Polytope of Type {8,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,24}*1152a
if this polytope has a name.
Group : SmallGroup(1152,12919)
Rank : 3
Schlafli Type : {8,24}
Number of vertices, edges, etc : 24, 288, 72
Order of s₀s₁s₂ : 8
Order of s₀s₁s₂s₁ : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,24}*576a, {8,12}*576b
   4-fold quotients : {4,12}*288
   8-fold quotients : {4,6}*144
   9-fold quotients : {8,8}*128a
   16-fold quotients : {4,6}*72
   18-fold quotients : {4,8}*64a, {8,4}*64b
   36-fold quotients : {4,4}*32, {2,8}*32
   72-fold quotients : {2,4}*16, {4,2}*16
   144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope