Polytope of Type {4,87}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,87}*1392
if this polytope has a name.
Group : SmallGroup(1392,188)
Rank : 3
Schlafli Type : {4,87}
Number of vertices, edges, etc : 8, 348, 174
Order of s0s1s2 : 174
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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 : {4,87}*696
4-fold quotients : {2,87}*348
12-fold quotients : {2,29}*116
29-fold quotients : {4,3}*48
58-fold quotients : {4,3}*24
116-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,351)( 2,352)( 3,349)( 4,350)( 5,355)( 6,356)( 7,353)( 8,354)
( 9,359)( 10,360)( 11,357)( 12,358)( 13,363)( 14,364)( 15,361)( 16,362)
( 17,367)( 18,368)( 19,365)( 20,366)( 21,371)( 22,372)( 23,369)( 24,370)
( 25,375)( 26,376)( 27,373)( 28,374)( 29,379)( 30,380)( 31,377)( 32,378)
( 33,383)( 34,384)( 35,381)( 36,382)( 37,387)( 38,388)( 39,385)( 40,386)
( 41,391)( 42,392)( 43,389)( 44,390)( 45,395)( 46,396)( 47,393)( 48,394)
( 49,399)( 50,400)( 51,397)( 52,398)( 53,403)( 54,404)( 55,401)( 56,402)
( 57,407)( 58,408)( 59,405)( 60,406)( 61,411)( 62,412)( 63,409)( 64,410)
( 65,415)( 66,416)( 67,413)( 68,414)( 69,419)( 70,420)( 71,417)( 72,418)
( 73,423)( 74,424)( 75,421)( 76,422)( 77,427)( 78,428)( 79,425)( 80,426)
( 81,431)( 82,432)( 83,429)( 84,430)( 85,435)( 86,436)( 87,433)( 88,434)
( 89,439)( 90,440)( 91,437)( 92,438)( 93,443)( 94,444)( 95,441)( 96,442)
( 97,447)( 98,448)( 99,445)(100,446)(101,451)(102,452)(103,449)(104,450)
(105,455)(106,456)(107,453)(108,454)(109,459)(110,460)(111,457)(112,458)
(113,463)(114,464)(115,461)(116,462)(117,467)(118,468)(119,465)(120,466)
(121,471)(122,472)(123,469)(124,470)(125,475)(126,476)(127,473)(128,474)
(129,479)(130,480)(131,477)(132,478)(133,483)(134,484)(135,481)(136,482)
(137,487)(138,488)(139,485)(140,486)(141,491)(142,492)(143,489)(144,490)
(145,495)(146,496)(147,493)(148,494)(149,499)(150,500)(151,497)(152,498)
(153,503)(154,504)(155,501)(156,502)(157,507)(158,508)(159,505)(160,506)
(161,511)(162,512)(163,509)(164,510)(165,515)(166,516)(167,513)(168,514)
(169,519)(170,520)(171,517)(172,518)(173,523)(174,524)(175,521)(176,522)
(177,527)(178,528)(179,525)(180,526)(181,531)(182,532)(183,529)(184,530)
(185,535)(186,536)(187,533)(188,534)(189,539)(190,540)(191,537)(192,538)
(193,543)(194,544)(195,541)(196,542)(197,547)(198,548)(199,545)(200,546)
(201,551)(202,552)(203,549)(204,550)(205,555)(206,556)(207,553)(208,554)
(209,559)(210,560)(211,557)(212,558)(213,563)(214,564)(215,561)(216,562)
(217,567)(218,568)(219,565)(220,566)(221,571)(222,572)(223,569)(224,570)
(225,575)(226,576)(227,573)(228,574)(229,579)(230,580)(231,577)(232,578)
(233,583)(234,584)(235,581)(236,582)(237,587)(238,588)(239,585)(240,586)
(241,591)(242,592)(243,589)(244,590)(245,595)(246,596)(247,593)(248,594)
(249,599)(250,600)(251,597)(252,598)(253,603)(254,604)(255,601)(256,602)
(257,607)(258,608)(259,605)(260,606)(261,611)(262,612)(263,609)(264,610)
(265,615)(266,616)(267,613)(268,614)(269,619)(270,620)(271,617)(272,618)
(273,623)(274,624)(275,621)(276,622)(277,627)(278,628)(279,625)(280,626)
(281,631)(282,632)(283,629)(284,630)(285,635)(286,636)(287,633)(288,634)
(289,639)(290,640)(291,637)(292,638)(293,643)(294,644)(295,641)(296,642)
(297,647)(298,648)(299,645)(300,646)(301,651)(302,652)(303,649)(304,650)
(305,655)(306,656)(307,653)(308,654)(309,659)(310,660)(311,657)(312,658)
(313,663)(314,664)(315,661)(316,662)(317,667)(318,668)(319,665)(320,666)
(321,671)(322,672)(323,669)(324,670)(325,675)(326,676)(327,673)(328,674)
(329,679)(330,680)(331,677)(332,678)(333,683)(334,684)(335,681)(336,682)
(337,687)(338,688)(339,685)(340,686)(341,691)(342,692)(343,689)(344,690)
(345,695)(346,696)(347,693)(348,694);;
s1 := ( 3, 4)( 5,113)( 6,114)( 7,116)( 8,115)( 9,109)( 10,110)( 11,112)
( 12,111)( 13,105)( 14,106)( 15,108)( 16,107)( 17,101)( 18,102)( 19,104)
( 20,103)( 21, 97)( 22, 98)( 23,100)( 24, 99)( 25, 93)( 26, 94)( 27, 96)
( 28, 95)( 29, 89)( 30, 90)( 31, 92)( 32, 91)( 33, 85)( 34, 86)( 35, 88)
( 36, 87)( 37, 81)( 38, 82)( 39, 84)( 40, 83)( 41, 77)( 42, 78)( 43, 80)
( 44, 79)( 45, 73)( 46, 74)( 47, 76)( 48, 75)( 49, 69)( 50, 70)( 51, 72)
( 52, 71)( 53, 65)( 54, 66)( 55, 68)( 56, 67)( 57, 61)( 58, 62)( 59, 64)
( 60, 63)(117,233)(118,234)(119,236)(120,235)(121,345)(122,346)(123,348)
(124,347)(125,341)(126,342)(127,344)(128,343)(129,337)(130,338)(131,340)
(132,339)(133,333)(134,334)(135,336)(136,335)(137,329)(138,330)(139,332)
(140,331)(141,325)(142,326)(143,328)(144,327)(145,321)(146,322)(147,324)
(148,323)(149,317)(150,318)(151,320)(152,319)(153,313)(154,314)(155,316)
(156,315)(157,309)(158,310)(159,312)(160,311)(161,305)(162,306)(163,308)
(164,307)(165,301)(166,302)(167,304)(168,303)(169,297)(170,298)(171,300)
(172,299)(173,293)(174,294)(175,296)(176,295)(177,289)(178,290)(179,292)
(180,291)(181,285)(182,286)(183,288)(184,287)(185,281)(186,282)(187,284)
(188,283)(189,277)(190,278)(191,280)(192,279)(193,273)(194,274)(195,276)
(196,275)(197,269)(198,270)(199,272)(200,271)(201,265)(202,266)(203,268)
(204,267)(205,261)(206,262)(207,264)(208,263)(209,257)(210,258)(211,260)
(212,259)(213,253)(214,254)(215,256)(216,255)(217,249)(218,250)(219,252)
(220,251)(221,245)(222,246)(223,248)(224,247)(225,241)(226,242)(227,244)
(228,243)(229,237)(230,238)(231,240)(232,239)(351,352)(353,461)(354,462)
(355,464)(356,463)(357,457)(358,458)(359,460)(360,459)(361,453)(362,454)
(363,456)(364,455)(365,449)(366,450)(367,452)(368,451)(369,445)(370,446)
(371,448)(372,447)(373,441)(374,442)(375,444)(376,443)(377,437)(378,438)
(379,440)(380,439)(381,433)(382,434)(383,436)(384,435)(385,429)(386,430)
(387,432)(388,431)(389,425)(390,426)(391,428)(392,427)(393,421)(394,422)
(395,424)(396,423)(397,417)(398,418)(399,420)(400,419)(401,413)(402,414)
(403,416)(404,415)(405,409)(406,410)(407,412)(408,411)(465,581)(466,582)
(467,584)(468,583)(469,693)(470,694)(471,696)(472,695)(473,689)(474,690)
(475,692)(476,691)(477,685)(478,686)(479,688)(480,687)(481,681)(482,682)
(483,684)(484,683)(485,677)(486,678)(487,680)(488,679)(489,673)(490,674)
(491,676)(492,675)(493,669)(494,670)(495,672)(496,671)(497,665)(498,666)
(499,668)(500,667)(501,661)(502,662)(503,664)(504,663)(505,657)(506,658)
(507,660)(508,659)(509,653)(510,654)(511,656)(512,655)(513,649)(514,650)
(515,652)(516,651)(517,645)(518,646)(519,648)(520,647)(521,641)(522,642)
(523,644)(524,643)(525,637)(526,638)(527,640)(528,639)(529,633)(530,634)
(531,636)(532,635)(533,629)(534,630)(535,632)(536,631)(537,625)(538,626)
(539,628)(540,627)(541,621)(542,622)(543,624)(544,623)(545,617)(546,618)
(547,620)(548,619)(549,613)(550,614)(551,616)(552,615)(553,609)(554,610)
(555,612)(556,611)(557,605)(558,606)(559,608)(560,607)(561,601)(562,602)
(563,604)(564,603)(565,597)(566,598)(567,600)(568,599)(569,593)(570,594)
(571,596)(572,595)(573,589)(574,590)(575,592)(576,591)(577,585)(578,586)
(579,588)(580,587);;
s2 := ( 1,121)( 2,124)( 3,123)( 4,122)( 5,117)( 6,120)( 7,119)( 8,118)
( 9,229)( 10,232)( 11,231)( 12,230)( 13,225)( 14,228)( 15,227)( 16,226)
( 17,221)( 18,224)( 19,223)( 20,222)( 21,217)( 22,220)( 23,219)( 24,218)
( 25,213)( 26,216)( 27,215)( 28,214)( 29,209)( 30,212)( 31,211)( 32,210)
( 33,205)( 34,208)( 35,207)( 36,206)( 37,201)( 38,204)( 39,203)( 40,202)
( 41,197)( 42,200)( 43,199)( 44,198)( 45,193)( 46,196)( 47,195)( 48,194)
( 49,189)( 50,192)( 51,191)( 52,190)( 53,185)( 54,188)( 55,187)( 56,186)
( 57,181)( 58,184)( 59,183)( 60,182)( 61,177)( 62,180)( 63,179)( 64,178)
( 65,173)( 66,176)( 67,175)( 68,174)( 69,169)( 70,172)( 71,171)( 72,170)
( 73,165)( 74,168)( 75,167)( 76,166)( 77,161)( 78,164)( 79,163)( 80,162)
( 81,157)( 82,160)( 83,159)( 84,158)( 85,153)( 86,156)( 87,155)( 88,154)
( 89,149)( 90,152)( 91,151)( 92,150)( 93,145)( 94,148)( 95,147)( 96,146)
( 97,141)( 98,144)( 99,143)(100,142)(101,137)(102,140)(103,139)(104,138)
(105,133)(106,136)(107,135)(108,134)(109,129)(110,132)(111,131)(112,130)
(113,125)(114,128)(115,127)(116,126)(233,237)(234,240)(235,239)(236,238)
(241,345)(242,348)(243,347)(244,346)(245,341)(246,344)(247,343)(248,342)
(249,337)(250,340)(251,339)(252,338)(253,333)(254,336)(255,335)(256,334)
(257,329)(258,332)(259,331)(260,330)(261,325)(262,328)(263,327)(264,326)
(265,321)(266,324)(267,323)(268,322)(269,317)(270,320)(271,319)(272,318)
(273,313)(274,316)(275,315)(276,314)(277,309)(278,312)(279,311)(280,310)
(281,305)(282,308)(283,307)(284,306)(285,301)(286,304)(287,303)(288,302)
(289,297)(290,300)(291,299)(292,298)(294,296)(349,469)(350,472)(351,471)
(352,470)(353,465)(354,468)(355,467)(356,466)(357,577)(358,580)(359,579)
(360,578)(361,573)(362,576)(363,575)(364,574)(365,569)(366,572)(367,571)
(368,570)(369,565)(370,568)(371,567)(372,566)(373,561)(374,564)(375,563)
(376,562)(377,557)(378,560)(379,559)(380,558)(381,553)(382,556)(383,555)
(384,554)(385,549)(386,552)(387,551)(388,550)(389,545)(390,548)(391,547)
(392,546)(393,541)(394,544)(395,543)(396,542)(397,537)(398,540)(399,539)
(400,538)(401,533)(402,536)(403,535)(404,534)(405,529)(406,532)(407,531)
(408,530)(409,525)(410,528)(411,527)(412,526)(413,521)(414,524)(415,523)
(416,522)(417,517)(418,520)(419,519)(420,518)(421,513)(422,516)(423,515)
(424,514)(425,509)(426,512)(427,511)(428,510)(429,505)(430,508)(431,507)
(432,506)(433,501)(434,504)(435,503)(436,502)(437,497)(438,500)(439,499)
(440,498)(441,493)(442,496)(443,495)(444,494)(445,489)(446,492)(447,491)
(448,490)(449,485)(450,488)(451,487)(452,486)(453,481)(454,484)(455,483)
(456,482)(457,477)(458,480)(459,479)(460,478)(461,473)(462,476)(463,475)
(464,474)(581,585)(582,588)(583,587)(584,586)(589,693)(590,696)(591,695)
(592,694)(593,689)(594,692)(595,691)(596,690)(597,685)(598,688)(599,687)
(600,686)(601,681)(602,684)(603,683)(604,682)(605,677)(606,680)(607,679)
(608,678)(609,673)(610,676)(611,675)(612,674)(613,669)(614,672)(615,671)
(616,670)(617,665)(618,668)(619,667)(620,666)(621,661)(622,664)(623,663)
(624,662)(625,657)(626,660)(627,659)(628,658)(629,653)(630,656)(631,655)
(632,654)(633,649)(634,652)(635,651)(636,650)(637,645)(638,648)(639,647)
(640,646)(642,644);;
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*s2*s1*s0*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(696)!( 1,351)( 2,352)( 3,349)( 4,350)( 5,355)( 6,356)( 7,353)
( 8,354)( 9,359)( 10,360)( 11,357)( 12,358)( 13,363)( 14,364)( 15,361)
( 16,362)( 17,367)( 18,368)( 19,365)( 20,366)( 21,371)( 22,372)( 23,369)
( 24,370)( 25,375)( 26,376)( 27,373)( 28,374)( 29,379)( 30,380)( 31,377)
( 32,378)( 33,383)( 34,384)( 35,381)( 36,382)( 37,387)( 38,388)( 39,385)
( 40,386)( 41,391)( 42,392)( 43,389)( 44,390)( 45,395)( 46,396)( 47,393)
( 48,394)( 49,399)( 50,400)( 51,397)( 52,398)( 53,403)( 54,404)( 55,401)
( 56,402)( 57,407)( 58,408)( 59,405)( 60,406)( 61,411)( 62,412)( 63,409)
( 64,410)( 65,415)( 66,416)( 67,413)( 68,414)( 69,419)( 70,420)( 71,417)
( 72,418)( 73,423)( 74,424)( 75,421)( 76,422)( 77,427)( 78,428)( 79,425)
( 80,426)( 81,431)( 82,432)( 83,429)( 84,430)( 85,435)( 86,436)( 87,433)
( 88,434)( 89,439)( 90,440)( 91,437)( 92,438)( 93,443)( 94,444)( 95,441)
( 96,442)( 97,447)( 98,448)( 99,445)(100,446)(101,451)(102,452)(103,449)
(104,450)(105,455)(106,456)(107,453)(108,454)(109,459)(110,460)(111,457)
(112,458)(113,463)(114,464)(115,461)(116,462)(117,467)(118,468)(119,465)
(120,466)(121,471)(122,472)(123,469)(124,470)(125,475)(126,476)(127,473)
(128,474)(129,479)(130,480)(131,477)(132,478)(133,483)(134,484)(135,481)
(136,482)(137,487)(138,488)(139,485)(140,486)(141,491)(142,492)(143,489)
(144,490)(145,495)(146,496)(147,493)(148,494)(149,499)(150,500)(151,497)
(152,498)(153,503)(154,504)(155,501)(156,502)(157,507)(158,508)(159,505)
(160,506)(161,511)(162,512)(163,509)(164,510)(165,515)(166,516)(167,513)
(168,514)(169,519)(170,520)(171,517)(172,518)(173,523)(174,524)(175,521)
(176,522)(177,527)(178,528)(179,525)(180,526)(181,531)(182,532)(183,529)
(184,530)(185,535)(186,536)(187,533)(188,534)(189,539)(190,540)(191,537)
(192,538)(193,543)(194,544)(195,541)(196,542)(197,547)(198,548)(199,545)
(200,546)(201,551)(202,552)(203,549)(204,550)(205,555)(206,556)(207,553)
(208,554)(209,559)(210,560)(211,557)(212,558)(213,563)(214,564)(215,561)
(216,562)(217,567)(218,568)(219,565)(220,566)(221,571)(222,572)(223,569)
(224,570)(225,575)(226,576)(227,573)(228,574)(229,579)(230,580)(231,577)
(232,578)(233,583)(234,584)(235,581)(236,582)(237,587)(238,588)(239,585)
(240,586)(241,591)(242,592)(243,589)(244,590)(245,595)(246,596)(247,593)
(248,594)(249,599)(250,600)(251,597)(252,598)(253,603)(254,604)(255,601)
(256,602)(257,607)(258,608)(259,605)(260,606)(261,611)(262,612)(263,609)
(264,610)(265,615)(266,616)(267,613)(268,614)(269,619)(270,620)(271,617)
(272,618)(273,623)(274,624)(275,621)(276,622)(277,627)(278,628)(279,625)
(280,626)(281,631)(282,632)(283,629)(284,630)(285,635)(286,636)(287,633)
(288,634)(289,639)(290,640)(291,637)(292,638)(293,643)(294,644)(295,641)
(296,642)(297,647)(298,648)(299,645)(300,646)(301,651)(302,652)(303,649)
(304,650)(305,655)(306,656)(307,653)(308,654)(309,659)(310,660)(311,657)
(312,658)(313,663)(314,664)(315,661)(316,662)(317,667)(318,668)(319,665)
(320,666)(321,671)(322,672)(323,669)(324,670)(325,675)(326,676)(327,673)
(328,674)(329,679)(330,680)(331,677)(332,678)(333,683)(334,684)(335,681)
(336,682)(337,687)(338,688)(339,685)(340,686)(341,691)(342,692)(343,689)
(344,690)(345,695)(346,696)(347,693)(348,694);
s1 := Sym(696)!( 3, 4)( 5,113)( 6,114)( 7,116)( 8,115)( 9,109)( 10,110)
( 11,112)( 12,111)( 13,105)( 14,106)( 15,108)( 16,107)( 17,101)( 18,102)
( 19,104)( 20,103)( 21, 97)( 22, 98)( 23,100)( 24, 99)( 25, 93)( 26, 94)
( 27, 96)( 28, 95)( 29, 89)( 30, 90)( 31, 92)( 32, 91)( 33, 85)( 34, 86)
( 35, 88)( 36, 87)( 37, 81)( 38, 82)( 39, 84)( 40, 83)( 41, 77)( 42, 78)
( 43, 80)( 44, 79)( 45, 73)( 46, 74)( 47, 76)( 48, 75)( 49, 69)( 50, 70)
( 51, 72)( 52, 71)( 53, 65)( 54, 66)( 55, 68)( 56, 67)( 57, 61)( 58, 62)
( 59, 64)( 60, 63)(117,233)(118,234)(119,236)(120,235)(121,345)(122,346)
(123,348)(124,347)(125,341)(126,342)(127,344)(128,343)(129,337)(130,338)
(131,340)(132,339)(133,333)(134,334)(135,336)(136,335)(137,329)(138,330)
(139,332)(140,331)(141,325)(142,326)(143,328)(144,327)(145,321)(146,322)
(147,324)(148,323)(149,317)(150,318)(151,320)(152,319)(153,313)(154,314)
(155,316)(156,315)(157,309)(158,310)(159,312)(160,311)(161,305)(162,306)
(163,308)(164,307)(165,301)(166,302)(167,304)(168,303)(169,297)(170,298)
(171,300)(172,299)(173,293)(174,294)(175,296)(176,295)(177,289)(178,290)
(179,292)(180,291)(181,285)(182,286)(183,288)(184,287)(185,281)(186,282)
(187,284)(188,283)(189,277)(190,278)(191,280)(192,279)(193,273)(194,274)
(195,276)(196,275)(197,269)(198,270)(199,272)(200,271)(201,265)(202,266)
(203,268)(204,267)(205,261)(206,262)(207,264)(208,263)(209,257)(210,258)
(211,260)(212,259)(213,253)(214,254)(215,256)(216,255)(217,249)(218,250)
(219,252)(220,251)(221,245)(222,246)(223,248)(224,247)(225,241)(226,242)
(227,244)(228,243)(229,237)(230,238)(231,240)(232,239)(351,352)(353,461)
(354,462)(355,464)(356,463)(357,457)(358,458)(359,460)(360,459)(361,453)
(362,454)(363,456)(364,455)(365,449)(366,450)(367,452)(368,451)(369,445)
(370,446)(371,448)(372,447)(373,441)(374,442)(375,444)(376,443)(377,437)
(378,438)(379,440)(380,439)(381,433)(382,434)(383,436)(384,435)(385,429)
(386,430)(387,432)(388,431)(389,425)(390,426)(391,428)(392,427)(393,421)
(394,422)(395,424)(396,423)(397,417)(398,418)(399,420)(400,419)(401,413)
(402,414)(403,416)(404,415)(405,409)(406,410)(407,412)(408,411)(465,581)
(466,582)(467,584)(468,583)(469,693)(470,694)(471,696)(472,695)(473,689)
(474,690)(475,692)(476,691)(477,685)(478,686)(479,688)(480,687)(481,681)
(482,682)(483,684)(484,683)(485,677)(486,678)(487,680)(488,679)(489,673)
(490,674)(491,676)(492,675)(493,669)(494,670)(495,672)(496,671)(497,665)
(498,666)(499,668)(500,667)(501,661)(502,662)(503,664)(504,663)(505,657)
(506,658)(507,660)(508,659)(509,653)(510,654)(511,656)(512,655)(513,649)
(514,650)(515,652)(516,651)(517,645)(518,646)(519,648)(520,647)(521,641)
(522,642)(523,644)(524,643)(525,637)(526,638)(527,640)(528,639)(529,633)
(530,634)(531,636)(532,635)(533,629)(534,630)(535,632)(536,631)(537,625)
(538,626)(539,628)(540,627)(541,621)(542,622)(543,624)(544,623)(545,617)
(546,618)(547,620)(548,619)(549,613)(550,614)(551,616)(552,615)(553,609)
(554,610)(555,612)(556,611)(557,605)(558,606)(559,608)(560,607)(561,601)
(562,602)(563,604)(564,603)(565,597)(566,598)(567,600)(568,599)(569,593)
(570,594)(571,596)(572,595)(573,589)(574,590)(575,592)(576,591)(577,585)
(578,586)(579,588)(580,587);
s2 := Sym(696)!( 1,121)( 2,124)( 3,123)( 4,122)( 5,117)( 6,120)( 7,119)
( 8,118)( 9,229)( 10,232)( 11,231)( 12,230)( 13,225)( 14,228)( 15,227)
( 16,226)( 17,221)( 18,224)( 19,223)( 20,222)( 21,217)( 22,220)( 23,219)
( 24,218)( 25,213)( 26,216)( 27,215)( 28,214)( 29,209)( 30,212)( 31,211)
( 32,210)( 33,205)( 34,208)( 35,207)( 36,206)( 37,201)( 38,204)( 39,203)
( 40,202)( 41,197)( 42,200)( 43,199)( 44,198)( 45,193)( 46,196)( 47,195)
( 48,194)( 49,189)( 50,192)( 51,191)( 52,190)( 53,185)( 54,188)( 55,187)
( 56,186)( 57,181)( 58,184)( 59,183)( 60,182)( 61,177)( 62,180)( 63,179)
( 64,178)( 65,173)( 66,176)( 67,175)( 68,174)( 69,169)( 70,172)( 71,171)
( 72,170)( 73,165)( 74,168)( 75,167)( 76,166)( 77,161)( 78,164)( 79,163)
( 80,162)( 81,157)( 82,160)( 83,159)( 84,158)( 85,153)( 86,156)( 87,155)
( 88,154)( 89,149)( 90,152)( 91,151)( 92,150)( 93,145)( 94,148)( 95,147)
( 96,146)( 97,141)( 98,144)( 99,143)(100,142)(101,137)(102,140)(103,139)
(104,138)(105,133)(106,136)(107,135)(108,134)(109,129)(110,132)(111,131)
(112,130)(113,125)(114,128)(115,127)(116,126)(233,237)(234,240)(235,239)
(236,238)(241,345)(242,348)(243,347)(244,346)(245,341)(246,344)(247,343)
(248,342)(249,337)(250,340)(251,339)(252,338)(253,333)(254,336)(255,335)
(256,334)(257,329)(258,332)(259,331)(260,330)(261,325)(262,328)(263,327)
(264,326)(265,321)(266,324)(267,323)(268,322)(269,317)(270,320)(271,319)
(272,318)(273,313)(274,316)(275,315)(276,314)(277,309)(278,312)(279,311)
(280,310)(281,305)(282,308)(283,307)(284,306)(285,301)(286,304)(287,303)
(288,302)(289,297)(290,300)(291,299)(292,298)(294,296)(349,469)(350,472)
(351,471)(352,470)(353,465)(354,468)(355,467)(356,466)(357,577)(358,580)
(359,579)(360,578)(361,573)(362,576)(363,575)(364,574)(365,569)(366,572)
(367,571)(368,570)(369,565)(370,568)(371,567)(372,566)(373,561)(374,564)
(375,563)(376,562)(377,557)(378,560)(379,559)(380,558)(381,553)(382,556)
(383,555)(384,554)(385,549)(386,552)(387,551)(388,550)(389,545)(390,548)
(391,547)(392,546)(393,541)(394,544)(395,543)(396,542)(397,537)(398,540)
(399,539)(400,538)(401,533)(402,536)(403,535)(404,534)(405,529)(406,532)
(407,531)(408,530)(409,525)(410,528)(411,527)(412,526)(413,521)(414,524)
(415,523)(416,522)(417,517)(418,520)(419,519)(420,518)(421,513)(422,516)
(423,515)(424,514)(425,509)(426,512)(427,511)(428,510)(429,505)(430,508)
(431,507)(432,506)(433,501)(434,504)(435,503)(436,502)(437,497)(438,500)
(439,499)(440,498)(441,493)(442,496)(443,495)(444,494)(445,489)(446,492)
(447,491)(448,490)(449,485)(450,488)(451,487)(452,486)(453,481)(454,484)
(455,483)(456,482)(457,477)(458,480)(459,479)(460,478)(461,473)(462,476)
(463,475)(464,474)(581,585)(582,588)(583,587)(584,586)(589,693)(590,696)
(591,695)(592,694)(593,689)(594,692)(595,691)(596,690)(597,685)(598,688)
(599,687)(600,686)(601,681)(602,684)(603,683)(604,682)(605,677)(606,680)
(607,679)(608,678)(609,673)(610,676)(611,675)(612,674)(613,669)(614,672)
(615,671)(616,670)(617,665)(618,668)(619,667)(620,666)(621,661)(622,664)
(623,663)(624,662)(625,657)(626,660)(627,659)(628,658)(629,653)(630,656)
(631,655)(632,654)(633,649)(634,652)(635,651)(636,650)(637,645)(638,648)
(639,647)(640,646)(642,644);
poly := sub<Sym(696)|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*s2*s1*s0*s1*s2*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 >;
References : None.
to this polytope