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Polytope of Type {4,12,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,4}*1152a
if this polytope has a name.
Group : SmallGroup(1152,43028)
Rank : 4
Schlafli Type : {4,12,4}
Number of vertices, edges, etc : 4, 72, 72, 12
Order of s0s1s2s3 : 4
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   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 : {4,6,4}*576b, {2,12,4}*576
   4-fold quotients : {2,6,4}*288
   8-fold quotients : {2,6,4}*144
   9-fold quotients : {4,4,4}*128
   18-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64
   36-fold quotients : {2,2,4}*32, {2,4,2}*32, {4,2,2}*32
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1, 73)(  2, 74)(  3, 75)(  4, 76)(  5, 77)(  6, 78)(  7, 79)(  8, 80)
(  9, 81)( 10, 82)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)( 16, 88)
( 17, 89)( 18, 90)( 19, 91)( 20, 92)( 21, 93)( 22, 94)( 23, 95)( 24, 96)
( 25, 97)( 26, 98)( 27, 99)( 28,100)( 29,101)( 30,102)( 31,103)( 32,104)
( 33,105)( 34,106)( 35,107)( 36,108)( 37,109)( 38,110)( 39,111)( 40,112)
( 41,113)( 42,114)( 43,115)( 44,116)( 45,117)( 46,118)( 47,119)( 48,120)
( 49,121)( 50,122)( 51,123)( 52,124)( 53,125)( 54,126)( 55,127)( 56,128)
( 57,129)( 58,130)( 59,131)( 60,132)( 61,133)( 62,134)( 63,135)( 64,136)
( 65,137)( 66,138)( 67,139)( 68,140)( 69,141)( 70,142)( 71,143)( 72,144)
(145,217)(146,218)(147,219)(148,220)(149,221)(150,222)(151,223)(152,224)
(153,225)(154,226)(155,227)(156,228)(157,229)(158,230)(159,231)(160,232)
(161,233)(162,234)(163,235)(164,236)(165,237)(166,238)(167,239)(168,240)
(169,241)(170,242)(171,243)(172,244)(173,245)(174,246)(175,247)(176,248)
(177,249)(178,250)(179,251)(180,252)(181,253)(182,254)(183,255)(184,256)
(185,257)(186,258)(187,259)(188,260)(189,261)(190,262)(191,263)(192,264)
(193,265)(194,266)(195,267)(196,268)(197,269)(198,270)(199,271)(200,272)
(201,273)(202,274)(203,275)(204,276)(205,277)(206,278)(207,279)(208,280)
(209,281)(210,282)(211,283)(212,284)(213,285)(214,286)(215,287)(216,288)
(289,361)(290,362)(291,363)(292,364)(293,365)(294,366)(295,367)(296,368)
(297,369)(298,370)(299,371)(300,372)(301,373)(302,374)(303,375)(304,376)
(305,377)(306,378)(307,379)(308,380)(309,381)(310,382)(311,383)(312,384)
(313,385)(314,386)(315,387)(316,388)(317,389)(318,390)(319,391)(320,392)
(321,393)(322,394)(323,395)(324,396)(325,397)(326,398)(327,399)(328,400)
(329,401)(330,402)(331,403)(332,404)(333,405)(334,406)(335,407)(336,408)
(337,409)(338,410)(339,411)(340,412)(341,413)(342,414)(343,415)(344,416)
(345,417)(346,418)(347,419)(348,420)(349,421)(350,422)(351,423)(352,424)
(353,425)(354,426)(355,427)(356,428)(357,429)(358,430)(359,431)(360,432)
(433,505)(434,506)(435,507)(436,508)(437,509)(438,510)(439,511)(440,512)
(441,513)(442,514)(443,515)(444,516)(445,517)(446,518)(447,519)(448,520)
(449,521)(450,522)(451,523)(452,524)(453,525)(454,526)(455,527)(456,528)
(457,529)(458,530)(459,531)(460,532)(461,533)(462,534)(463,535)(464,536)
(465,537)(466,538)(467,539)(468,540)(469,541)(470,542)(471,543)(472,544)
(473,545)(474,546)(475,547)(476,548)(477,549)(478,550)(479,551)(480,552)
(481,553)(482,554)(483,555)(484,556)(485,557)(486,558)(487,559)(488,560)
(489,561)(490,562)(491,563)(492,564)(493,565)(494,566)(495,567)(496,568)
(497,569)(498,570)(499,571)(500,572)(501,573)(502,574)(503,575)(504,576);;
s1 := (  1, 10)(  2, 12)(  3, 11)(  4, 16)(  5, 18)(  6, 17)(  7, 13)(  8, 15)
(  9, 14)( 19, 28)( 20, 30)( 21, 29)( 22, 34)( 23, 36)( 24, 35)( 25, 31)
( 26, 33)( 27, 32)( 37, 46)( 38, 48)( 39, 47)( 40, 52)( 41, 54)( 42, 53)
( 43, 49)( 44, 51)( 45, 50)( 55, 64)( 56, 66)( 57, 65)( 58, 70)( 59, 72)
( 60, 71)( 61, 67)( 62, 69)( 63, 68)( 73,118)( 74,120)( 75,119)( 76,124)
( 77,126)( 78,125)( 79,121)( 80,123)( 81,122)( 82,109)( 83,111)( 84,110)
( 85,115)( 86,117)( 87,116)( 88,112)( 89,114)( 90,113)( 91,136)( 92,138)
( 93,137)( 94,142)( 95,144)( 96,143)( 97,139)( 98,141)( 99,140)(100,127)
(101,129)(102,128)(103,133)(104,135)(105,134)(106,130)(107,132)(108,131)
(145,172)(146,174)(147,173)(148,178)(149,180)(150,179)(151,175)(152,177)
(153,176)(154,163)(155,165)(156,164)(157,169)(158,171)(159,170)(160,166)
(161,168)(162,167)(181,208)(182,210)(183,209)(184,214)(185,216)(186,215)
(187,211)(188,213)(189,212)(190,199)(191,201)(192,200)(193,205)(194,207)
(195,206)(196,202)(197,204)(198,203)(217,280)(218,282)(219,281)(220,286)
(221,288)(222,287)(223,283)(224,285)(225,284)(226,271)(227,273)(228,272)
(229,277)(230,279)(231,278)(232,274)(233,276)(234,275)(235,262)(236,264)
(237,263)(238,268)(239,270)(240,269)(241,265)(242,267)(243,266)(244,253)
(245,255)(246,254)(247,259)(248,261)(249,260)(250,256)(251,258)(252,257)
(289,334)(290,336)(291,335)(292,340)(293,342)(294,341)(295,337)(296,339)
(297,338)(298,325)(299,327)(300,326)(301,331)(302,333)(303,332)(304,328)
(305,330)(306,329)(307,352)(308,354)(309,353)(310,358)(311,360)(312,359)
(313,355)(314,357)(315,356)(316,343)(317,345)(318,344)(319,349)(320,351)
(321,350)(322,346)(323,348)(324,347)(361,370)(362,372)(363,371)(364,376)
(365,378)(366,377)(367,373)(368,375)(369,374)(379,388)(380,390)(381,389)
(382,394)(383,396)(384,395)(385,391)(386,393)(387,392)(397,406)(398,408)
(399,407)(400,412)(401,414)(402,413)(403,409)(404,411)(405,410)(415,424)
(416,426)(417,425)(418,430)(419,432)(420,431)(421,427)(422,429)(423,428)
(433,496)(434,498)(435,497)(436,502)(437,504)(438,503)(439,499)(440,501)
(441,500)(442,487)(443,489)(444,488)(445,493)(446,495)(447,494)(448,490)
(449,492)(450,491)(451,478)(452,480)(453,479)(454,484)(455,486)(456,485)
(457,481)(458,483)(459,482)(460,469)(461,471)(462,470)(463,475)(464,477)
(465,476)(466,472)(467,474)(468,473)(505,532)(506,534)(507,533)(508,538)
(509,540)(510,539)(511,535)(512,537)(513,536)(514,523)(515,525)(516,524)
(517,529)(518,531)(519,530)(520,526)(521,528)(522,527)(541,568)(542,570)
(543,569)(544,574)(545,576)(546,575)(547,571)(548,573)(549,572)(550,559)
(551,561)(552,560)(553,565)(554,567)(555,566)(556,562)(557,564)(558,563);;
s2 := (  1,146)(  2,145)(  3,147)(  4,150)(  5,149)(  6,148)(  7,151)(  8,153)
(  9,152)( 10,155)( 11,154)( 12,156)( 13,159)( 14,158)( 15,157)( 16,160)
( 17,162)( 18,161)( 19,164)( 20,163)( 21,165)( 22,168)( 23,167)( 24,166)
( 25,169)( 26,171)( 27,170)( 28,173)( 29,172)( 30,174)( 31,177)( 32,176)
( 33,175)( 34,178)( 35,180)( 36,179)( 37,182)( 38,181)( 39,183)( 40,186)
( 41,185)( 42,184)( 43,187)( 44,189)( 45,188)( 46,191)( 47,190)( 48,192)
( 49,195)( 50,194)( 51,193)( 52,196)( 53,198)( 54,197)( 55,200)( 56,199)
( 57,201)( 58,204)( 59,203)( 60,202)( 61,205)( 62,207)( 63,206)( 64,209)
( 65,208)( 66,210)( 67,213)( 68,212)( 69,211)( 70,214)( 71,216)( 72,215)
( 73,218)( 74,217)( 75,219)( 76,222)( 77,221)( 78,220)( 79,223)( 80,225)
( 81,224)( 82,227)( 83,226)( 84,228)( 85,231)( 86,230)( 87,229)( 88,232)
( 89,234)( 90,233)( 91,236)( 92,235)( 93,237)( 94,240)( 95,239)( 96,238)
( 97,241)( 98,243)( 99,242)(100,245)(101,244)(102,246)(103,249)(104,248)
(105,247)(106,250)(107,252)(108,251)(109,254)(110,253)(111,255)(112,258)
(113,257)(114,256)(115,259)(116,261)(117,260)(118,263)(119,262)(120,264)
(121,267)(122,266)(123,265)(124,268)(125,270)(126,269)(127,272)(128,271)
(129,273)(130,276)(131,275)(132,274)(133,277)(134,279)(135,278)(136,281)
(137,280)(138,282)(139,285)(140,284)(141,283)(142,286)(143,288)(144,287)
(289,434)(290,433)(291,435)(292,438)(293,437)(294,436)(295,439)(296,441)
(297,440)(298,443)(299,442)(300,444)(301,447)(302,446)(303,445)(304,448)
(305,450)(306,449)(307,452)(308,451)(309,453)(310,456)(311,455)(312,454)
(313,457)(314,459)(315,458)(316,461)(317,460)(318,462)(319,465)(320,464)
(321,463)(322,466)(323,468)(324,467)(325,470)(326,469)(327,471)(328,474)
(329,473)(330,472)(331,475)(332,477)(333,476)(334,479)(335,478)(336,480)
(337,483)(338,482)(339,481)(340,484)(341,486)(342,485)(343,488)(344,487)
(345,489)(346,492)(347,491)(348,490)(349,493)(350,495)(351,494)(352,497)
(353,496)(354,498)(355,501)(356,500)(357,499)(358,502)(359,504)(360,503)
(361,506)(362,505)(363,507)(364,510)(365,509)(366,508)(367,511)(368,513)
(369,512)(370,515)(371,514)(372,516)(373,519)(374,518)(375,517)(376,520)
(377,522)(378,521)(379,524)(380,523)(381,525)(382,528)(383,527)(384,526)
(385,529)(386,531)(387,530)(388,533)(389,532)(390,534)(391,537)(392,536)
(393,535)(394,538)(395,540)(396,539)(397,542)(398,541)(399,543)(400,546)
(401,545)(402,544)(403,547)(404,549)(405,548)(406,551)(407,550)(408,552)
(409,555)(410,554)(411,553)(412,556)(413,558)(414,557)(415,560)(416,559)
(417,561)(418,564)(419,563)(420,562)(421,565)(422,567)(423,566)(424,569)
(425,568)(426,570)(427,573)(428,572)(429,571)(430,574)(431,576)(432,575);;
s3 := (  1,361)(  2,366)(  3,368)(  4,364)(  5,369)(  6,362)(  7,367)(  8,363)
(  9,365)( 10,370)( 11,375)( 12,377)( 13,373)( 14,378)( 15,371)( 16,376)
( 17,372)( 18,374)( 19,379)( 20,384)( 21,386)( 22,382)( 23,387)( 24,380)
( 25,385)( 26,381)( 27,383)( 28,388)( 29,393)( 30,395)( 31,391)( 32,396)
( 33,389)( 34,394)( 35,390)( 36,392)( 37,397)( 38,402)( 39,404)( 40,400)
( 41,405)( 42,398)( 43,403)( 44,399)( 45,401)( 46,406)( 47,411)( 48,413)
( 49,409)( 50,414)( 51,407)( 52,412)( 53,408)( 54,410)( 55,415)( 56,420)
( 57,422)( 58,418)( 59,423)( 60,416)( 61,421)( 62,417)( 63,419)( 64,424)
( 65,429)( 66,431)( 67,427)( 68,432)( 69,425)( 70,430)( 71,426)( 72,428)
( 73,289)( 74,294)( 75,296)( 76,292)( 77,297)( 78,290)( 79,295)( 80,291)
( 81,293)( 82,298)( 83,303)( 84,305)( 85,301)( 86,306)( 87,299)( 88,304)
( 89,300)( 90,302)( 91,307)( 92,312)( 93,314)( 94,310)( 95,315)( 96,308)
( 97,313)( 98,309)( 99,311)(100,316)(101,321)(102,323)(103,319)(104,324)
(105,317)(106,322)(107,318)(108,320)(109,325)(110,330)(111,332)(112,328)
(113,333)(114,326)(115,331)(116,327)(117,329)(118,334)(119,339)(120,341)
(121,337)(122,342)(123,335)(124,340)(125,336)(126,338)(127,343)(128,348)
(129,350)(130,346)(131,351)(132,344)(133,349)(134,345)(135,347)(136,352)
(137,357)(138,359)(139,355)(140,360)(141,353)(142,358)(143,354)(144,356)
(145,514)(146,519)(147,521)(148,517)(149,522)(150,515)(151,520)(152,516)
(153,518)(154,505)(155,510)(156,512)(157,508)(158,513)(159,506)(160,511)
(161,507)(162,509)(163,532)(164,537)(165,539)(166,535)(167,540)(168,533)
(169,538)(170,534)(171,536)(172,523)(173,528)(174,530)(175,526)(176,531)
(177,524)(178,529)(179,525)(180,527)(181,550)(182,555)(183,557)(184,553)
(185,558)(186,551)(187,556)(188,552)(189,554)(190,541)(191,546)(192,548)
(193,544)(194,549)(195,542)(196,547)(197,543)(198,545)(199,568)(200,573)
(201,575)(202,571)(203,576)(204,569)(205,574)(206,570)(207,572)(208,559)
(209,564)(210,566)(211,562)(212,567)(213,560)(214,565)(215,561)(216,563)
(217,442)(218,447)(219,449)(220,445)(221,450)(222,443)(223,448)(224,444)
(225,446)(226,433)(227,438)(228,440)(229,436)(230,441)(231,434)(232,439)
(233,435)(234,437)(235,460)(236,465)(237,467)(238,463)(239,468)(240,461)
(241,466)(242,462)(243,464)(244,451)(245,456)(246,458)(247,454)(248,459)
(249,452)(250,457)(251,453)(252,455)(253,478)(254,483)(255,485)(256,481)
(257,486)(258,479)(259,484)(260,480)(261,482)(262,469)(263,474)(264,476)
(265,472)(266,477)(267,470)(268,475)(269,471)(270,473)(271,496)(272,501)
(273,503)(274,499)(275,504)(276,497)(277,502)(278,498)(279,500)(280,487)
(281,492)(282,494)(283,490)(284,495)(285,488)(286,493)(287,489)(288,491);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*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*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(576)!(  1, 73)(  2, 74)(  3, 75)(  4, 76)(  5, 77)(  6, 78)(  7, 79)
(  8, 80)(  9, 81)( 10, 82)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)
( 16, 88)( 17, 89)( 18, 90)( 19, 91)( 20, 92)( 21, 93)( 22, 94)( 23, 95)
( 24, 96)( 25, 97)( 26, 98)( 27, 99)( 28,100)( 29,101)( 30,102)( 31,103)
( 32,104)( 33,105)( 34,106)( 35,107)( 36,108)( 37,109)( 38,110)( 39,111)
( 40,112)( 41,113)( 42,114)( 43,115)( 44,116)( 45,117)( 46,118)( 47,119)
( 48,120)( 49,121)( 50,122)( 51,123)( 52,124)( 53,125)( 54,126)( 55,127)
( 56,128)( 57,129)( 58,130)( 59,131)( 60,132)( 61,133)( 62,134)( 63,135)
( 64,136)( 65,137)( 66,138)( 67,139)( 68,140)( 69,141)( 70,142)( 71,143)
( 72,144)(145,217)(146,218)(147,219)(148,220)(149,221)(150,222)(151,223)
(152,224)(153,225)(154,226)(155,227)(156,228)(157,229)(158,230)(159,231)
(160,232)(161,233)(162,234)(163,235)(164,236)(165,237)(166,238)(167,239)
(168,240)(169,241)(170,242)(171,243)(172,244)(173,245)(174,246)(175,247)
(176,248)(177,249)(178,250)(179,251)(180,252)(181,253)(182,254)(183,255)
(184,256)(185,257)(186,258)(187,259)(188,260)(189,261)(190,262)(191,263)
(192,264)(193,265)(194,266)(195,267)(196,268)(197,269)(198,270)(199,271)
(200,272)(201,273)(202,274)(203,275)(204,276)(205,277)(206,278)(207,279)
(208,280)(209,281)(210,282)(211,283)(212,284)(213,285)(214,286)(215,287)
(216,288)(289,361)(290,362)(291,363)(292,364)(293,365)(294,366)(295,367)
(296,368)(297,369)(298,370)(299,371)(300,372)(301,373)(302,374)(303,375)
(304,376)(305,377)(306,378)(307,379)(308,380)(309,381)(310,382)(311,383)
(312,384)(313,385)(314,386)(315,387)(316,388)(317,389)(318,390)(319,391)
(320,392)(321,393)(322,394)(323,395)(324,396)(325,397)(326,398)(327,399)
(328,400)(329,401)(330,402)(331,403)(332,404)(333,405)(334,406)(335,407)
(336,408)(337,409)(338,410)(339,411)(340,412)(341,413)(342,414)(343,415)
(344,416)(345,417)(346,418)(347,419)(348,420)(349,421)(350,422)(351,423)
(352,424)(353,425)(354,426)(355,427)(356,428)(357,429)(358,430)(359,431)
(360,432)(433,505)(434,506)(435,507)(436,508)(437,509)(438,510)(439,511)
(440,512)(441,513)(442,514)(443,515)(444,516)(445,517)(446,518)(447,519)
(448,520)(449,521)(450,522)(451,523)(452,524)(453,525)(454,526)(455,527)
(456,528)(457,529)(458,530)(459,531)(460,532)(461,533)(462,534)(463,535)
(464,536)(465,537)(466,538)(467,539)(468,540)(469,541)(470,542)(471,543)
(472,544)(473,545)(474,546)(475,547)(476,548)(477,549)(478,550)(479,551)
(480,552)(481,553)(482,554)(483,555)(484,556)(485,557)(486,558)(487,559)
(488,560)(489,561)(490,562)(491,563)(492,564)(493,565)(494,566)(495,567)
(496,568)(497,569)(498,570)(499,571)(500,572)(501,573)(502,574)(503,575)
(504,576);
s1 := Sym(576)!(  1, 10)(  2, 12)(  3, 11)(  4, 16)(  5, 18)(  6, 17)(  7, 13)
(  8, 15)(  9, 14)( 19, 28)( 20, 30)( 21, 29)( 22, 34)( 23, 36)( 24, 35)
( 25, 31)( 26, 33)( 27, 32)( 37, 46)( 38, 48)( 39, 47)( 40, 52)( 41, 54)
( 42, 53)( 43, 49)( 44, 51)( 45, 50)( 55, 64)( 56, 66)( 57, 65)( 58, 70)
( 59, 72)( 60, 71)( 61, 67)( 62, 69)( 63, 68)( 73,118)( 74,120)( 75,119)
( 76,124)( 77,126)( 78,125)( 79,121)( 80,123)( 81,122)( 82,109)( 83,111)
( 84,110)( 85,115)( 86,117)( 87,116)( 88,112)( 89,114)( 90,113)( 91,136)
( 92,138)( 93,137)( 94,142)( 95,144)( 96,143)( 97,139)( 98,141)( 99,140)
(100,127)(101,129)(102,128)(103,133)(104,135)(105,134)(106,130)(107,132)
(108,131)(145,172)(146,174)(147,173)(148,178)(149,180)(150,179)(151,175)
(152,177)(153,176)(154,163)(155,165)(156,164)(157,169)(158,171)(159,170)
(160,166)(161,168)(162,167)(181,208)(182,210)(183,209)(184,214)(185,216)
(186,215)(187,211)(188,213)(189,212)(190,199)(191,201)(192,200)(193,205)
(194,207)(195,206)(196,202)(197,204)(198,203)(217,280)(218,282)(219,281)
(220,286)(221,288)(222,287)(223,283)(224,285)(225,284)(226,271)(227,273)
(228,272)(229,277)(230,279)(231,278)(232,274)(233,276)(234,275)(235,262)
(236,264)(237,263)(238,268)(239,270)(240,269)(241,265)(242,267)(243,266)
(244,253)(245,255)(246,254)(247,259)(248,261)(249,260)(250,256)(251,258)
(252,257)(289,334)(290,336)(291,335)(292,340)(293,342)(294,341)(295,337)
(296,339)(297,338)(298,325)(299,327)(300,326)(301,331)(302,333)(303,332)
(304,328)(305,330)(306,329)(307,352)(308,354)(309,353)(310,358)(311,360)
(312,359)(313,355)(314,357)(315,356)(316,343)(317,345)(318,344)(319,349)
(320,351)(321,350)(322,346)(323,348)(324,347)(361,370)(362,372)(363,371)
(364,376)(365,378)(366,377)(367,373)(368,375)(369,374)(379,388)(380,390)
(381,389)(382,394)(383,396)(384,395)(385,391)(386,393)(387,392)(397,406)
(398,408)(399,407)(400,412)(401,414)(402,413)(403,409)(404,411)(405,410)
(415,424)(416,426)(417,425)(418,430)(419,432)(420,431)(421,427)(422,429)
(423,428)(433,496)(434,498)(435,497)(436,502)(437,504)(438,503)(439,499)
(440,501)(441,500)(442,487)(443,489)(444,488)(445,493)(446,495)(447,494)
(448,490)(449,492)(450,491)(451,478)(452,480)(453,479)(454,484)(455,486)
(456,485)(457,481)(458,483)(459,482)(460,469)(461,471)(462,470)(463,475)
(464,477)(465,476)(466,472)(467,474)(468,473)(505,532)(506,534)(507,533)
(508,538)(509,540)(510,539)(511,535)(512,537)(513,536)(514,523)(515,525)
(516,524)(517,529)(518,531)(519,530)(520,526)(521,528)(522,527)(541,568)
(542,570)(543,569)(544,574)(545,576)(546,575)(547,571)(548,573)(549,572)
(550,559)(551,561)(552,560)(553,565)(554,567)(555,566)(556,562)(557,564)
(558,563);
s2 := Sym(576)!(  1,146)(  2,145)(  3,147)(  4,150)(  5,149)(  6,148)(  7,151)
(  8,153)(  9,152)( 10,155)( 11,154)( 12,156)( 13,159)( 14,158)( 15,157)
( 16,160)( 17,162)( 18,161)( 19,164)( 20,163)( 21,165)( 22,168)( 23,167)
( 24,166)( 25,169)( 26,171)( 27,170)( 28,173)( 29,172)( 30,174)( 31,177)
( 32,176)( 33,175)( 34,178)( 35,180)( 36,179)( 37,182)( 38,181)( 39,183)
( 40,186)( 41,185)( 42,184)( 43,187)( 44,189)( 45,188)( 46,191)( 47,190)
( 48,192)( 49,195)( 50,194)( 51,193)( 52,196)( 53,198)( 54,197)( 55,200)
( 56,199)( 57,201)( 58,204)( 59,203)( 60,202)( 61,205)( 62,207)( 63,206)
( 64,209)( 65,208)( 66,210)( 67,213)( 68,212)( 69,211)( 70,214)( 71,216)
( 72,215)( 73,218)( 74,217)( 75,219)( 76,222)( 77,221)( 78,220)( 79,223)
( 80,225)( 81,224)( 82,227)( 83,226)( 84,228)( 85,231)( 86,230)( 87,229)
( 88,232)( 89,234)( 90,233)( 91,236)( 92,235)( 93,237)( 94,240)( 95,239)
( 96,238)( 97,241)( 98,243)( 99,242)(100,245)(101,244)(102,246)(103,249)
(104,248)(105,247)(106,250)(107,252)(108,251)(109,254)(110,253)(111,255)
(112,258)(113,257)(114,256)(115,259)(116,261)(117,260)(118,263)(119,262)
(120,264)(121,267)(122,266)(123,265)(124,268)(125,270)(126,269)(127,272)
(128,271)(129,273)(130,276)(131,275)(132,274)(133,277)(134,279)(135,278)
(136,281)(137,280)(138,282)(139,285)(140,284)(141,283)(142,286)(143,288)
(144,287)(289,434)(290,433)(291,435)(292,438)(293,437)(294,436)(295,439)
(296,441)(297,440)(298,443)(299,442)(300,444)(301,447)(302,446)(303,445)
(304,448)(305,450)(306,449)(307,452)(308,451)(309,453)(310,456)(311,455)
(312,454)(313,457)(314,459)(315,458)(316,461)(317,460)(318,462)(319,465)
(320,464)(321,463)(322,466)(323,468)(324,467)(325,470)(326,469)(327,471)
(328,474)(329,473)(330,472)(331,475)(332,477)(333,476)(334,479)(335,478)
(336,480)(337,483)(338,482)(339,481)(340,484)(341,486)(342,485)(343,488)
(344,487)(345,489)(346,492)(347,491)(348,490)(349,493)(350,495)(351,494)
(352,497)(353,496)(354,498)(355,501)(356,500)(357,499)(358,502)(359,504)
(360,503)(361,506)(362,505)(363,507)(364,510)(365,509)(366,508)(367,511)
(368,513)(369,512)(370,515)(371,514)(372,516)(373,519)(374,518)(375,517)
(376,520)(377,522)(378,521)(379,524)(380,523)(381,525)(382,528)(383,527)
(384,526)(385,529)(386,531)(387,530)(388,533)(389,532)(390,534)(391,537)
(392,536)(393,535)(394,538)(395,540)(396,539)(397,542)(398,541)(399,543)
(400,546)(401,545)(402,544)(403,547)(404,549)(405,548)(406,551)(407,550)
(408,552)(409,555)(410,554)(411,553)(412,556)(413,558)(414,557)(415,560)
(416,559)(417,561)(418,564)(419,563)(420,562)(421,565)(422,567)(423,566)
(424,569)(425,568)(426,570)(427,573)(428,572)(429,571)(430,574)(431,576)
(432,575);
s3 := Sym(576)!(  1,361)(  2,366)(  3,368)(  4,364)(  5,369)(  6,362)(  7,367)
(  8,363)(  9,365)( 10,370)( 11,375)( 12,377)( 13,373)( 14,378)( 15,371)
( 16,376)( 17,372)( 18,374)( 19,379)( 20,384)( 21,386)( 22,382)( 23,387)
( 24,380)( 25,385)( 26,381)( 27,383)( 28,388)( 29,393)( 30,395)( 31,391)
( 32,396)( 33,389)( 34,394)( 35,390)( 36,392)( 37,397)( 38,402)( 39,404)
( 40,400)( 41,405)( 42,398)( 43,403)( 44,399)( 45,401)( 46,406)( 47,411)
( 48,413)( 49,409)( 50,414)( 51,407)( 52,412)( 53,408)( 54,410)( 55,415)
( 56,420)( 57,422)( 58,418)( 59,423)( 60,416)( 61,421)( 62,417)( 63,419)
( 64,424)( 65,429)( 66,431)( 67,427)( 68,432)( 69,425)( 70,430)( 71,426)
( 72,428)( 73,289)( 74,294)( 75,296)( 76,292)( 77,297)( 78,290)( 79,295)
( 80,291)( 81,293)( 82,298)( 83,303)( 84,305)( 85,301)( 86,306)( 87,299)
( 88,304)( 89,300)( 90,302)( 91,307)( 92,312)( 93,314)( 94,310)( 95,315)
( 96,308)( 97,313)( 98,309)( 99,311)(100,316)(101,321)(102,323)(103,319)
(104,324)(105,317)(106,322)(107,318)(108,320)(109,325)(110,330)(111,332)
(112,328)(113,333)(114,326)(115,331)(116,327)(117,329)(118,334)(119,339)
(120,341)(121,337)(122,342)(123,335)(124,340)(125,336)(126,338)(127,343)
(128,348)(129,350)(130,346)(131,351)(132,344)(133,349)(134,345)(135,347)
(136,352)(137,357)(138,359)(139,355)(140,360)(141,353)(142,358)(143,354)
(144,356)(145,514)(146,519)(147,521)(148,517)(149,522)(150,515)(151,520)
(152,516)(153,518)(154,505)(155,510)(156,512)(157,508)(158,513)(159,506)
(160,511)(161,507)(162,509)(163,532)(164,537)(165,539)(166,535)(167,540)
(168,533)(169,538)(170,534)(171,536)(172,523)(173,528)(174,530)(175,526)
(176,531)(177,524)(178,529)(179,525)(180,527)(181,550)(182,555)(183,557)
(184,553)(185,558)(186,551)(187,556)(188,552)(189,554)(190,541)(191,546)
(192,548)(193,544)(194,549)(195,542)(196,547)(197,543)(198,545)(199,568)
(200,573)(201,575)(202,571)(203,576)(204,569)(205,574)(206,570)(207,572)
(208,559)(209,564)(210,566)(211,562)(212,567)(213,560)(214,565)(215,561)
(216,563)(217,442)(218,447)(219,449)(220,445)(221,450)(222,443)(223,448)
(224,444)(225,446)(226,433)(227,438)(228,440)(229,436)(230,441)(231,434)
(232,439)(233,435)(234,437)(235,460)(236,465)(237,467)(238,463)(239,468)
(240,461)(241,466)(242,462)(243,464)(244,451)(245,456)(246,458)(247,454)
(248,459)(249,452)(250,457)(251,453)(252,455)(253,478)(254,483)(255,485)
(256,481)(257,486)(258,479)(259,484)(260,480)(261,482)(262,469)(263,474)
(264,476)(265,472)(266,477)(267,470)(268,475)(269,471)(270,473)(271,496)
(272,501)(273,503)(274,499)(275,504)(276,497)(277,502)(278,498)(279,500)
(280,487)(281,492)(282,494)(283,490)(284,495)(285,488)(286,493)(287,489)
(288,491);
poly := sub<Sym(576)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*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*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 
References : None.
to this polytope