Polytope of Type {194,4}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope