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Polytope of Type {12,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,16}*1152a
if this polytope has a name.
Group : SmallGroup(1152,32085)
Rank : 3
Schlafli Type : {12,16}
Number of vertices, edges, etc : 36, 288, 48
Order of s0s1s2 : 16
Order of s0s1s2s1 : 6
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 : {6,16}*576, {12,8}*576a
   4-fold quotients : {6,8}*288, {12,4}*288
   8-fold quotients : {6,4}*144
   9-fold quotients : {4,16}*128a
   16-fold quotients : {6,4}*72
   18-fold quotients : {4,8}*64a, {2,16}*64
   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)(  4,151)(  5,153)(  6,152)(  7,148)(  8,150)
(  9,149)( 10,154)( 11,156)( 12,155)( 13,160)( 14,162)( 15,161)( 16,157)
( 17,159)( 18,158)( 19,163)( 20,165)( 21,164)( 22,169)( 23,171)( 24,170)
( 25,166)( 26,168)( 27,167)( 28,172)( 29,174)( 30,173)( 31,178)( 32,180)
( 33,179)( 34,175)( 35,177)( 36,176)( 37,181)( 38,183)( 39,182)( 40,187)
( 41,189)( 42,188)( 43,184)( 44,186)( 45,185)( 46,190)( 47,192)( 48,191)
( 49,196)( 50,198)( 51,197)( 52,193)( 53,195)( 54,194)( 55,199)( 56,201)
( 57,200)( 58,205)( 59,207)( 60,206)( 61,202)( 62,204)( 63,203)( 64,208)
( 65,210)( 66,209)( 67,214)( 68,216)( 69,215)( 70,211)( 71,213)( 72,212)
( 73,217)( 74,219)( 75,218)( 76,223)( 77,225)( 78,224)( 79,220)( 80,222)
( 81,221)( 82,226)( 83,228)( 84,227)( 85,232)( 86,234)( 87,233)( 88,229)
( 89,231)( 90,230)( 91,235)( 92,237)( 93,236)( 94,241)( 95,243)( 96,242)
( 97,238)( 98,240)( 99,239)(100,244)(101,246)(102,245)(103,250)(104,252)
(105,251)(106,247)(107,249)(108,248)(109,253)(110,255)(111,254)(112,259)
(113,261)(114,260)(115,256)(116,258)(117,257)(118,262)(119,264)(120,263)
(121,268)(122,270)(123,269)(124,265)(125,267)(126,266)(127,271)(128,273)
(129,272)(130,277)(131,279)(132,278)(133,274)(134,276)(135,275)(136,280)
(137,282)(138,281)(139,286)(140,288)(141,287)(142,283)(143,285)(144,284)
(289,433)(290,435)(291,434)(292,439)(293,441)(294,440)(295,436)(296,438)
(297,437)(298,442)(299,444)(300,443)(301,448)(302,450)(303,449)(304,445)
(305,447)(306,446)(307,451)(308,453)(309,452)(310,457)(311,459)(312,458)
(313,454)(314,456)(315,455)(316,460)(317,462)(318,461)(319,466)(320,468)
(321,467)(322,463)(323,465)(324,464)(325,469)(326,471)(327,470)(328,475)
(329,477)(330,476)(331,472)(332,474)(333,473)(334,478)(335,480)(336,479)
(337,484)(338,486)(339,485)(340,481)(341,483)(342,482)(343,487)(344,489)
(345,488)(346,493)(347,495)(348,494)(349,490)(350,492)(351,491)(352,496)
(353,498)(354,497)(355,502)(356,504)(357,503)(358,499)(359,501)(360,500)
(361,505)(362,507)(363,506)(364,511)(365,513)(366,512)(367,508)(368,510)
(369,509)(370,514)(371,516)(372,515)(373,520)(374,522)(375,521)(376,517)
(377,519)(378,518)(379,523)(380,525)(381,524)(382,529)(383,531)(384,530)
(385,526)(386,528)(387,527)(388,532)(389,534)(390,533)(391,538)(392,540)
(393,539)(394,535)(395,537)(396,536)(397,541)(398,543)(399,542)(400,547)
(401,549)(402,548)(403,544)(404,546)(405,545)(406,550)(407,552)(408,551)
(409,556)(410,558)(411,557)(412,553)(413,555)(414,554)(415,559)(416,561)
(417,560)(418,565)(419,567)(420,566)(421,562)(422,564)(423,563)(424,568)
(425,570)(426,569)(427,574)(428,576)(429,575)(430,571)(431,573)(432,572);;
s1 := (  1, 76)(  2, 74)(  3, 81)(  4, 73)(  5, 80)(  6, 78)(  7, 79)(  8, 77)
(  9, 75)( 10, 85)( 11, 83)( 12, 90)( 13, 82)( 14, 89)( 15, 87)( 16, 88)
( 17, 86)( 18, 84)( 19,103)( 20,101)( 21,108)( 22,100)( 23,107)( 24,105)
( 25,106)( 26,104)( 27,102)( 28, 94)( 29, 92)( 30, 99)( 31, 91)( 32, 98)
( 33, 96)( 34, 97)( 35, 95)( 36, 93)( 37,112)( 38,110)( 39,117)( 40,109)
( 41,116)( 42,114)( 43,115)( 44,113)( 45,111)( 46,121)( 47,119)( 48,126)
( 49,118)( 50,125)( 51,123)( 52,124)( 53,122)( 54,120)( 55,139)( 56,137)
( 57,144)( 58,136)( 59,143)( 60,141)( 61,142)( 62,140)( 63,138)( 64,130)
( 65,128)( 66,135)( 67,127)( 68,134)( 69,132)( 70,133)( 71,131)( 72,129)
(145,256)(146,254)(147,261)(148,253)(149,260)(150,258)(151,259)(152,257)
(153,255)(154,265)(155,263)(156,270)(157,262)(158,269)(159,267)(160,268)
(161,266)(162,264)(163,283)(164,281)(165,288)(166,280)(167,287)(168,285)
(169,286)(170,284)(171,282)(172,274)(173,272)(174,279)(175,271)(176,278)
(177,276)(178,277)(179,275)(180,273)(181,220)(182,218)(183,225)(184,217)
(185,224)(186,222)(187,223)(188,221)(189,219)(190,229)(191,227)(192,234)
(193,226)(194,233)(195,231)(196,232)(197,230)(198,228)(199,247)(200,245)
(201,252)(202,244)(203,251)(204,249)(205,250)(206,248)(207,246)(208,238)
(209,236)(210,243)(211,235)(212,242)(213,240)(214,241)(215,239)(216,237)
(289,319)(290,317)(291,324)(292,316)(293,323)(294,321)(295,322)(296,320)
(297,318)(298,310)(299,308)(300,315)(301,307)(302,314)(303,312)(304,313)
(305,311)(306,309)(325,355)(326,353)(327,360)(328,352)(329,359)(330,357)
(331,358)(332,356)(333,354)(334,346)(335,344)(336,351)(337,343)(338,350)
(339,348)(340,349)(341,347)(342,345)(361,364)(363,369)(365,368)(370,373)
(372,378)(374,377)(379,391)(380,389)(381,396)(382,388)(383,395)(384,393)
(385,394)(386,392)(387,390)(397,400)(399,405)(401,404)(406,409)(408,414)
(410,413)(415,427)(416,425)(417,432)(418,424)(419,431)(420,429)(421,430)
(422,428)(423,426)(433,499)(434,497)(435,504)(436,496)(437,503)(438,501)
(439,502)(440,500)(441,498)(442,490)(443,488)(444,495)(445,487)(446,494)
(447,492)(448,493)(449,491)(450,489)(451,481)(452,479)(453,486)(454,478)
(455,485)(456,483)(457,484)(458,482)(459,480)(460,472)(461,470)(462,477)
(463,469)(464,476)(465,474)(466,475)(467,473)(468,471)(505,544)(506,542)
(507,549)(508,541)(509,548)(510,546)(511,547)(512,545)(513,543)(514,553)
(515,551)(516,558)(517,550)(518,557)(519,555)(520,556)(521,554)(522,552)
(523,571)(524,569)(525,576)(526,568)(527,575)(528,573)(529,574)(530,572)
(531,570)(532,562)(533,560)(534,567)(535,559)(536,566)(537,564)(538,565)
(539,563)(540,561);;
s2 := (  1,289)(  2,291)(  3,290)(  4,293)(  5,292)(  6,294)(  7,297)(  8,296)
(  9,295)( 10,298)( 11,300)( 12,299)( 13,302)( 14,301)( 15,303)( 16,306)
( 17,305)( 18,304)( 19,316)( 20,318)( 21,317)( 22,320)( 23,319)( 24,321)
( 25,324)( 26,323)( 27,322)( 28,307)( 29,309)( 30,308)( 31,311)( 32,310)
( 33,312)( 34,315)( 35,314)( 36,313)( 37,325)( 38,327)( 39,326)( 40,329)
( 41,328)( 42,330)( 43,333)( 44,332)( 45,331)( 46,334)( 47,336)( 48,335)
( 49,338)( 50,337)( 51,339)( 52,342)( 53,341)( 54,340)( 55,352)( 56,354)
( 57,353)( 58,356)( 59,355)( 60,357)( 61,360)( 62,359)( 63,358)( 64,343)
( 65,345)( 66,344)( 67,347)( 68,346)( 69,348)( 70,351)( 71,350)( 72,349)
( 73,379)( 74,381)( 75,380)( 76,383)( 77,382)( 78,384)( 79,387)( 80,386)
( 81,385)( 82,388)( 83,390)( 84,389)( 85,392)( 86,391)( 87,393)( 88,396)
( 89,395)( 90,394)( 91,361)( 92,363)( 93,362)( 94,365)( 95,364)( 96,366)
( 97,369)( 98,368)( 99,367)(100,370)(101,372)(102,371)(103,374)(104,373)
(105,375)(106,378)(107,377)(108,376)(109,415)(110,417)(111,416)(112,419)
(113,418)(114,420)(115,423)(116,422)(117,421)(118,424)(119,426)(120,425)
(121,428)(122,427)(123,429)(124,432)(125,431)(126,430)(127,397)(128,399)
(129,398)(130,401)(131,400)(132,402)(133,405)(134,404)(135,403)(136,406)
(137,408)(138,407)(139,410)(140,409)(141,411)(142,414)(143,413)(144,412)
(145,433)(146,435)(147,434)(148,437)(149,436)(150,438)(151,441)(152,440)
(153,439)(154,442)(155,444)(156,443)(157,446)(158,445)(159,447)(160,450)
(161,449)(162,448)(163,460)(164,462)(165,461)(166,464)(167,463)(168,465)
(169,468)(170,467)(171,466)(172,451)(173,453)(174,452)(175,455)(176,454)
(177,456)(178,459)(179,458)(180,457)(181,469)(182,471)(183,470)(184,473)
(185,472)(186,474)(187,477)(188,476)(189,475)(190,478)(191,480)(192,479)
(193,482)(194,481)(195,483)(196,486)(197,485)(198,484)(199,496)(200,498)
(201,497)(202,500)(203,499)(204,501)(205,504)(206,503)(207,502)(208,487)
(209,489)(210,488)(211,491)(212,490)(213,492)(214,495)(215,494)(216,493)
(217,523)(218,525)(219,524)(220,527)(221,526)(222,528)(223,531)(224,530)
(225,529)(226,532)(227,534)(228,533)(229,536)(230,535)(231,537)(232,540)
(233,539)(234,538)(235,505)(236,507)(237,506)(238,509)(239,508)(240,510)
(241,513)(242,512)(243,511)(244,514)(245,516)(246,515)(247,518)(248,517)
(249,519)(250,522)(251,521)(252,520)(253,559)(254,561)(255,560)(256,563)
(257,562)(258,564)(259,567)(260,566)(261,565)(262,568)(263,570)(264,569)
(265,572)(266,571)(267,573)(268,576)(269,575)(270,574)(271,541)(272,543)
(273,542)(274,545)(275,544)(276,546)(277,549)(278,548)(279,547)(280,550)
(281,552)(282,551)(283,554)(284,553)(285,555)(286,558)(287,557)(288,556);;
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, s2*s0*s1*s2*s0*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*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(576)!(  1,145)(  2,147)(  3,146)(  4,151)(  5,153)(  6,152)(  7,148)
(  8,150)(  9,149)( 10,154)( 11,156)( 12,155)( 13,160)( 14,162)( 15,161)
( 16,157)( 17,159)( 18,158)( 19,163)( 20,165)( 21,164)( 22,169)( 23,171)
( 24,170)( 25,166)( 26,168)( 27,167)( 28,172)( 29,174)( 30,173)( 31,178)
( 32,180)( 33,179)( 34,175)( 35,177)( 36,176)( 37,181)( 38,183)( 39,182)
( 40,187)( 41,189)( 42,188)( 43,184)( 44,186)( 45,185)( 46,190)( 47,192)
( 48,191)( 49,196)( 50,198)( 51,197)( 52,193)( 53,195)( 54,194)( 55,199)
( 56,201)( 57,200)( 58,205)( 59,207)( 60,206)( 61,202)( 62,204)( 63,203)
( 64,208)( 65,210)( 66,209)( 67,214)( 68,216)( 69,215)( 70,211)( 71,213)
( 72,212)( 73,217)( 74,219)( 75,218)( 76,223)( 77,225)( 78,224)( 79,220)
( 80,222)( 81,221)( 82,226)( 83,228)( 84,227)( 85,232)( 86,234)( 87,233)
( 88,229)( 89,231)( 90,230)( 91,235)( 92,237)( 93,236)( 94,241)( 95,243)
( 96,242)( 97,238)( 98,240)( 99,239)(100,244)(101,246)(102,245)(103,250)
(104,252)(105,251)(106,247)(107,249)(108,248)(109,253)(110,255)(111,254)
(112,259)(113,261)(114,260)(115,256)(116,258)(117,257)(118,262)(119,264)
(120,263)(121,268)(122,270)(123,269)(124,265)(125,267)(126,266)(127,271)
(128,273)(129,272)(130,277)(131,279)(132,278)(133,274)(134,276)(135,275)
(136,280)(137,282)(138,281)(139,286)(140,288)(141,287)(142,283)(143,285)
(144,284)(289,433)(290,435)(291,434)(292,439)(293,441)(294,440)(295,436)
(296,438)(297,437)(298,442)(299,444)(300,443)(301,448)(302,450)(303,449)
(304,445)(305,447)(306,446)(307,451)(308,453)(309,452)(310,457)(311,459)
(312,458)(313,454)(314,456)(315,455)(316,460)(317,462)(318,461)(319,466)
(320,468)(321,467)(322,463)(323,465)(324,464)(325,469)(326,471)(327,470)
(328,475)(329,477)(330,476)(331,472)(332,474)(333,473)(334,478)(335,480)
(336,479)(337,484)(338,486)(339,485)(340,481)(341,483)(342,482)(343,487)
(344,489)(345,488)(346,493)(347,495)(348,494)(349,490)(350,492)(351,491)
(352,496)(353,498)(354,497)(355,502)(356,504)(357,503)(358,499)(359,501)
(360,500)(361,505)(362,507)(363,506)(364,511)(365,513)(366,512)(367,508)
(368,510)(369,509)(370,514)(371,516)(372,515)(373,520)(374,522)(375,521)
(376,517)(377,519)(378,518)(379,523)(380,525)(381,524)(382,529)(383,531)
(384,530)(385,526)(386,528)(387,527)(388,532)(389,534)(390,533)(391,538)
(392,540)(393,539)(394,535)(395,537)(396,536)(397,541)(398,543)(399,542)
(400,547)(401,549)(402,548)(403,544)(404,546)(405,545)(406,550)(407,552)
(408,551)(409,556)(410,558)(411,557)(412,553)(413,555)(414,554)(415,559)
(416,561)(417,560)(418,565)(419,567)(420,566)(421,562)(422,564)(423,563)
(424,568)(425,570)(426,569)(427,574)(428,576)(429,575)(430,571)(431,573)
(432,572);
s1 := Sym(576)!(  1, 76)(  2, 74)(  3, 81)(  4, 73)(  5, 80)(  6, 78)(  7, 79)
(  8, 77)(  9, 75)( 10, 85)( 11, 83)( 12, 90)( 13, 82)( 14, 89)( 15, 87)
( 16, 88)( 17, 86)( 18, 84)( 19,103)( 20,101)( 21,108)( 22,100)( 23,107)
( 24,105)( 25,106)( 26,104)( 27,102)( 28, 94)( 29, 92)( 30, 99)( 31, 91)
( 32, 98)( 33, 96)( 34, 97)( 35, 95)( 36, 93)( 37,112)( 38,110)( 39,117)
( 40,109)( 41,116)( 42,114)( 43,115)( 44,113)( 45,111)( 46,121)( 47,119)
( 48,126)( 49,118)( 50,125)( 51,123)( 52,124)( 53,122)( 54,120)( 55,139)
( 56,137)( 57,144)( 58,136)( 59,143)( 60,141)( 61,142)( 62,140)( 63,138)
( 64,130)( 65,128)( 66,135)( 67,127)( 68,134)( 69,132)( 70,133)( 71,131)
( 72,129)(145,256)(146,254)(147,261)(148,253)(149,260)(150,258)(151,259)
(152,257)(153,255)(154,265)(155,263)(156,270)(157,262)(158,269)(159,267)
(160,268)(161,266)(162,264)(163,283)(164,281)(165,288)(166,280)(167,287)
(168,285)(169,286)(170,284)(171,282)(172,274)(173,272)(174,279)(175,271)
(176,278)(177,276)(178,277)(179,275)(180,273)(181,220)(182,218)(183,225)
(184,217)(185,224)(186,222)(187,223)(188,221)(189,219)(190,229)(191,227)
(192,234)(193,226)(194,233)(195,231)(196,232)(197,230)(198,228)(199,247)
(200,245)(201,252)(202,244)(203,251)(204,249)(205,250)(206,248)(207,246)
(208,238)(209,236)(210,243)(211,235)(212,242)(213,240)(214,241)(215,239)
(216,237)(289,319)(290,317)(291,324)(292,316)(293,323)(294,321)(295,322)
(296,320)(297,318)(298,310)(299,308)(300,315)(301,307)(302,314)(303,312)
(304,313)(305,311)(306,309)(325,355)(326,353)(327,360)(328,352)(329,359)
(330,357)(331,358)(332,356)(333,354)(334,346)(335,344)(336,351)(337,343)
(338,350)(339,348)(340,349)(341,347)(342,345)(361,364)(363,369)(365,368)
(370,373)(372,378)(374,377)(379,391)(380,389)(381,396)(382,388)(383,395)
(384,393)(385,394)(386,392)(387,390)(397,400)(399,405)(401,404)(406,409)
(408,414)(410,413)(415,427)(416,425)(417,432)(418,424)(419,431)(420,429)
(421,430)(422,428)(423,426)(433,499)(434,497)(435,504)(436,496)(437,503)
(438,501)(439,502)(440,500)(441,498)(442,490)(443,488)(444,495)(445,487)
(446,494)(447,492)(448,493)(449,491)(450,489)(451,481)(452,479)(453,486)
(454,478)(455,485)(456,483)(457,484)(458,482)(459,480)(460,472)(461,470)
(462,477)(463,469)(464,476)(465,474)(466,475)(467,473)(468,471)(505,544)
(506,542)(507,549)(508,541)(509,548)(510,546)(511,547)(512,545)(513,543)
(514,553)(515,551)(516,558)(517,550)(518,557)(519,555)(520,556)(521,554)
(522,552)(523,571)(524,569)(525,576)(526,568)(527,575)(528,573)(529,574)
(530,572)(531,570)(532,562)(533,560)(534,567)(535,559)(536,566)(537,564)
(538,565)(539,563)(540,561);
s2 := Sym(576)!(  1,289)(  2,291)(  3,290)(  4,293)(  5,292)(  6,294)(  7,297)
(  8,296)(  9,295)( 10,298)( 11,300)( 12,299)( 13,302)( 14,301)( 15,303)
( 16,306)( 17,305)( 18,304)( 19,316)( 20,318)( 21,317)( 22,320)( 23,319)
( 24,321)( 25,324)( 26,323)( 27,322)( 28,307)( 29,309)( 30,308)( 31,311)
( 32,310)( 33,312)( 34,315)( 35,314)( 36,313)( 37,325)( 38,327)( 39,326)
( 40,329)( 41,328)( 42,330)( 43,333)( 44,332)( 45,331)( 46,334)( 47,336)
( 48,335)( 49,338)( 50,337)( 51,339)( 52,342)( 53,341)( 54,340)( 55,352)
( 56,354)( 57,353)( 58,356)( 59,355)( 60,357)( 61,360)( 62,359)( 63,358)
( 64,343)( 65,345)( 66,344)( 67,347)( 68,346)( 69,348)( 70,351)( 71,350)
( 72,349)( 73,379)( 74,381)( 75,380)( 76,383)( 77,382)( 78,384)( 79,387)
( 80,386)( 81,385)( 82,388)( 83,390)( 84,389)( 85,392)( 86,391)( 87,393)
( 88,396)( 89,395)( 90,394)( 91,361)( 92,363)( 93,362)( 94,365)( 95,364)
( 96,366)( 97,369)( 98,368)( 99,367)(100,370)(101,372)(102,371)(103,374)
(104,373)(105,375)(106,378)(107,377)(108,376)(109,415)(110,417)(111,416)
(112,419)(113,418)(114,420)(115,423)(116,422)(117,421)(118,424)(119,426)
(120,425)(121,428)(122,427)(123,429)(124,432)(125,431)(126,430)(127,397)
(128,399)(129,398)(130,401)(131,400)(132,402)(133,405)(134,404)(135,403)
(136,406)(137,408)(138,407)(139,410)(140,409)(141,411)(142,414)(143,413)
(144,412)(145,433)(146,435)(147,434)(148,437)(149,436)(150,438)(151,441)
(152,440)(153,439)(154,442)(155,444)(156,443)(157,446)(158,445)(159,447)
(160,450)(161,449)(162,448)(163,460)(164,462)(165,461)(166,464)(167,463)
(168,465)(169,468)(170,467)(171,466)(172,451)(173,453)(174,452)(175,455)
(176,454)(177,456)(178,459)(179,458)(180,457)(181,469)(182,471)(183,470)
(184,473)(185,472)(186,474)(187,477)(188,476)(189,475)(190,478)(191,480)
(192,479)(193,482)(194,481)(195,483)(196,486)(197,485)(198,484)(199,496)
(200,498)(201,497)(202,500)(203,499)(204,501)(205,504)(206,503)(207,502)
(208,487)(209,489)(210,488)(211,491)(212,490)(213,492)(214,495)(215,494)
(216,493)(217,523)(218,525)(219,524)(220,527)(221,526)(222,528)(223,531)
(224,530)(225,529)(226,532)(227,534)(228,533)(229,536)(230,535)(231,537)
(232,540)(233,539)(234,538)(235,505)(236,507)(237,506)(238,509)(239,508)
(240,510)(241,513)(242,512)(243,511)(244,514)(245,516)(246,515)(247,518)
(248,517)(249,519)(250,522)(251,521)(252,520)(253,559)(254,561)(255,560)
(256,563)(257,562)(258,564)(259,567)(260,566)(261,565)(262,568)(263,570)
(264,569)(265,572)(266,571)(267,573)(268,576)(269,575)(270,574)(271,541)
(272,543)(273,542)(274,545)(275,544)(276,546)(277,549)(278,548)(279,547)
(280,550)(281,552)(282,551)(283,554)(284,553)(285,555)(286,558)(287,557)
(288,556);
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, s2*s0*s1*s2*s0*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*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*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 >; 
 
References : None.
to this polytope