704)(608,705)(609,706)(610,707)(611,708)(612,709)
(613,710)(614,711)(615,712)(616,713)(617,714)(618,715)(619,716)(620,717)
(621,718)(622,719)(623,720)(624,721)(625,722)(626,723)(627,724)(628,725)
(629,726)(630,727)(631,728)(632,729)(633,730)(634,731)(635,732)(636,733)
(637,734)(638,735)(639,736)(640,737)(641,738)(642,739)(643,740)(644,741)
(645,742)(646,743)(647,744)(648,745)(649,746)(650,747)(651,748)(652,749)
(653,750)(654,751)(655,752)(656,753)(657,754)(658,755)(659,756)(660,757)
(661,758)(662,759)(663,760)(664,761)(665,762)(666,763)(667,764)(668,765)
(669,766)(670,767)(671,768)(672,769)(673,770)(674,771)(675,772)(676,773)
(677,774)(678,775)(679,776);
s1 := Sym(776)!(  1,583)(  2,679)(  3,678)(  4,677)(  5,676)(  6,675)(  7,674)
(  8,673)(  9,672)( 10,671)( 11,670)( 12,669)( 13,668)( 14,667)( 15,666)
( 16,665)( 17,664)( 18,663)( 19,662)( 20,661)( 21,660)( 22,659)( 23,658)
( 24,657)( 25,656)( 26,655)( 27,654)( 28,653)( 29,652)( 30,651)( 31,650)
( 32,649)( 33,648)( 34,647)( 35,646)( 36,645)( 37,644)( 38,643)( 39,642)
( 40,641)( 41,640)( 42,639)( 43,638)( 44,637)( 45,636)( 46,635)( 47,634)
( 48,633)( 49,632)( 50,631)( 51,630)( 52,629)( 53,628)( 54,627)( 55,626)
( 56,625)( 57,624)( 58,623)( 59,622)( 60,621)( 61,620)( 62,619)( 63,618)
( 64,617)( 65,616)( 66,615)( 67,614)( 68,613)( 69,612)( 70,611)( 71,610)
( 72,609)( 73,608)( 74,607)( 75,606)( 76,605)( 77,604)( 78,603)( 79,602)
( 80,601)( 81,600)( 82,599)( 83,598)( 84,597)( 85,596)( 86,595)( 87,594)
( 88,593)( 89,592)( 90,591)( 91,590)( 92,589)( 93,588)( 94,587)( 95,586)
( 96,585)( 97,584)( 98,680)( 99,776)(100,775)(101,774)(102,773)(103,772)
(104,771)(105,770)(106,769)(107,768)(108,767)(109,766)(110,765)(111,764)
(112,763)(113,762)(114,761)(115,760)(116,759)(117,758)(118,757)(119,756)
(120,755)(121,754)(122,753)(123,752)(124,751)(125,750)(126,749)(127,748)
(128,747)(129,746)(130,745)(131,744)(132,743)(133,742)(134,741)(135,740)
(136,739)(137,738)(138,737)(139,736)(140,735)(141,734)(142,733)(143,732)
(144,731)(145,730)(146,729)(147,728)(148,727)(149,726)(150,725)(151,724)
(152,723)(153,722)(154,721)(155,720)(156,719)(157,718)(158,717)(159,716)
(160,715)(161,714)(162,713)(163,712)(164,711)(165,710)(166,709)(167,708)
(168,707)(169,706)(170,705)(171,704)(172,703)(173,702)(174,701)(175,700)
(176,699)(177,698)(178,697)(179,696)(180,695)(181,694)(182,693)(183,692)
(184,691)(185,690)(186,689)(187,688)(188,687)(189,686)(190,685)(191,684)
(192,683)(193,682)(194,681)(195,389)(196,485)(197,484)(198,483)(199,482)
(200,481)(201,480)(202,479)(203,478)(204,477)(205,476)(206,475)(207,474)
(208,473)(209,472)(210,471)(211,470)(212,469)(213,468)(214,467)(215,466)
(216,465)(217,464)(218,463)(219,462)(220,461)(221,460)(222,459)(223,458)
(224,457)(225,456)(226,455)(227,454)(228,453)(229,452)(230,451)(231,450)
(232,449)(233,448)(234,447)(235,446)(236,445)(237,444)(238,443)(239,442)
(240,441)(241,440)(242,439)(243,438)(244,437)(245,436)(246,435)(247,434)
(248,433)(249,432)(250,431)(251,430)(252,429)(253,428)(254,427)(255,426)
(256,425)(257,424)(258,423)(259,422)(260,421)(261,420)(262,419)(263,418)
(264,417)(265,416)(266,415)(267,414)(268,413)(269,412)(270,411)(271,410)
(272,409)(273,408)(274,407)(275,406)(276,405)(277,404)(278,403)(279,402)
(280,401)(281,400)(282,399)(283,398)(284,397)(285,396)(286,395)(287,394)
(288,393)(289,392)(290,391)(291,390)(292,486)(293,582)(294,581)(295,580)
(296,579)(297,578)(298,577)(299,576)(300,575)(301,574)(302,573)(303,572)
(304,571)(305,570)(306,569)(307,568)(308,567)(309,566)(310,565)(311,564)
(312,563)(313,562)(314,561)(315,560)(316,559)(317,558)(318,557)(319,556)
(320,555)(321,554)(322,553)(323,552)(324,551)(325,550)(326,549)(327,548)
(328,547)(329,546)(330,545)(331,544)(332,543)(333,542)(334,541)(335,540)
(336,539)(337,538)(338,537)(339,536)(340,535)(341,534)(342,533)(343,532)
(344,531)(345,530)(346,529)(347,528)(348,527)(349,526)(350,525)(351,524)
(352,523)(353,522)(354,521)(355,520)(356,519)(357,518)(358,517)(359,516)
(360,515)(361,514)(362,513)(363,512)(364,511)(365,510)(366,509)(367,508)
(368,507)(369,506)(370,505)(371,504)(372,503)(373,502)(374,501)(375,500)
(376,499)(377,498)(378,497)(379,496)(380,495)(381,494)(382,493)(383,492)
(384,491)(385,490)(386,489)(387,488)(388,487);
s2 := Sym(776)!(  1,196)(  2,195)(  3,291)(  4,290)(  5,289)(  6,288)(  7,287)
(  8,286)(  9,285)( 10,284)( 11,283)( 12,282)( 13,281)( 14,280)( 15,279)
( 16,278)( 17,277)( 18,276)( 19,275)( 20,274)( 21,273)( 22,272)( 23,271)
( 24,270)( 25,269)( 26,268)( 27,267)( 28,266)( 29,265)( 30,264)( 31,263)
( 32,262)( 33,261)( 34,260)( 35,259)( 36,258)( 37,257)( 38,256)( 39,255)
( 40,254)( 41,253)( 42,252)( 43,251)( 44,250)( 45,249)( 46,248)( 47,247)
( 48,246)( 49,245)( 50,244)( 51,243)( 52,242)( 53,241)( 54,240)( 55,239)
( 56,238)( 57,237)( 58,236)( 59,235)( 60,234)( 61,233)( 62,232)( 63,231)
( 64,230)( 65,229)( 66,228)( 67,227)( 68,226)( 69,225)( 70,224)( 71,223)
( 72,222)( 73,221)( 74,220)( 75,219)( 76,218)( 77,217)( 78,216)( 79,215)
( 80,214)( 81,213)( 82,212)( 83,211)( 84,210)( 85,209)( 86,208)( 87,207)
( 88,206)( 89,205)( 90,204)( 91,203)( 92,202)( 93,201)( 94,200)( 95,199)
( 96,198)( 97,197)( 98,293)( 99,292)(100,388)(101,387)(102,386)(103,385)
(104,384)(105,383)(106,382)(107,381)(108,380)(109,379)(110,378)(111,377)
(112,376)(113,375)(114,374)(115,373)(116,372)(117,371)(118,370)(119,369)
(120,368)(121,367)(122,366)(123,365)(124,364)(125,363)(126,362)(127,361)
(128,360)(129,359)(130,358)(131,357)(132,356)(133,355)(134,354)(135,353)
(136,352)(137,351)(138,350)(139,349)(140,348)(141,347)(142,346)(143,345)
(144,344)(145,343)(146,342)(147,341)(148,340)(149,339)(150,338)(151,337)
(152,336)(153,335)(154,334)(155,333)(156,332)(157,331)(158,330)(159,329)
(160,328)(161,327)(162,326)(163,325)(164,324)(165,323)(166,322)(167,321)
(168,320)(169,319)(170,318)(171,317)(172,316)(173,315)(174,314)(175,313)
(176,312)(177,311)(178,310)(179,309)(180,308)(181,307)(182,306)(183,305)
(184,304)(185,303)(186,302)(187,301)(188,300)(189,299)(190,298)(191,297)
(192,296)(193,295)(194,294)(389,584)(390,583)(391,679)(392,678)(393,677)
(394,676)(395,675)(396,674)(397,673)(398,672)(399,671)(400,670)(401,669)
(402,668)(403,667)(404,666)(405,665)(406,664)(407,663)(408,662)(409,661)
(410,660)(411,659)(412,658)(413,657)(414,656)(415,655)(416,654)(417,653)
(418,652)(419,651)(420,650)(421,649)(422,648)(423,647)(424,646)(425,645)
(426,644)(427,643)(428,642)(429,641)(430,640)(431,639)(432,638)(433,637)
(434,636)(435,635)(436,634)(437,633)(438,632)(439,631)(440,630)(441,629)
(442,628)(443,627)(444,626)(445,625)(446,624)(447,623)(448,622)(449,621)
(450,620)(451,619)(452,618)(453,617)(454,616)(455,615)(456,614)(457,613)
(458,612)(459,611)(460,610)(461,609)(462,608)(463,607)(464,606)(465,605)
(466,604)(467,603)(468,602)(469,601)(470,600)(471,599)(472,598)(473,597)
(474,596)(475,595)(476,594)(477,593)(478,592)(479,591)(480,590)(481,589)
(482,588)(483,587)(484,586)(485,585)(486,681)(487,680)(488,776)(489,775)
(490,774)(491,773)(492,772)(493,771)(494,770)(495,769)(496,768)(497,767)
(498,766)(499,765)(500,764)(501,763)(502,762)(503,761)(504,760)(505,759)
(506,758)(507,757)(508,756)(509,755)(510,754)(511,753)(512,752)(513,751)
(514,750)(515,749)(516,748)(517,747)(518,746)(519,745)(520,744)(521,743)
(522,742)(523,741)(524,740)(525,739)(526,738)(527,737)(528,736)(529,735)
(530,734)(531,733)(532,732)(533,731)(534,730)(535,729)(536,728)(537,727)
(538,726)(539,725)(540,724)(541,723)(542,722)(543,721)(544,720)(545,719)
(546,718)(547,717)(548,716)(549,715)(550,714)(551,713)(552,712)(553,711)
(554,710)(555,709)(556,708)(557,707)(558,706)(559,705)(560,704)(561,703)
(562,702)(563,701)(564,700)(565,699)(566,698)(567,697)(568,696)(569,695)
(570,694)(571,693)(572,692)(573,691)(574,690)(575,689)(576,688)(577,687)
(578,686)(579,685)(580,684)(581,683)(582,682);
poly := sub<Sym(776)|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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope