Polytope of Type {8,86}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,86}*1376
Also Known As : {8,86|2}. if this polytope has another name.
Group : SmallGroup(1376,155)
Rank : 3
Schlafli Type : {8,86}
Number of vertices, edges, etc : 8, 344, 86
Order of s₀s₁s₂ : 344
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 : {4,86}*688
   4-fold quotients : {2,86}*344
   8-fold quotients : {2,43}*172
   43-fold quotients : {8,2}*32
   86-fold quotients : {4,2}*16
   172-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope