Polytope of Type {8,18}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,18}*1152d
if this polytope has a name.
Group : SmallGroup(1152,154283)
Rank : 3
Schlafli Type : {8,18}
Number of vertices, edges, etc : 32, 288, 72
Order of s₀s₁s₂ : 18
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 : {8,9}*576
   3-fold quotients : {8,6}*384e
   4-fold quotients : {4,18}*288
   6-fold quotients : {8,3}*192
   8-fold quotients : {4,9}*144, {4,18}*144b, {4,18}*144c
   12-fold quotients : {4,6}*96
   16-fold quotients : {4,9}*72, {2,18}*72
   24-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   32-fold quotients : {2,9}*36
   48-fold quotients : {4,3}*24, {2,6}*24
   96-fold quotients : {2,3}*12
   144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope