Polytope of Type {146,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {146,4}*1168
Also Known As : {146,4|2}. if this polytope has another name.
Group : SmallGroup(1168,34)
Rank : 3
Schlafli Type : {146,4}
Number of vertices, edges, etc : 146, 292, 4
Order of s0s1s2 : 292
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 : {146,2}*584
4-fold quotients : {73,2}*292
73-fold quotients : {2,4}*16
146-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,147)( 2,219)( 3,218)( 4,217)( 5,216)( 6,215)( 7,214)( 8,213)
( 9,212)( 10,211)( 11,210)( 12,209)( 13,208)( 14,207)( 15,206)( 16,205)
( 17,204)( 18,203)( 19,202)( 20,201)( 21,200)( 22,199)( 23,198)( 24,197)
( 25,196)( 26,195)( 27,194)( 28,193)( 29,192)( 30,191)( 31,190)( 32,189)
( 33,188)( 34,187)( 35,186)( 36,185)( 37,184)( 38,183)( 39,182)( 40,181)
( 41,180)( 42,179)( 43,178)( 44,177)( 45,176)( 46,175)( 47,174)( 48,173)
( 49,172)( 50,171)( 51,170)( 52,169)( 53,168)( 54,167)( 55,166)( 56,165)
( 57,164)( 58,163)( 59,162)( 60,161)( 61,160)( 62,159)( 63,158)( 64,157)
( 65,156)( 66,155)( 67,154)( 68,153)( 69,152)( 70,151)( 71,150)( 72,149)
( 73,148)( 74,220)( 75,292)( 76,291)( 77,290)( 78,289)( 79,288)( 80,287)
( 81,286)( 82,285)( 83,284)( 84,283)( 85,282)( 86,281)( 87,280)( 88,279)
( 89,278)( 90,277)( 91,276)( 92,275)( 93,274)( 94,273)( 95,272)( 96,271)
( 97,270)( 98,269)( 99,268)(100,267)(101,266)(102,265)(103,264)(104,263)
(105,262)(106,261)(107,260)(108,259)(109,258)(110,257)(111,256)(112,255)
(113,254)(114,253)(115,252)(116,251)(117,250)(118,249)(119,248)(120,247)
(121,246)(122,245)(123,244)(124,243)(125,242)(126,241)(127,240)(128,239)
(129,238)(130,237)(131,236)(132,235)(133,234)(134,233)(135,232)(136,231)
(137,230)(138,229)(139,228)(140,227)(141,226)(142,225)(143,224)(144,223)
(145,222)(146,221)(293,439)(294,511)(295,510)(296,509)(297,508)(298,507)
(299,506)(300,505)(301,504)(302,503)(303,502)(304,501)(305,500)(306,499)
(307,498)(308,497)(309,496)(310,495)(311,494)(312,493)(313,492)(314,491)
(315,490)(316,489)(317,488)(318,487)(319,486)(320,485)(321,484)(322,483)
(323,482)(324,481)(325,480)(326,479)(327,478)(328,477)(329,476)(330,475)
(331,474)(332,473)(333,472)(334,471)(335,470)(336,469)(337,468)(338,467)
(339,466)(340,465)(341,464)(342,463)(343,462)(344,461)(345,460)(346,459)
(347,458)(348,457)(349,456)(350,455)(351,454)(352,453)(353,452)(354,451)
(355,450)(356,449)(357,448)(358,447)(359,446)(360,445)(361,444)(362,443)
(363,442)(364,441)(365,440)(366,512)(367,584)(368,583)(369,582)(370,581)
(371,580)(372,579)(373,578)(374,577)(375,576)(376,575)(377,574)(378,573)
(379,572)(380,571)(381,570)(382,569)(383,568)(384,567)(385,566)(386,565)
(387,564)(388,563)(389,562)(390,561)(391,560)(392,559)(393,558)(394,557)
(395,556)(396,555)(397,554)(398,553)(399,552)(400,551)(401,550)(402,549)
(403,548)(404,547)(405,546)(406,545)(407,544)(408,543)(409,542)(410,541)
(411,540)(412,539)(413,538)(414,537)(415,536)(416,535)(417,534)(418,533)
(419,532)(420,531)(421,530)(422,529)(423,528)(424,527)(425,526)(426,525)
(427,524)(428,523)(429,522)(430,521)(431,520)(432,519)(433,518)(434,517)
(435,516)(436,515)(437,514)(438,513);;
s1 := ( 1,148)( 2,147)( 3,219)( 4,218)( 5,217)( 6,216)( 7,215)( 8,214)
( 9,213)( 10,212)( 11,211)( 12,210)( 13,209)( 14,208)( 15,207)( 16,206)
( 17,205)( 18,204)( 19,203)( 20,202)( 21,201)( 22,200)( 23,199)( 24,198)
( 25,197)( 26,196)( 27,195)( 28,194)( 29,193)( 30,192)( 31,191)( 32,190)
( 33,189)( 34,188)( 35,187)( 36,186)( 37,185)( 38,184)( 39,183)( 40,182)
( 41,181)( 42,180)( 43,179)( 44,178)( 45,177)( 46,176)( 47,175)( 48,174)
( 49,173)( 50,172)( 51,171)( 52,170)( 53,169)( 54,168)( 55,167)( 56,166)
( 57,165)( 58,164)( 59,163)( 60,162)( 61,161)( 62,160)( 63,159)( 64,158)
( 65,157)( 66,156)( 67,155)( 68,154)( 69,153)( 70,152)( 71,151)( 72,150)
( 73,149)( 74,221)( 75,220)( 76,292)( 77,291)( 78,290)( 79,289)( 80,288)
( 81,287)( 82,286)( 83,285)( 84,284)( 85,283)( 86,282)( 87,281)( 88,280)
( 89,279)( 90,278)( 91,277)( 92,276)( 93,275)( 94,274)( 95,273)( 96,272)
( 97,271)( 98,270)( 99,269)(100,268)(101,267)(102,266)(103,265)(104,264)
(105,263)(106,262)(107,261)(108,260)(109,259)(110,258)(111,257)(112,256)
(113,255)(114,254)(115,253)(116,252)(117,251)(118,250)(119,249)(120,248)
(121,247)(122,246)(123,245)(124,244)(125,243)(126,242)(127,241)(128,240)
(129,239)(130,238)(131,237)(132,236)(133,235)(134,234)(135,233)(136,232)
(137,231)(138,230)(139,229)(140,228)(141,227)(142,226)(143,225)(144,224)
(145,223)(146,222)(293,513)(294,512)(295,584)(296,583)(297,582)(298,581)
(299,580)(300,579)(301,578)(302,577)(303,576)(304,575)(305,574)(306,573)
(307,572)(308,571)(309,570)(310,569)(311,568)(312,567)(313,566)(314,565)
(315,564)(316,563)(317,562)(318,561)(319,560)(320,559)(321,558)(322,557)
(323,556)(324,555)(325,554)(326,553)(327,552)(328,551)(329,550)(330,549)
(331,548)(332,547)(333,546)(334,545)(335,544)(336,543)(337,542)(338,541)
(339,540)(340,539)(341,538)(342,537)(343,536)(344,535)(345,534)(346,533)
(347,532)(348,531)(349,530)(350,529)(351,528)(352,527)(353,526)(354,525)
(355,524)(356,523)(357,522)(358,521)(359,520)(360,519)(361,518)(362,517)
(363,516)(364,515)(365,514)(366,440)(367,439)(368,511)(369,510)(370,509)
(371,508)(372,507)(373,506)(374,505)(375,504)(376,503)(377,502)(378,501)
(379,500)(380,499)(381,498)(382,497)(383,496)(384,495)(385,494)(386,493)
(387,492)(388,491)(389,490)(390,489)(391,488)(392,487)(393,486)(394,485)
(395,484)(396,483)(397,482)(398,481)(399,480)(400,479)(401,478)(402,477)
(403,476)(404,475)(405,474)(406,473)(407,472)(408,471)(409,470)(410,469)
(411,468)(412,467)(413,466)(414,465)(415,464)(416,463)(417,462)(418,461)
(419,460)(420,459)(421,458)(422,457)(423,456)(424,455)(425,454)(426,453)
(427,452)(428,451)(429,450)(430,449)(431,448)(432,447)(433,446)(434,445)
(435,444)(436,443)(437,442)(438,441);;
s2 := ( 1,293)( 2,294)( 3,295)( 4,296)( 5,297)( 6,298)( 7,299)( 8,300)
( 9,301)( 10,302)( 11,303)( 12,304)( 13,305)( 14,306)( 15,307)( 16,308)
( 17,309)( 18,310)( 19,311)( 20,312)( 21,313)( 22,314)( 23,315)( 24,316)
( 25,317)( 26,318)( 27,319)( 28,320)( 29,321)( 30,322)( 31,323)( 32,324)
( 33,325)( 34,326)( 35,327)( 36,328)( 37,329)( 38,330)( 39,331)( 40,332)
( 41,333)( 42,334)( 43,335)( 44,336)( 45,337)( 46,338)( 47,339)( 48,340)
( 49,341)( 50,342)( 51,343)( 52,344)( 53,345)( 54,346)( 55,347)( 56,348)
( 57,349)( 58,350)( 59,351)( 60,352)( 61,353)( 62,354)( 63,355)( 64,356)
( 65,357)( 66,358)( 67,359)( 68,360)( 69,361)( 70,362)( 71,363)( 72,364)
( 73,365)( 74,366)( 75,367)( 76,368)( 77,369)( 78,370)( 79,371)( 80,372)
( 81,373)( 82,374)( 83,375)( 84,376)( 85,377)( 86,378)( 87,379)( 88,380)
( 89,381)( 90,382)( 91,383)( 92,384)( 93,385)( 94,386)( 95,387)( 96,388)
( 97,389)( 98,390)( 99,391)(100,392)(101,393)(102,394)(103,395)(104,396)
(105,397)(106,398)(107,399)(108,400)(109,401)(110,402)(111,403)(112,404)
(113,405)(114,406)(115,407)(116,408)(117,409)(118,410)(119,411)(120,412)
(121,413)(122,414)(123,415)(124,416)(125,417)(126,418)(127,419)(128,420)
(129,421)(130,422)(131,423)(132,424)(133,425)(134,426)(135,427)(136,428)
(137,429)(138,430)(139,431)(140,432)(141,433)(142,434)(143,435)(144,436)
(145,437)(146,438)(147,439)(148,440)(149,441)(150,442)(151,443)(152,444)
(153,445)(154,446)(155,447)(156,448)(157,449)(158,450)(159,451)(160,452)
(161,453)(162,454)(163,455)(164,456)(165,457)(166,458)(167,459)(168,460)
(169,461)(170,462)(171,463)(172,464)(173,465)(174,466)(175,467)(176,468)
(177,469)(178,470)(179,471)(180,472)(181,473)(182,474)(183,475)(184,476)
(185,477)(186,478)(187,479)(188,480)(189,481)(190,482)(191,483)(192,484)
(193,485)(194,486)(195,487)(196,488)(197,489)(198,490)(199,491)(200,492)
(201,493)(202,494)(203,495)(204,496)(205,497)(206,498)(207,499)(208,500)
(209,501)(210,502)(211,503)(212,504)(213,505)(214,506)(215,507)(216,508)
(217,509)(218,510)(219,511)(220,512)(221,513)(222,514)(223,515)(224,516)
(225,517)(226,518)(227,519)(228,520)(229,521)(230,522)(231,523)(232,524)
(233,525)(234,526)(235,527)(236,528)(237,529)(238,530)(239,531)(240,532)
(241,533)(242,534)(243,535)(244,536)(245,537)(246,538)(247,539)(248,540)
(249,541)(250,542)(251,543)(252,544)(253,545)(254,546)(255,547)(256,548)
(257,549)(258,550)(259,551)(260,552)(261,553)(262,554)(263,555)(264,556)
(265,557)(266,558)(267,559)(268,560)(269,561)(270,562)(271,563)(272,564)
(273,565)(274,566)(275,567)(276,568)(277,569)(278,570)(279,571)(280,572)
(281,573)(282,574)(283,575)(284,576)(285,577)(286,578)(287,579)(288,580)
(289,581)(290,582)(291,583)(292,584);;
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, 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*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(584)!( 1,147)( 2,219)( 3,218)( 4,217)( 5,216)( 6,215)( 7,214)
( 8,213)( 9,212)( 10,211)( 11,210)( 12,209)( 13,208)( 14,207)( 15,206)
( 16,205)( 17,204)( 18,203)( 19,202)( 20,201)( 21,200)( 22,199)( 23,198)
( 24,197)( 25,196)( 26,195)( 27,194)( 28,193)( 29,192)( 30,191)( 31,190)
( 32,189)( 33,188)( 34,187)( 35,186)( 36,185)( 37,184)( 38,183)( 39,182)
( 40,181)( 41,180)( 42,179)( 43,178)( 44,177)( 45,176)( 46,175)( 47,174)
( 48,173)( 49,172)( 50,171)( 51,170)( 52,169)( 53,168)( 54,167)( 55,166)
( 56,165)( 57,164)( 58,163)( 59,162)( 60,161)( 61,160)( 62,159)( 63,158)
( 64,157)( 65,156)( 66,155)( 67,154)( 68,153)( 69,152)( 70,151)( 71,150)
( 72,149)( 73,148)( 74,220)( 75,292)( 76,291)( 77,290)( 78,289)( 79,288)
( 80,287)( 81,286)( 82,285)( 83,284)( 84,283)( 85,282)( 86,281)( 87,280)
( 88,279)( 89,278)( 90,277)( 91,276)( 92,275)( 93,274)( 94,273)( 95,272)
( 96,271)( 97,270)( 98,269)( 99,268)(100,267)(101,266)(102,265)(103,264)
(104,263)(105,262)(106,261)(107,260)(108,259)(109,258)(110,257)(111,256)
(112,255)(113,254)(114,253)(115,252)(116,251)(117,250)(118,249)(119,248)
(120,247)(121,246)(122,245)(123,244)(124,243)(125,242)(126,241)(127,240)
(128,239)(129,238)(130,237)(131,236)(132,235)(133,234)(134,233)(135,232)
(136,231)(137,230)(138,229)(139,228)(140,227)(141,226)(142,225)(143,224)
(144,223)(145,222)(146,221)(293,439)(294,511)(295,510)(296,509)(297,508)
(298,507)(299,506)(300,505)(301,504)(302,503)(303,502)(304,501)(305,500)
(306,499)(307,498)(308,497)(309,496)(310,495)(311,494)(312,493)(313,492)
(314,491)(315,490)(316,489)(317,488)(318,487)(319,486)(320,485)(321,484)
(322,483)(323,482)(324,481)(325,480)(326,479)(327,478)(328,477)(329,476)
(330,475)(331,474)(332,473)(333,472)(334,471)(335,470)(336,469)(337,468)
(338,467)(339,466)(340,465)(341,464)(342,463)(343,462)(344,461)(345,460)
(346,459)(347,458)(348,457)(349,456)(350,455)(351,454)(352,453)(353,452)
(354,451)(355,450)(356,449)(357,448)(358,447)(359,446)(360,445)(361,444)
(362,443)(363,442)(364,441)(365,440)(366,512)(367,584)(368,583)(369,582)
(370,581)(371,580)(372,579)(373,578)(374,577)(375,576)(376,575)(377,574)
(378,573)(379,572)(380,571)(381,570)(382,569)(383,568)(384,567)(385,566)
(386,565)(387,564)(388,563)(389,562)(390,561)(391,560)(392,559)(393,558)
(394,557)(395,556)(396,555)(397,554)(398,553)(399,552)(400,551)(401,550)
(402,549)(403,548)(404,547)(405,546)(406,545)(407,544)(408,543)(409,542)
(410,541)(411,540)(412,539)(413,538)(414,537)(415,536)(416,535)(417,534)
(418,533)(419,532)(420,531)(421,530)(422,529)(423,528)(424,527)(425,526)
(426,525)(427,524)(428,523)(429,522)(430,521)(431,520)(432,519)(433,518)
(434,517)(435,516)(436,515)(437,514)(438,513);
s1 := Sym(584)!( 1,148)( 2,147)( 3,219)( 4,218)( 5,217)( 6,216)( 7,215)
( 8,214)( 9,213)( 10,212)( 11,211)( 12,210)( 13,209)( 14,208)( 15,207)
( 16,206)( 17,205)( 18,204)( 19,203)( 20,202)( 21,201)( 22,200)( 23,199)
( 24,198)( 25,197)( 26,196)( 27,195)( 28,194)( 29,193)( 30,192)( 31,191)
( 32,190)( 33,189)( 34,188)( 35,187)( 36,186)( 37,185)( 38,184)( 39,183)
( 40,182)( 41,181)( 42,180)( 43,179)( 44,178)( 45,177)( 46,176)( 47,175)
( 48,174)( 49,173)( 50,172)( 51,171)( 52,170)( 53,169)( 54,168)( 55,167)
( 56,166)( 57,165)( 58,164)( 59,163)( 60,162)( 61,161)( 62,160)( 63,159)
( 64,158)( 65,157)( 66,156)( 67,155)( 68,154)( 69,153)( 70,152)( 71,151)
( 72,150)( 73,149)( 74,221)( 75,220)( 76,292)( 77,291)( 78,290)( 79,289)
( 80,288)( 81,287)( 82,286)( 83,285)( 84,284)( 85,283)( 86,282)( 87,281)
( 88,280)( 89,279)( 90,278)( 91,277)( 92,276)( 93,275)( 94,274)( 95,273)
( 96,272)( 97,271)( 98,270)( 99,269)(100,268)(101,267)(102,266)(103,265)
(104,264)(105,263)(106,262)(107,261)(108,260)(109,259)(110,258)(111,257)
(112,256)(113,255)(114,254)(115,253)(116,252)(117,251)(118,250)(119,249)
(120,248)(121,247)(122,246)(123,245)(124,244)(125,243)(126,242)(127,241)
(128,240)(129,239)(130,238)(131,237)(132,236)(133,235)(134,234)(135,233)
(136,232)(137,231)(138,230)(139,229)(140,228)(141,227)(142,226)(143,225)
(144,224)(145,223)(146,222)(293,513)(294,512)(295,584)(296,583)(297,582)
(298,581)(299,580)(300,579)(301,578)(302,577)(303,576)(304,575)(305,574)
(306,573)(307,572)(308,571)(309,570)(310,569)(311,568)(312,567)(313,566)
(314,565)(315,564)(316,563)(317,562)(318,561)(319,560)(320,559)(321,558)
(322,557)(323,556)(324,555)(325,554)(326,553)(327,552)(328,551)(329,550)
(330,549)(331,548)(332,547)(333,546)(334,545)(335,544)(336,543)(337,542)
(338,541)(339,540)(340,539)(341,538)(342,537)(343,536)(344,535)(345,534)
(346,533)(347,532)(348,531)(349,530)(350,529)(351,528)(352,527)(353,526)
(354,525)(355,524)(356,523)(357,522)(358,521)(359,520)(360,519)(361,518)
(362,517)(363,516)(364,515)(365,514)(366,440)(367,439)(368,511)(369,510)
(370,509)(371,508)(372,507)(373,506)(374,505)(375,504)(376,503)(377,502)
(378,501)(379,500)(380,499)(381,498)(382,497)(383,496)(384,495)(385,494)
(386,493)(387,492)(388,491)(389,490)(390,489)(391,488)(392,487)(393,486)
(394,485)(395,484)(396,483)(397,482)(398,481)(399,480)(400,479)(401,478)
(402,477)(403,476)(404,475)(405,474)(406,473)(407,472)(408,471)(409,470)
(410,469)(411,468)(412,467)(413,466)(414,465)(415,464)(416,463)(417,462)
(418,461)(419,460)(420,459)(421,458)(422,457)(423,456)(424,455)(425,454)
(426,453)(427,452)(428,451)(429,450)(430,449)(431,448)(432,447)(433,446)
(434,445)(435,444)(436,443)(437,442)(438,441);
s2 := Sym(584)!( 1,293)( 2,294)( 3,295)( 4,296)( 5,297)( 6,298)( 7,299)
( 8,300)( 9,301)( 10,302)( 11,303)( 12,304)( 13,305)( 14,306)( 15,307)
( 16,308)( 17,309)( 18,310)( 19,311)( 20,312)( 21,313)( 22,314)( 23,315)
( 24,316)( 25,317)( 26,318)( 27,319)( 28,320)( 29,321)( 30,322)( 31,323)
( 32,324)( 33,325)( 34,326)( 35,327)( 36,328)( 37,329)( 38,330)( 39,331)
( 40,332)( 41,333)( 42,334)( 43,335)( 44,336)( 45,337)( 46,338)( 47,339)
( 48,340)( 49,341)( 50,342)( 51,343)( 52,344)( 53,345)( 54,346)( 55,347)
( 56,348)( 57,349)( 58,350)( 59,351)( 60,352)( 61,353)( 62,354)( 63,355)
( 64,356)( 65,357)( 66,358)( 67,359)( 68,360)( 69,361)( 70,362)( 71,363)
( 72,364)( 73,365)( 74,366)( 75,367)( 76,368)( 77,369)( 78,370)( 79,371)
( 80,372)( 81,373)( 82,374)( 83,375)( 84,376)( 85,377)( 86,378)( 87,379)
( 88,380)( 89,381)( 90,382)( 91,383)( 92,384)( 93,385)( 94,386)( 95,387)
( 96,388)( 97,389)( 98,390)( 99,391)(100,392)(101,393)(102,394)(103,395)
(104,396)(105,397)(106,398)(107,399)(108,400)(109,401)(110,402)(111,403)
(112,404)(113,405)(114,406)(115,407)(116,408)(117,409)(118,410)(119,411)
(120,412)(121,413)(122,414)(123,415)(124,416)(125,417)(126,418)(127,419)
(128,420)(129,421)(130,422)(131,423)(132,424)(133,425)(134,426)(135,427)
(136,428)(137,429)(138,430)(139,431)(140,432)(141,433)(142,434)(143,435)
(144,436)(145,437)(146,438)(147,439)(148,440)(149,441)(150,442)(151,443)
(152,444)(153,445)(154,446)(155,447)(156,448)(157,449)(158,450)(159,451)
(160,452)(161,453)(162,454)(163,455)(164,456)(165,457)(166,458)(167,459)
(168,460)(169,461)(170,462)(171,463)(172,464)(173,465)(174,466)(175,467)
(176,468)(177,469)(178,470)(179,471)(180,472)(181,473)(182,474)(183,475)
(184,476)(185,477)(186,478)(187,479)(188,480)(189,481)(190,482)(191,483)
(192,484)(193,485)(194,486)(195,487)(196,488)(197,489)(198,490)(199,491)
(200,492)(201,493)(202,494)(203,495)(204,496)(205,497)(206,498)(207,499)
(208,500)(209,501)(210,502)(211,503)(212,504)(213,505)(214,506)(215,507)
(216,508)(217,509)(218,510)(219,511)(220,512)(221,513)(222,514)(223,515)
(224,516)(225,517)(226,518)(227,519)(228,520)(229,521)(230,522)(231,523)
(232,524)(233,525)(234,526)(235,527)(236,528)(237,529)(238,530)(239,531)
(240,532)(241,533)(242,534)(243,535)(244,536)(245,537)(246,538)(247,539)
(248,540)(249,541)(250,542)(251,543)(252,544)(253,545)(254,546)(255,547)
(256,548)(257,549)(258,550)(259,551)(260,552)(261,553)(262,554)(263,555)
(264,556)(265,557)(266,558)(267,559)(268,560)(269,561)(270,562)(271,563)
(272,564)(273,565)(274,566)(275,567)(276,568)(277,569)(278,570)(279,571)
(280,572)(281,573)(282,574)(283,575)(284,576)(285,577)(286,578)(287,579)
(288,580)(289,581)(290,582)(291,583)(292,584);
poly := sub<Sym(584)|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, 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*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