Polytope of Type {4,172}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,172}*1376
Also Known As : {4,172|2}. if this polytope has another name.
Group : SmallGroup(1376,116)
Rank : 3
Schlafli Type : {4,172}
Number of vertices, edges, etc : 4, 344, 172
Order of s₀s₁s₂ : 172
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 : {2,172}*688, {4,86}*688
   4-fold quotients : {2,86}*344
   8-fold quotients : {2,43}*172
   43-fold quotients : {4,4}*32
   86-fold quotients : {2,4}*16, {4,2}*16
   172-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope