Polytope of Type {8,39}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,39}*1248
if this polytope has a name.
Group : SmallGroup(1248,1239)
Rank : 3
Schlafli Type : {8,39}
Number of vertices, edges, etc : 16, 312, 78
Order of s₀s₁s₂ : 156
Order of s₀s₁s₂s₁ : 8
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 : {4,39}*624
   4-fold quotients : {4,39}*312
   8-fold quotients : {2,39}*156
   13-fold quotients : {8,3}*96
   24-fold quotients : {2,13}*52
   26-fold quotients : {4,3}*48
   52-fold quotients : {4,3}*24
   104-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope