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Polytope of Type {74,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {74,8}*1184
Also Known As : {74,8|2}. if this polytope has another name.
Group : SmallGroup(1184,155)
Rank : 3
Schlafli Type : {74,8}
Number of vertices, edges, etc : 74, 296, 8
Order of s0s1s2 : 296
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 : {74,4}*592
   4-fold quotients : {74,2}*296
   8-fold quotients : {37,2}*148
   37-fold quotients : {2,8}*32
   74-fold quotients : {2,4}*16
   148-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,149)(  2,185)(  3,184)(  4,183)(  5,182)(  6,181)(  7,180)(  8,179)
(  9,178)( 10,177)( 11,176)( 12,175)( 13,174)( 14,173)( 15,172)( 16,171)
( 17,170)( 18,169)( 19,168)( 20,167)( 21,166)( 22,165)( 23,164)( 24,163)
( 25,162)( 26,161)( 27,160)( 28,159)( 29,158)( 30,157)( 31,156)( 32,155)
( 33,154)( 34,153)( 35,152)( 36,151)( 37,150)( 38,186)( 39,222)( 40,221)
( 41,220)( 42,219)( 43,218)( 44,217)( 45,216)( 46,215)( 47,214)( 48,213)
( 49,212)( 50,211)( 51,210)( 52,209)( 53,208)( 54,207)( 55,206)( 56,205)
( 57,204)( 58,203)( 59,202)( 60,201)( 61,200)( 62,199)( 63,198)( 64,197)
( 65,196)( 66,195)( 67,194)( 68,193)( 69,192)( 70,191)( 71,190)( 72,189)
( 73,188)( 74,187)( 75,223)( 76,259)( 77,258)( 78,257)( 79,256)( 80,255)
( 81,254)( 82,253)( 83,252)( 84,251)( 85,250)( 86,249)( 87,248)( 88,247)
( 89,246)( 90,245)( 91,244)( 92,243)( 93,242)( 94,241)( 95,240)( 96,239)
( 97,238)( 98,237)( 99,236)(100,235)(101,234)(102,233)(103,232)(104,231)
(105,230)(106,229)(107,228)(108,227)(109,226)(110,225)(111,224)(112,260)
(113,296)(114,295)(115,294)(116,293)(117,292)(118,291)(119,290)(120,289)
(121,288)(122,287)(123,286)(124,285)(125,284)(126,283)(127,282)(128,281)
(129,280)(130,279)(131,278)(132,277)(133,276)(134,275)(135,274)(136,273)
(137,272)(138,271)(139,270)(140,269)(141,268)(142,267)(143,266)(144,265)
(145,264)(146,263)(147,262)(148,261)(297,445)(298,481)(299,480)(300,479)
(301,478)(302,477)(303,476)(304,475)(305,474)(306,473)(307,472)(308,471)
(309,470)(310,469)(311,468)(312,467)(313,466)(314,465)(315,464)(316,463)
(317,462)(318,461)(319,460)(320,459)(321,458)(322,457)(323,456)(324,455)
(325,454)(326,453)(327,452)(328,451)(329,450)(330,449)(331,448)(332,447)
(333,446)(334,482)(335,518)(336,517)(337,516)(338,515)(339,514)(340,513)
(341,512)(342,511)(343,510)(344,509)(345,508)(346,507)(347,506)(348,505)
(349,504)(350,503)(351,502)(352,501)(353,500)(354,499)(355,498)(356,497)
(357,496)(358,495)(359,494)(360,493)(361,492)(362,491)(363,490)(364,489)
(365,488)(366,487)(367,486)(368,485)(369,484)(370,483)(371,519)(372,555)
(373,554)(374,553)(375,552)(376,551)(377,550)(378,549)(379,548)(380,547)
(381,546)(382,545)(383,544)(384,543)(385,542)(386,541)(387,540)(388,539)
(389,538)(390,537)(391,536)(392,535)(393,534)(394,533)(395,532)(396,531)
(397,530)(398,529)(399,528)(400,527)(401,526)(402,525)(403,524)(404,523)
(405,522)(406,521)(407,520)(408,556)(409,592)(410,591)(411,590)(412,589)
(413,588)(414,587)(415,586)(416,585)(417,584)(418,583)(419,582)(420,581)
(421,580)(422,579)(423,578)(424,577)(425,576)(426,575)(427,574)(428,573)
(429,572)(430,571)(431,570)(432,569)(433,568)(434,567)(435,566)(436,565)
(437,564)(438,563)(439,562)(440,561)(441,560)(442,559)(443,558)(444,557);;
s1 := (  1,150)(  2,149)(  3,185)(  4,184)(  5,183)(  6,182)(  7,181)(  8,180)
(  9,179)( 10,178)( 11,177)( 12,176)( 13,175)( 14,174)( 15,173)( 16,172)
( 17,171)( 18,170)( 19,169)( 20,168)( 21,167)( 22,166)( 23,165)( 24,164)
( 25,163)( 26,162)( 27,161)( 28,160)( 29,159)( 30,158)( 31,157)( 32,156)
( 33,155)( 34,154)( 35,153)( 36,152)( 37,151)( 38,187)( 39,186)( 40,222)
( 41,221)( 42,220)( 43,219)( 44,218)( 45,217)( 46,216)( 47,215)( 48,214)
( 49,213)( 50,212)( 51,211)( 52,210)( 53,209)( 54,208)( 55,207)( 56,206)
( 57,205)( 58,204)( 59,203)( 60,202)( 61,201)( 62,200)( 63,199)( 64,198)
( 65,197)( 66,196)( 67,195)( 68,194)( 69,193)( 70,192)( 71,191)( 72,190)
( 73,189)( 74,188)( 75,261)( 76,260)( 77,296)( 78,295)( 79,294)( 80,293)
( 81,292)( 82,291)( 83,290)( 84,289)( 85,288)( 86,287)( 87,286)( 88,285)
( 89,284)( 90,283)( 91,282)( 92,281)( 93,280)( 94,279)( 95,278)( 96,277)
( 97,276)( 98,275)( 99,274)(100,273)(101,272)(102,271)(103,270)(104,269)
(105,268)(106,267)(107,266)(108,265)(109,264)(110,263)(111,262)(112,224)
(113,223)(114,259)(115,258)(116,257)(117,256)(118,255)(119,254)(120,253)
(121,252)(122,251)(123,250)(124,249)(125,248)(126,247)(127,246)(128,245)
(129,244)(130,243)(131,242)(132,241)(133,240)(134,239)(135,238)(136,237)
(137,236)(138,235)(139,234)(140,233)(141,232)(142,231)(143,230)(144,229)
(145,228)(146,227)(147,226)(148,225)(297,520)(298,519)(299,555)(300,554)
(301,553)(302,552)(303,551)(304,550)(305,549)(306,548)(307,547)(308,546)
(309,545)(310,544)(311,543)(312,542)(313,541)(314,540)(315,539)(316,538)
(317,537)(318,536)(319,535)(320,534)(321,533)(322,532)(323,531)(324,530)
(325,529)(326,528)(327,527)(328,526)(329,525)(330,524)(331,523)(332,522)
(333,521)(334,557)(335,556)(336,592)(337,591)(338,590)(339,589)(340,588)
(341,587)(342,586)(343,585)(344,584)(345,583)(346,582)(347,581)(348,580)
(349,579)(350,578)(351,577)(352,576)(353,575)(354,574)(355,573)(356,572)
(357,571)(358,570)(359,569)(360,568)(361,567)(362,566)(363,565)(364,564)
(365,563)(366,562)(367,561)(368,560)(369,559)(370,558)(371,446)(372,445)
(373,481)(374,480)(375,479)(376,478)(377,477)(378,476)(379,475)(380,474)
(381,473)(382,472)(383,471)(384,470)(385,469)(386,468)(387,467)(388,466)
(389,465)(390,464)(391,463)(392,462)(393,461)(394,460)(395,459)(396,458)
(397,457)(398,456)(399,455)(400,454)(401,453)(402,452)(403,451)(404,450)
(405,449)(406,448)(407,447)(408,483)(409,482)(410,518)(411,517)(412,516)
(413,515)(414,514)(415,513)(416,512)(417,511)(418,510)(419,509)(420,508)
(421,507)(422,506)(423,505)(424,504)(425,503)(426,502)(427,501)(428,500)
(429,499)(430,498)(431,497)(432,496)(433,495)(434,494)(435,493)(436,492)
(437,491)(438,490)(439,489)(440,488)(441,487)(442,486)(443,485)(444,484);;
s2 := (  1,297)(  2,298)(  3,299)(  4,300)(  5,301)(  6,302)(  7,303)(  8,304)
(  9,305)( 10,306)( 11,307)( 12,308)( 13,309)( 14,310)( 15,311)( 16,312)
( 17,313)( 18,314)( 19,315)( 20,316)( 21,317)( 22,318)( 23,319)( 24,320)
( 25,321)( 26,322)( 27,323)( 28,324)( 29,325)( 30,326)( 31,327)( 32,328)
( 33,329)( 34,330)( 35,331)( 36,332)( 37,333)( 38,334)( 39,335)( 40,336)
( 41,337)( 42,338)( 43,339)( 44,340)( 45,341)( 46,342)( 47,343)( 48,344)
( 49,345)( 50,346)( 51,347)( 52,348)( 53,349)( 54,350)( 55,351)( 56,352)
( 57,353)( 58,354)( 59,355)( 60,356)( 61,357)( 62,358)( 63,359)( 64,360)
( 65,361)( 66,362)( 67,363)( 68,364)( 69,365)( 70,366)( 71,367)( 72,368)
( 73,369)( 74,370)( 75,408)( 76,409)( 77,410)( 78,411)( 79,412)( 80,413)
( 81,414)( 82,415)( 83,416)( 84,417)( 85,418)( 86,419)( 87,420)( 88,421)
( 89,422)( 90,423)( 91,424)( 92,425)( 93,426)( 94,427)( 95,428)( 96,429)
( 97,430)( 98,431)( 99,432)(100,433)(101,434)(102,435)(103,436)(104,437)
(105,438)(106,439)(107,440)(108,441)(109,442)(110,443)(111,444)(112,371)
(113,372)(114,373)(115,374)(116,375)(117,376)(118,377)(119,378)(120,379)
(121,380)(122,381)(123,382)(124,383)(125,384)(126,385)(127,386)(128,387)
(129,388)(130,389)(131,390)(132,391)(133,392)(134,393)(135,394)(136,395)
(137,396)(138,397)(139,398)(140,399)(141,400)(142,401)(143,402)(144,403)
(145,404)(146,405)(147,406)(148,407)(149,445)(150,446)(151,447)(152,448)
(153,449)(154,450)(155,451)(156,452)(157,453)(158,454)(159,455)(160,456)
(161,457)(162,458)(163,459)(164,460)(165,461)(166,462)(167,463)(168,464)
(169,465)(170,466)(171,467)(172,468)(173,469)(174,470)(175,471)(176,472)
(177,473)(178,474)(179,475)(180,476)(181,477)(182,478)(183,479)(184,480)
(185,481)(186,482)(187,483)(188,484)(189,485)(190,486)(191,487)(192,488)
(193,489)(194,490)(195,491)(196,492)(197,493)(198,494)(199,495)(200,496)
(201,497)(202,498)(203,499)(204,500)(205,501)(206,502)(207,503)(208,504)
(209,505)(210,506)(211,507)(212,508)(213,509)(214,510)(215,511)(216,512)
(217,513)(218,514)(219,515)(220,516)(221,517)(222,518)(223,556)(224,557)
(225,558)(226,559)(227,560)(228,561)(229,562)(230,563)(231,564)(232,565)
(233,566)(234,567)(235,568)(236,569)(237,570)(238,571)(239,572)(240,573)
(241,574)(242,575)(243,576)(244,577)(245,578)(246,579)(247,580)(248,581)
(249,582)(250,583)(251,584)(252,585)(253,586)(254,587)(255,588)(256,589)
(257,590)(258,591)(259,592)(260,519)(261,520)(262,521)(263,522)(264,523)
(265,524)(266,525)(267,526)(268,527)(269,528)(270,529)(271,530)(272,531)
(273,532)(274,533)(275,534)(276,535)(277,536)(278,537)(279,538)(280,539)
(281,540)(282,541)(283,542)(284,543)(285,544)(286,545)(287,546)(288,547)
(289,548)(290,549)(291,550)(292,551)(293,552)(294,553)(295,554)(296,555);;
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*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(592)!(  1,149)(  2,185)(  3,184)(  4,183)(  5,182)(  6,181)(  7,180)
(  8,179)(  9,178)( 10,177)( 11,176)( 12,175)( 13,174)( 14,173)( 15,172)
( 16,171)( 17,170)( 18,169)( 19,168)( 20,167)( 21,166)( 22,165)( 23,164)
( 24,163)( 25,162)( 26,161)( 27,160)( 28,159)( 29,158)( 30,157)( 31,156)
( 32,155)( 33,154)( 34,153)( 35,152)( 36,151)( 37,150)( 38,186)( 39,222)
( 40,221)( 41,220)( 42,219)( 43,218)( 44,217)( 45,216)( 46,215)( 47,214)
( 48,213)( 49,212)( 50,211)( 51,210)( 52,209)( 53,208)( 54,207)( 55,206)
( 56,205)( 57,204)( 58,203)( 59,202)( 60,201)( 61,200)( 62,199)( 63,198)
( 64,197)( 65,196)( 66,195)( 67,194)( 68,193)( 69,192)( 70,191)( 71,190)
( 72,189)( 73,188)( 74,187)( 75,223)( 76,259)( 77,258)( 78,257)( 79,256)
( 80,255)( 81,254)( 82,253)( 83,252)( 84,251)( 85,250)( 86,249)( 87,248)
( 88,247)( 89,246)( 90,245)( 91,244)( 92,243)( 93,242)( 94,241)( 95,240)
( 96,239)( 97,238)( 98,237)( 99,236)(100,235)(101,234)(102,233)(103,232)
(104,231)(105,230)(106,229)(107,228)(108,227)(109,226)(110,225)(111,224)
(112,260)(113,296)(114,295)(115,294)(116,293)(117,292)(118,291)(119,290)
(120,289)(121,288)(122,287)(123,286)(124,285)(125,284)(126,283)(127,282)
(128,281)(129,280)(130,279)(131,278)(132,277)(133,276)(134,275)(135,274)
(136,273)(137,272)(138,271)(139,270)(140,269)(141,268)(142,267)(143,266)
(144,265)(145,264)(146,263)(147,262)(148,261)(297,445)(298,481)(299,480)
(300,479)(301,478)(302,477)(303,476)(304,475)(305,474)(306,473)(307,472)
(308,471)(309,470)(310,469)(311,468)(312,467)(313,466)(314,465)(315,464)
(316,463)(317,462)(318,461)(319,460)(320,459)(321,458)(322,457)(323,456)
(324,455)(325,454)(326,453)(327,452)(328,451)(329,450)(330,449)(331,448)
(332,447)(333,446)(334,482)(335,518)(336,517)(337,516)(338,515)(339,514)
(340,513)(341,512)(342,511)(343,510)(344,509)(345,508)(346,507)(347,506)
(348,505)(349,504)(350,503)(351,502)(352,501)(353,500)(354,499)(355,498)
(356,497)(357,496)(358,495)(359,494)(360,493)(361,492)(362,491)(363,490)
(364,489)(365,488)(366,487)(367,486)(368,485)(369,484)(370,483)(371,519)
(372,555)(373,554)(374,553)(375,552)(376,551)(377,550)(378,549)(379,548)
(380,547)(381,546)(382,545)(383,544)(384,543)(385,542)(386,541)(387,540)
(388,539)(389,538)(390,537)(391,536)(392,535)(393,534)(394,533)(395,532)
(396,531)(397,530)(398,529)(399,528)(400,527)(401,526)(402,525)(403,524)
(404,523)(405,522)(406,521)(407,520)(408,556)(409,592)(410,591)(411,590)
(412,589)(413,588)(414,587)(415,586)(416,585)(417,584)(418,583)(419,582)
(420,581)(421,580)(422,579)(423,578)(424,577)(425,576)(426,575)(427,574)
(428,573)(429,572)(430,571)(431,570)(432,569)(433,568)(434,567)(435,566)
(436,565)(437,564)(438,563)(439,562)(440,561)(441,560)(442,559)(443,558)
(444,557);
s1 := Sym(592)!(  1,150)(  2,149)(  3,185)(  4,184)(  5,183)(  6,182)(  7,181)
(  8,180)(  9,179)( 10,178)( 11,177)( 12,176)( 13,175)( 14,174)( 15,173)
( 16,172)( 17,171)( 18,170)( 19,169)( 20,168)( 21,167)( 22,166)( 23,165)
( 24,164)( 25,163)( 26,162)( 27,161)( 28,160)( 29,159)( 30,158)( 31,157)
( 32,156)( 33,155)( 34,154)( 35,153)( 36,152)( 37,151)( 38,187)( 39,186)
( 40,222)( 41,221)( 42,220)( 43,219)( 44,218)( 45,217)( 46,216)( 47,215)
( 48,214)( 49,213)( 50,212)( 51,211)( 52,210)( 53,209)( 54,208)( 55,207)
( 56,206)( 57,205)( 58,204)( 59,203)( 60,202)( 61,201)( 62,200)( 63,199)
( 64,198)( 65,197)( 66,196)( 67,195)( 68,194)( 69,193)( 70,192)( 71,191)
( 72,190)( 73,189)( 74,188)( 75,261)( 76,260)( 77,296)( 78,295)( 79,294)
( 80,293)( 81,292)( 82,291)( 83,290)( 84,289)( 85,288)( 86,287)( 87,286)
( 88,285)( 89,284)( 90,283)( 91,282)( 92,281)( 93,280)( 94,279)( 95,278)
( 96,277)( 97,276)( 98,275)( 99,274)(100,273)(101,272)(102,271)(103,270)
(104,269)(105,268)(106,267)(107,266)(108,265)(109,264)(110,263)(111,262)
(112,224)(113,223)(114,259)(115,258)(116,257)(117,256)(118,255)(119,254)
(120,253)(121,252)(122,251)(123,250)(124,249)(125,248)(126,247)(127,246)
(128,245)(129,244)(130,243)(131,242)(132,241)(133,240)(134,239)(135,238)
(136,237)(137,236)(138,235)(139,234)(140,233)(141,232)(142,231)(143,230)
(144,229)(145,228)(146,227)(147,226)(148,225)(297,520)(298,519)(299,555)
(300,554)(301,553)(302,552)(303,551)(304,550)(305,549)(306,548)(307,547)
(308,546)(309,545)(310,544)(311,543)(312,542)(313,541)(314,540)(315,539)
(316,538)(317,537)(318,536)(319,535)(320,534)(321,533)(322,532)(323,531)
(324,530)(325,529)(326,528)(327,527)(328,526)(329,525)(330,524)(331,523)
(332,522)(333,521)(334,557)(335,556)(336,592)(337,591)(338,590)(339,589)
(340,588)(341,587)(342,586)(343,585)(344,584)(345,583)(346,582)(347,581)
(348,580)(349,579)(350,578)(351,577)(352,576)(353,575)(354,574)(355,573)
(356,572)(357,571)(358,570)(359,569)(360,568)(361,567)(362,566)(363,565)
(364,564)(365,563)(366,562)(367,561)(368,560)(369,559)(370,558)(371,446)
(372,445)(373,481)(374,480)(375,479)(376,478)(377,477)(378,476)(379,475)
(380,474)(381,473)(382,472)(383,471)(384,470)(385,469)(386,468)(387,467)
(388,466)(389,465)(390,464)(391,463)(392,462)(393,461)(394,460)(395,459)
(396,458)(397,457)(398,456)(399,455)(400,454)(401,453)(402,452)(403,451)
(404,450)(405,449)(406,448)(407,447)(408,483)(409,482)(410,518)(411,517)
(412,516)(413,515)(414,514)(415,513)(416,512)(417,511)(418,510)(419,509)
(420,508)(421,507)(422,506)(423,505)(424,504)(425,503)(426,502)(427,501)
(428,500)(429,499)(430,498)(431,497)(432,496)(433,495)(434,494)(435,493)
(436,492)(437,491)(438,490)(439,489)(440,488)(441,487)(442,486)(443,485)
(444,484);
s2 := Sym(592)!(  1,297)(  2,298)(  3,299)(  4,300)(  5,301)(  6,302)(  7,303)
(  8,304)(  9,305)( 10,306)( 11,307)( 12,308)( 13,309)( 14,310)( 15,311)
( 16,312)( 17,313)( 18,314)( 19,315)( 20,316)( 21,317)( 22,318)( 23,319)
( 24,320)( 25,321)( 26,322)( 27,323)( 28,324)( 29,325)( 30,326)( 31,327)
( 32,328)( 33,329)( 34,330)( 35,331)( 36,332)( 37,333)( 38,334)( 39,335)
( 40,336)( 41,337)( 42,338)( 43,339)( 44,340)( 45,341)( 46,342)( 47,343)
( 48,344)( 49,345)( 50,346)( 51,347)( 52,348)( 53,349)( 54,350)( 55,351)
( 56,352)( 57,353)( 58,354)( 59,355)( 60,356)( 61,357)( 62,358)( 63,359)
( 64,360)( 65,361)( 66,362)( 67,363)( 68,364)( 69,365)( 70,366)( 71,367)
( 72,368)( 73,369)( 74,370)( 75,408)( 76,409)( 77,410)( 78,411)( 79,412)
( 80,413)( 81,414)( 82,415)( 83,416)( 84,417)( 85,418)( 86,419)( 87,420)
( 88,421)( 89,422)( 90,423)( 91,424)( 92,425)( 93,426)( 94,427)( 95,428)
( 96,429)( 97,430)( 98,431)( 99,432)(100,433)(101,434)(102,435)(103,436)
(104,437)(105,438)(106,439)(107,440)(108,441)(109,442)(110,443)(111,444)
(112,371)(113,372)(114,373)(115,374)(116,375)(117,376)(118,377)(119,378)
(120,379)(121,380)(122,381)(123,382)(124,383)(125,384)(126,385)(127,386)
(128,387)(129,388)(130,389)(131,390)(132,391)(133,392)(134,393)(135,394)
(136,395)(137,396)(138,397)(139,398)(140,399)(141,400)(142,401)(143,402)
(144,403)(145,404)(146,405)(147,406)(148,407)(149,445)(150,446)(151,447)
(152,448)(153,449)(154,450)(155,451)(156,452)(157,453)(158,454)(159,455)
(160,456)(161,457)(162,458)(163,459)(164,460)(165,461)(166,462)(167,463)
(168,464)(169,465)(170,466)(171,467)(172,468)(173,469)(174,470)(175,471)
(176,472)(177,473)(178,474)(179,475)(180,476)(181,477)(182,478)(183,479)
(184,480)(185,481)(186,482)(187,483)(188,484)(189,485)(190,486)(191,487)
(192,488)(193,489)(194,490)(195,491)(196,492)(197,493)(198,494)(199,495)
(200,496)(201,497)(202,498)(203,499)(204,500)(205,501)(206,502)(207,503)
(208,504)(209,505)(210,506)(211,507)(212,508)(213,509)(214,510)(215,511)
(216,512)(217,513)(218,514)(219,515)(220,516)(221,517)(222,518)(223,556)
(224,557)(225,558)(226,559)(227,560)(228,561)(229,562)(230,563)(231,564)
(232,565)(233,566)(234,567)(235,568)(236,569)(237,570)(238,571)(239,572)
(240,573)(241,574)(242,575)(243,576)(244,577)(245,578)(246,579)(247,580)
(248,581)(249,582)(250,583)(251,584)(252,585)(253,586)(254,587)(255,588)
(256,589)(257,590)(258,591)(259,592)(260,519)(261,520)(262,521)(263,522)
(264,523)(265,524)(266,525)(267,526)(268,527)(269,528)(270,529)(271,530)
(272,531)(273,532)(274,533)(275,534)(276,535)(277,536)(278,537)(279,538)
(280,539)(281,540)(282,541)(283,542)(284,543)(285,544)(286,545)(287,546)
(288,547)(289,548)(290,549)(291,550)(292,551)(293,552)(294,553)(295,554)
(296,555);
poly := sub<Sym(592)|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*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 >; 
 
References : None.
to this polytope