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Polytope of Type {4,24,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,24,6}*1152d
if this polytope has a name.
Group : SmallGroup(1152,98790)
Rank : 4
Schlafli Type : {4,24,6}
Number of vertices, edges, etc : 4, 48, 72, 6
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
   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 : {4,12,6}*576c
   3-fold quotients : {4,8,6}*384b
   4-fold quotients : {4,6,6}*288c, {2,12,6}*288c
   6-fold quotients : {4,4,6}*192
   8-fold quotients : {4,6,3}*144, {2,6,6}*144b
   9-fold quotients : {4,8,2}*128b
   12-fold quotients : {2,4,6}*96a, {4,2,6}*96
   16-fold quotients : {2,6,3}*72
   18-fold quotients : {4,4,2}*64
   24-fold quotients : {4,2,3}*48, {2,2,6}*48
   36-fold quotients : {2,4,2}*32, {4,2,2}*32
   48-fold quotients : {2,2,3}*24
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,145)(  2,146)(  3,147)(  4,148)(  5,149)(  6,150)(  7,151)(  8,152)
(  9,153)( 10,154)( 11,155)( 12,156)( 13,157)( 14,158)( 15,159)( 16,160)
( 17,161)( 18,162)( 19,163)( 20,164)( 21,165)( 22,166)( 23,167)( 24,168)
( 25,169)( 26,170)( 27,171)( 28,172)( 29,173)( 30,174)( 31,175)( 32,176)
( 33,177)( 34,178)( 35,179)( 36,180)( 37,190)( 38,191)( 39,192)( 40,193)
( 41,194)( 42,195)( 43,196)( 44,197)( 45,198)( 46,181)( 47,182)( 48,183)
( 49,184)( 50,185)( 51,186)( 52,187)( 53,188)( 54,189)( 55,208)( 56,209)
( 57,210)( 58,211)( 59,212)( 60,213)( 61,214)( 62,215)( 63,216)( 64,199)
( 65,200)( 66,201)( 67,202)( 68,203)( 69,204)( 70,205)( 71,206)( 72,207)
( 73,217)( 74,218)( 75,219)( 76,220)( 77,221)( 78,222)( 79,223)( 80,224)
( 81,225)( 82,226)( 83,227)( 84,228)( 85,229)( 86,230)( 87,231)( 88,232)
( 89,233)( 90,234)( 91,235)( 92,236)( 93,237)( 94,238)( 95,239)( 96,240)
( 97,241)( 98,242)( 99,243)(100,244)(101,245)(102,246)(103,247)(104,248)
(105,249)(106,250)(107,251)(108,252)(109,262)(110,263)(111,264)(112,265)
(113,266)(114,267)(115,268)(116,269)(117,270)(118,253)(119,254)(120,255)
(121,256)(122,257)(123,258)(124,259)(125,260)(126,261)(127,280)(128,281)
(129,282)(130,283)(131,284)(132,285)(133,286)(134,287)(135,288)(136,271)
(137,272)(138,273)(139,274)(140,275)(141,276)(142,277)(143,278)(144,279)
(289,433)(290,434)(291,435)(292,436)(293,437)(294,438)(295,439)(296,440)
(297,441)(298,442)(299,443)(300,444)(301,445)(302,446)(303,447)(304,448)
(305,449)(306,450)(307,451)(308,452)(309,453)(310,454)(311,455)(312,456)
(313,457)(314,458)(315,459)(316,460)(317,461)(318,462)(319,463)(320,464)
(321,465)(322,466)(323,467)(324,468)(325,478)(326,479)(327,480)(328,481)
(329,482)(330,483)(331,484)(332,485)(333,486)(334,469)(335,470)(336,471)
(337,472)(338,473)(339,474)(340,475)(341,476)(342,477)(343,496)(344,497)
(345,498)(346,499)(347,500)(348,501)(349,502)(350,503)(351,504)(352,487)
(353,488)(354,489)(355,490)(356,491)(357,492)(358,493)(359,494)(360,495)
(361,505)(362,506)(363,507)(364,508)(365,509)(366,510)(367,511)(368,512)
(369,513)(370,514)(371,515)(372,516)(373,517)(374,518)(375,519)(376,520)
(377,521)(378,522)(379,523)(380,524)(381,525)(382,526)(383,527)(384,528)
(385,529)(386,530)(387,531)(388,532)(389,533)(390,534)(391,535)(392,536)
(393,537)(394,538)(395,539)(396,540)(397,550)(398,551)(399,552)(400,553)
(401,554)(402,555)(403,556)(404,557)(405,558)(406,541)(407,542)(408,543)
(409,544)(410,545)(411,546)(412,547)(413,548)(414,549)(415,568)(416,569)
(417,570)(418,571)(419,572)(420,573)(421,574)(422,575)(423,576)(424,559)
(425,560)(426,561)(427,562)(428,563)(429,564)(430,565)(431,566)(432,567);;
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)( 74, 78)( 75, 80)
( 77, 81)( 83, 87)( 84, 89)( 86, 90)( 92, 96)( 93, 98)( 95, 99)(101,105)
(102,107)(104,108)(109,118)(110,123)(111,125)(112,121)(113,126)(114,119)
(115,124)(116,120)(117,122)(127,136)(128,141)(129,143)(130,139)(131,144)
(132,137)(133,142)(134,138)(135,140)(145,163)(146,168)(147,170)(148,166)
(149,171)(150,164)(151,169)(152,165)(153,167)(154,172)(155,177)(156,179)
(157,175)(158,180)(159,173)(160,178)(161,174)(162,176)(181,208)(182,213)
(183,215)(184,211)(185,216)(186,209)(187,214)(188,210)(189,212)(190,199)
(191,204)(192,206)(193,202)(194,207)(195,200)(196,205)(197,201)(198,203)
(217,235)(218,240)(219,242)(220,238)(221,243)(222,236)(223,241)(224,237)
(225,239)(226,244)(227,249)(228,251)(229,247)(230,252)(231,245)(232,250)
(233,246)(234,248)(253,280)(254,285)(255,287)(256,283)(257,288)(258,281)
(259,286)(260,282)(261,284)(262,271)(263,276)(264,278)(265,274)(266,279)
(267,272)(268,277)(269,273)(270,275)(289,325)(290,330)(291,332)(292,328)
(293,333)(294,326)(295,331)(296,327)(297,329)(298,334)(299,339)(300,341)
(301,337)(302,342)(303,335)(304,340)(305,336)(306,338)(307,343)(308,348)
(309,350)(310,346)(311,351)(312,344)(313,349)(314,345)(315,347)(316,352)
(317,357)(318,359)(319,355)(320,360)(321,353)(322,358)(323,354)(324,356)
(361,397)(362,402)(363,404)(364,400)(365,405)(366,398)(367,403)(368,399)
(369,401)(370,406)(371,411)(372,413)(373,409)(374,414)(375,407)(376,412)
(377,408)(378,410)(379,415)(380,420)(381,422)(382,418)(383,423)(384,416)
(385,421)(386,417)(387,419)(388,424)(389,429)(390,431)(391,427)(392,432)
(393,425)(394,430)(395,426)(396,428)(433,496)(434,501)(435,503)(436,499)
(437,504)(438,497)(439,502)(440,498)(441,500)(442,487)(443,492)(444,494)
(445,490)(446,495)(447,488)(448,493)(449,489)(450,491)(451,478)(452,483)
(453,485)(454,481)(455,486)(456,479)(457,484)(458,480)(459,482)(460,469)
(461,474)(462,476)(463,472)(464,477)(465,470)(466,475)(467,471)(468,473)
(505,568)(506,573)(507,575)(508,571)(509,576)(510,569)(511,574)(512,570)
(513,572)(514,559)(515,564)(516,566)(517,562)(518,567)(519,560)(520,565)
(521,561)(522,563)(523,550)(524,555)(525,557)(526,553)(527,558)(528,551)
(529,556)(530,552)(531,554)(532,541)(533,546)(534,548)(535,544)(536,549)
(537,542)(538,547)(539,543)(540,545);;
s2 := (  1,362)(  2,361)(  3,363)(  4,368)(  5,367)(  6,369)(  7,365)(  8,364)
(  9,366)( 10,371)( 11,370)( 12,372)( 13,377)( 14,376)( 15,378)( 16,374)
( 17,373)( 18,375)( 19,389)( 20,388)( 21,390)( 22,395)( 23,394)( 24,396)
( 25,392)( 26,391)( 27,393)( 28,380)( 29,379)( 30,381)( 31,386)( 32,385)
( 33,387)( 34,383)( 35,382)( 36,384)( 37,407)( 38,406)( 39,408)( 40,413)
( 41,412)( 42,414)( 43,410)( 44,409)( 45,411)( 46,398)( 47,397)( 48,399)
( 49,404)( 50,403)( 51,405)( 52,401)( 53,400)( 54,402)( 55,416)( 56,415)
( 57,417)( 58,422)( 59,421)( 60,423)( 61,419)( 62,418)( 63,420)( 64,425)
( 65,424)( 66,426)( 67,431)( 68,430)( 69,432)( 70,428)( 71,427)( 72,429)
( 73,290)( 74,289)( 75,291)( 76,296)( 77,295)( 78,297)( 79,293)( 80,292)
( 81,294)( 82,299)( 83,298)( 84,300)( 85,305)( 86,304)( 87,306)( 88,302)
( 89,301)( 90,303)( 91,317)( 92,316)( 93,318)( 94,323)( 95,322)( 96,324)
( 97,320)( 98,319)( 99,321)(100,308)(101,307)(102,309)(103,314)(104,313)
(105,315)(106,311)(107,310)(108,312)(109,335)(110,334)(111,336)(112,341)
(113,340)(114,342)(115,338)(116,337)(117,339)(118,326)(119,325)(120,327)
(121,332)(122,331)(123,333)(124,329)(125,328)(126,330)(127,344)(128,343)
(129,345)(130,350)(131,349)(132,351)(133,347)(134,346)(135,348)(136,353)
(137,352)(138,354)(139,359)(140,358)(141,360)(142,356)(143,355)(144,357)
(145,506)(146,505)(147,507)(148,512)(149,511)(150,513)(151,509)(152,508)
(153,510)(154,515)(155,514)(156,516)(157,521)(158,520)(159,522)(160,518)
(161,517)(162,519)(163,533)(164,532)(165,534)(166,539)(167,538)(168,540)
(169,536)(170,535)(171,537)(172,524)(173,523)(174,525)(175,530)(176,529)
(177,531)(178,527)(179,526)(180,528)(181,551)(182,550)(183,552)(184,557)
(185,556)(186,558)(187,554)(188,553)(189,555)(190,542)(191,541)(192,543)
(193,548)(194,547)(195,549)(196,545)(197,544)(198,546)(199,560)(200,559)
(201,561)(202,566)(203,565)(204,567)(205,563)(206,562)(207,564)(208,569)
(209,568)(210,570)(211,575)(212,574)(213,576)(214,572)(215,571)(216,573)
(217,434)(218,433)(219,435)(220,440)(221,439)(222,441)(223,437)(224,436)
(225,438)(226,443)(227,442)(228,444)(229,449)(230,448)(231,450)(232,446)
(233,445)(234,447)(235,461)(236,460)(237,462)(238,467)(239,466)(240,468)
(241,464)(242,463)(243,465)(244,452)(245,451)(246,453)(247,458)(248,457)
(249,459)(250,455)(251,454)(252,456)(253,479)(254,478)(255,480)(256,485)
(257,484)(258,486)(259,482)(260,481)(261,483)(262,470)(263,469)(264,471)
(265,476)(266,475)(267,477)(268,473)(269,472)(270,474)(271,488)(272,487)
(273,489)(274,494)(275,493)(276,495)(277,491)(278,490)(279,492)(280,497)
(281,496)(282,498)(283,503)(284,502)(285,504)(286,500)(287,499)(288,501);;
s3 := (  1, 73)(  2, 75)(  3, 74)(  4, 79)(  5, 81)(  6, 80)(  7, 76)(  8, 78)
(  9, 77)( 10, 82)( 11, 84)( 12, 83)( 13, 88)( 14, 90)( 15, 89)( 16, 85)
( 17, 87)( 18, 86)( 19, 91)( 20, 93)( 21, 92)( 22, 97)( 23, 99)( 24, 98)
( 25, 94)( 26, 96)( 27, 95)( 28,100)( 29,102)( 30,101)( 31,106)( 32,108)
( 33,107)( 34,103)( 35,105)( 36,104)( 37,109)( 38,111)( 39,110)( 40,115)
( 41,117)( 42,116)( 43,112)( 44,114)( 45,113)( 46,118)( 47,120)( 48,119)
( 49,124)( 50,126)( 51,125)( 52,121)( 53,123)( 54,122)( 55,127)( 56,129)
( 57,128)( 58,133)( 59,135)( 60,134)( 61,130)( 62,132)( 63,131)( 64,136)
( 65,138)( 66,137)( 67,142)( 68,144)( 69,143)( 70,139)( 71,141)( 72,140)
(145,217)(146,219)(147,218)(148,223)(149,225)(150,224)(151,220)(152,222)
(153,221)(154,226)(155,228)(156,227)(157,232)(158,234)(159,233)(160,229)
(161,231)(162,230)(163,235)(164,237)(165,236)(166,241)(167,243)(168,242)
(169,238)(170,240)(171,239)(172,244)(173,246)(174,245)(175,250)(176,252)
(177,251)(178,247)(179,249)(180,248)(181,253)(182,255)(183,254)(184,259)
(185,261)(186,260)(187,256)(188,258)(189,257)(190,262)(191,264)(192,263)
(193,268)(194,270)(195,269)(196,265)(197,267)(198,266)(199,271)(200,273)
(201,272)(202,277)(203,279)(204,278)(205,274)(206,276)(207,275)(208,280)
(209,282)(210,281)(211,286)(212,288)(213,287)(214,283)(215,285)(216,284)
(289,361)(290,363)(291,362)(292,367)(293,369)(294,368)(295,364)(296,366)
(297,365)(298,370)(299,372)(300,371)(301,376)(302,378)(303,377)(304,373)
(305,375)(306,374)(307,379)(308,381)(309,380)(310,385)(311,387)(312,386)
(313,382)(314,384)(315,383)(316,388)(317,390)(318,389)(319,394)(320,396)
(321,395)(322,391)(323,393)(324,392)(325,397)(326,399)(327,398)(328,403)
(329,405)(330,404)(331,400)(332,402)(333,401)(334,406)(335,408)(336,407)
(337,412)(338,414)(339,413)(340,409)(341,411)(342,410)(343,415)(344,417)
(345,416)(346,421)(347,423)(348,422)(349,418)(350,420)(351,419)(352,424)
(353,426)(354,425)(355,430)(356,432)(357,431)(358,427)(359,429)(360,428)
(433,505)(434,507)(435,506)(436,511)(437,513)(438,512)(439,508)(440,510)
(441,509)(442,514)(443,516)(444,515)(445,520)(446,522)(447,521)(448,517)
(449,519)(450,518)(451,523)(452,525)(453,524)(454,529)(455,531)(456,530)
(457,526)(458,528)(459,527)(460,532)(461,534)(462,533)(463,538)(464,540)
(465,539)(466,535)(467,537)(468,536)(469,541)(470,543)(471,542)(472,547)
(473,549)(474,548)(475,544)(476,546)(477,545)(478,550)(479,552)(480,551)
(481,556)(482,558)(483,557)(484,553)(485,555)(486,554)(487,559)(488,561)
(489,560)(490,565)(491,567)(492,566)(493,562)(494,564)(495,563)(496,568)
(497,570)(498,569)(499,574)(500,576)(501,575)(502,571)(503,573)(504,572);;
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, 
s3*s0*s2*s1*s2*s3*s1*s2*s0*s1*s2*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(576)!(  1,145)(  2,146)(  3,147)(  4,148)(  5,149)(  6,150)(  7,151)
(  8,152)(  9,153)( 10,154)( 11,155)( 12,156)( 13,157)( 14,158)( 15,159)
( 16,160)( 17,161)( 18,162)( 19,163)( 20,164)( 21,165)( 22,166)( 23,167)
( 24,168)( 25,169)( 26,170)( 27,171)( 28,172)( 29,173)( 30,174)( 31,175)
( 32,176)( 33,177)( 34,178)( 35,179)( 36,180)( 37,190)( 38,191)( 39,192)
( 40,193)( 41,194)( 42,195)( 43,196)( 44,197)( 45,198)( 46,181)( 47,182)
( 48,183)( 49,184)( 50,185)( 51,186)( 52,187)( 53,188)( 54,189)( 55,208)
( 56,209)( 57,210)( 58,211)( 59,212)( 60,213)( 61,214)( 62,215)( 63,216)
( 64,199)( 65,200)( 66,201)( 67,202)( 68,203)( 69,204)( 70,205)( 71,206)
( 72,207)( 73,217)( 74,218)( 75,219)( 76,220)( 77,221)( 78,222)( 79,223)
( 80,224)( 81,225)( 82,226)( 83,227)( 84,228)( 85,229)( 86,230)( 87,231)
( 88,232)( 89,233)( 90,234)( 91,235)( 92,236)( 93,237)( 94,238)( 95,239)
( 96,240)( 97,241)( 98,242)( 99,243)(100,244)(101,245)(102,246)(103,247)
(104,248)(105,249)(106,250)(107,251)(108,252)(109,262)(110,263)(111,264)
(112,265)(113,266)(114,267)(115,268)(116,269)(117,270)(118,253)(119,254)
(120,255)(121,256)(122,257)(123,258)(124,259)(125,260)(126,261)(127,280)
(128,281)(129,282)(130,283)(131,284)(132,285)(133,286)(134,287)(135,288)
(136,271)(137,272)(138,273)(139,274)(140,275)(141,276)(142,277)(143,278)
(144,279)(289,433)(290,434)(291,435)(292,436)(293,437)(294,438)(295,439)
(296,440)(297,441)(298,442)(299,443)(300,444)(301,445)(302,446)(303,447)
(304,448)(305,449)(306,450)(307,451)(308,452)(309,453)(310,454)(311,455)
(312,456)(313,457)(314,458)(315,459)(316,460)(317,461)(318,462)(319,463)
(320,464)(321,465)(322,466)(323,467)(324,468)(325,478)(326,479)(327,480)
(328,481)(329,482)(330,483)(331,484)(332,485)(333,486)(334,469)(335,470)
(336,471)(337,472)(338,473)(339,474)(340,475)(341,476)(342,477)(343,496)
(344,497)(345,498)(346,499)(347,500)(348,501)(349,502)(350,503)(351,504)
(352,487)(353,488)(354,489)(355,490)(356,491)(357,492)(358,493)(359,494)
(360,495)(361,505)(362,506)(363,507)(364,508)(365,509)(366,510)(367,511)
(368,512)(369,513)(370,514)(371,515)(372,516)(373,517)(374,518)(375,519)
(376,520)(377,521)(378,522)(379,523)(380,524)(381,525)(382,526)(383,527)
(384,528)(385,529)(386,530)(387,531)(388,532)(389,533)(390,534)(391,535)
(392,536)(393,537)(394,538)(395,539)(396,540)(397,550)(398,551)(399,552)
(400,553)(401,554)(402,555)(403,556)(404,557)(405,558)(406,541)(407,542)
(408,543)(409,544)(410,545)(411,546)(412,547)(413,548)(414,549)(415,568)
(416,569)(417,570)(418,571)(419,572)(420,573)(421,574)(422,575)(423,576)
(424,559)(425,560)(426,561)(427,562)(428,563)(429,564)(430,565)(431,566)
(432,567);
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)( 74, 78)
( 75, 80)( 77, 81)( 83, 87)( 84, 89)( 86, 90)( 92, 96)( 93, 98)( 95, 99)
(101,105)(102,107)(104,108)(109,118)(110,123)(111,125)(112,121)(113,126)
(114,119)(115,124)(116,120)(117,122)(127,136)(128,141)(129,143)(130,139)
(131,144)(132,137)(133,142)(134,138)(135,140)(145,163)(146,168)(147,170)
(148,166)(149,171)(150,164)(151,169)(152,165)(153,167)(154,172)(155,177)
(156,179)(157,175)(158,180)(159,173)(160,178)(161,174)(162,176)(181,208)
(182,213)(183,215)(184,211)(185,216)(186,209)(187,214)(188,210)(189,212)
(190,199)(191,204)(192,206)(193,202)(194,207)(195,200)(196,205)(197,201)
(198,203)(217,235)(218,240)(219,242)(220,238)(221,243)(222,236)(223,241)
(224,237)(225,239)(226,244)(227,249)(228,251)(229,247)(230,252)(231,245)
(232,250)(233,246)(234,248)(253,280)(254,285)(255,287)(256,283)(257,288)
(258,281)(259,286)(260,282)(261,284)(262,271)(263,276)(264,278)(265,274)
(266,279)(267,272)(268,277)(269,273)(270,275)(289,325)(290,330)(291,332)
(292,328)(293,333)(294,326)(295,331)(296,327)(297,329)(298,334)(299,339)
(300,341)(301,337)(302,342)(303,335)(304,340)(305,336)(306,338)(307,343)
(308,348)(309,350)(310,346)(311,351)(312,344)(313,349)(314,345)(315,347)
(316,352)(317,357)(318,359)(319,355)(320,360)(321,353)(322,358)(323,354)
(324,356)(361,397)(362,402)(363,404)(364,400)(365,405)(366,398)(367,403)
(368,399)(369,401)(370,406)(371,411)(372,413)(373,409)(374,414)(375,407)
(376,412)(377,408)(378,410)(379,415)(380,420)(381,422)(382,418)(383,423)
(384,416)(385,421)(386,417)(387,419)(388,424)(389,429)(390,431)(391,427)
(392,432)(393,425)(394,430)(395,426)(396,428)(433,496)(434,501)(435,503)
(436,499)(437,504)(438,497)(439,502)(440,498)(441,500)(442,487)(443,492)
(444,494)(445,490)(446,495)(447,488)(448,493)(449,489)(450,491)(451,478)
(452,483)(453,485)(454,481)(455,486)(456,479)(457,484)(458,480)(459,482)
(460,469)(461,474)(462,476)(463,472)(464,477)(465,470)(466,475)(467,471)
(468,473)(505,568)(506,573)(507,575)(508,571)(509,576)(510,569)(511,574)
(512,570)(513,572)(514,559)(515,564)(516,566)(517,562)(518,567)(519,560)
(520,565)(521,561)(522,563)(523,550)(524,555)(525,557)(526,553)(527,558)
(528,551)(529,556)(530,552)(531,554)(532,541)(533,546)(534,548)(535,544)
(536,549)(537,542)(538,547)(539,543)(540,545);
s2 := Sym(576)!(  1,362)(  2,361)(  3,363)(  4,368)(  5,367)(  6,369)(  7,365)
(  8,364)(  9,366)( 10,371)( 11,370)( 12,372)( 13,377)( 14,376)( 15,378)
( 16,374)( 17,373)( 18,375)( 19,389)( 20,388)( 21,390)( 22,395)( 23,394)
( 24,396)( 25,392)( 26,391)( 27,393)( 28,380)( 29,379)( 30,381)( 31,386)
( 32,385)( 33,387)( 34,383)( 35,382)( 36,384)( 37,407)( 38,406)( 39,408)
( 40,413)( 41,412)( 42,414)( 43,410)( 44,409)( 45,411)( 46,398)( 47,397)
( 48,399)( 49,404)( 50,403)( 51,405)( 52,401)( 53,400)( 54,402)( 55,416)
( 56,415)( 57,417)( 58,422)( 59,421)( 60,423)( 61,419)( 62,418)( 63,420)
( 64,425)( 65,424)( 66,426)( 67,431)( 68,430)( 69,432)( 70,428)( 71,427)
( 72,429)( 73,290)( 74,289)( 75,291)( 76,296)( 77,295)( 78,297)( 79,293)
( 80,292)( 81,294)( 82,299)( 83,298)( 84,300)( 85,305)( 86,304)( 87,306)
( 88,302)( 89,301)( 90,303)( 91,317)( 92,316)( 93,318)( 94,323)( 95,322)
( 96,324)( 97,320)( 98,319)( 99,321)(100,308)(101,307)(102,309)(103,314)
(104,313)(105,315)(106,311)(107,310)(108,312)(109,335)(110,334)(111,336)
(112,341)(113,340)(114,342)(115,338)(116,337)(117,339)(118,326)(119,325)
(120,327)(121,332)(122,331)(123,333)(124,329)(125,328)(126,330)(127,344)
(128,343)(129,345)(130,350)(131,349)(132,351)(133,347)(134,346)(135,348)
(136,353)(137,352)(138,354)(139,359)(140,358)(141,360)(142,356)(143,355)
(144,357)(145,506)(146,505)(147,507)(148,512)(149,511)(150,513)(151,509)
(152,508)(153,510)(154,515)(155,514)(156,516)(157,521)(158,520)(159,522)
(160,518)(161,517)(162,519)(163,533)(164,532)(165,534)(166,539)(167,538)
(168,540)(169,536)(170,535)(171,537)(172,524)(173,523)(174,525)(175,530)
(176,529)(177,531)(178,527)(179,526)(180,528)(181,551)(182,550)(183,552)
(184,557)(185,556)(186,558)(187,554)(188,553)(189,555)(190,542)(191,541)
(192,543)(193,548)(194,547)(195,549)(196,545)(197,544)(198,546)(199,560)
(200,559)(201,561)(202,566)(203,565)(204,567)(205,563)(206,562)(207,564)
(208,569)(209,568)(210,570)(211,575)(212,574)(213,576)(214,572)(215,571)
(216,573)(217,434)(218,433)(219,435)(220,440)(221,439)(222,441)(223,437)
(224,436)(225,438)(226,443)(227,442)(228,444)(229,449)(230,448)(231,450)
(232,446)(233,445)(234,447)(235,461)(236,460)(237,462)(238,467)(239,466)
(240,468)(241,464)(242,463)(243,465)(244,452)(245,451)(246,453)(247,458)
(248,457)(249,459)(250,455)(251,454)(252,456)(253,479)(254,478)(255,480)
(256,485)(257,484)(258,486)(259,482)(260,481)(261,483)(262,470)(263,469)
(264,471)(265,476)(266,475)(267,477)(268,473)(269,472)(270,474)(271,488)
(272,487)(273,489)(274,494)(275,493)(276,495)(277,491)(278,490)(279,492)
(280,497)(281,496)(282,498)(283,503)(284,502)(285,504)(286,500)(287,499)
(288,501);
s3 := Sym(576)!(  1, 73)(  2, 75)(  3, 74)(  4, 79)(  5, 81)(  6, 80)(  7, 76)
(  8, 78)(  9, 77)( 10, 82)( 11, 84)( 12, 83)( 13, 88)( 14, 90)( 15, 89)
( 16, 85)( 17, 87)( 18, 86)( 19, 91)( 20, 93)( 21, 92)( 22, 97)( 23, 99)
( 24, 98)( 25, 94)( 26, 96)( 27, 95)( 28,100)( 29,102)( 30,101)( 31,106)
( 32,108)( 33,107)( 34,103)( 35,105)( 36,104)( 37,109)( 38,111)( 39,110)
( 40,115)( 41,117)( 42,116)( 43,112)( 44,114)( 45,113)( 46,118)( 47,120)
( 48,119)( 49,124)( 50,126)( 51,125)( 52,121)( 53,123)( 54,122)( 55,127)
( 56,129)( 57,128)( 58,133)( 59,135)( 60,134)( 61,130)( 62,132)( 63,131)
( 64,136)( 65,138)( 66,137)( 67,142)( 68,144)( 69,143)( 70,139)( 71,141)
( 72,140)(145,217)(146,219)(147,218)(148,223)(149,225)(150,224)(151,220)
(152,222)(153,221)(154,226)(155,228)(156,227)(157,232)(158,234)(159,233)
(160,229)(161,231)(162,230)(163,235)(164,237)(165,236)(166,241)(167,243)
(168,242)(169,238)(170,240)(171,239)(172,244)(173,246)(174,245)(175,250)
(176,252)(177,251)(178,247)(179,249)(180,248)(181,253)(182,255)(183,254)
(184,259)(185,261)(186,260)(187,256)(188,258)(189,257)(190,262)(191,264)
(192,263)(193,268)(194,270)(195,269)(196,265)(197,267)(198,266)(199,271)
(200,273)(201,272)(202,277)(203,279)(204,278)(205,274)(206,276)(207,275)
(208,280)(209,282)(210,281)(211,286)(212,288)(213,287)(214,283)(215,285)
(216,284)(289,361)(290,363)(291,362)(292,367)(293,369)(294,368)(295,364)
(296,366)(297,365)(298,370)(299,372)(300,371)(301,376)(302,378)(303,377)
(304,373)(305,375)(306,374)(307,379)(308,381)(309,380)(310,385)(311,387)
(312,386)(313,382)(314,384)(315,383)(316,388)(317,390)(318,389)(319,394)
(320,396)(321,395)(322,391)(323,393)(324,392)(325,397)(326,399)(327,398)
(328,403)(329,405)(330,404)(331,400)(332,402)(333,401)(334,406)(335,408)
(336,407)(337,412)(338,414)(339,413)(340,409)(341,411)(342,410)(343,415)
(344,417)(345,416)(346,421)(347,423)(348,422)(349,418)(350,420)(351,419)
(352,424)(353,426)(354,425)(355,430)(356,432)(357,431)(358,427)(359,429)
(360,428)(433,505)(434,507)(435,506)(436,511)(437,513)(438,512)(439,508)
(440,510)(441,509)(442,514)(443,516)(444,515)(445,520)(446,522)(447,521)
(448,517)(449,519)(450,518)(451,523)(452,525)(453,524)(454,529)(455,531)
(456,530)(457,526)(458,528)(459,527)(460,532)(461,534)(462,533)(463,538)
(464,540)(465,539)(466,535)(467,537)(468,536)(469,541)(470,543)(471,542)
(472,547)(473,549)(474,548)(475,544)(476,546)(477,545)(478,550)(479,552)
(480,551)(481,556)(482,558)(483,557)(484,553)(485,555)(486,554)(487,559)
(488,561)(489,560)(490,565)(491,567)(492,566)(493,562)(494,564)(495,563)
(496,568)(497,570)(498,569)(499,574)(500,576)(501,575)(502,571)(503,573)
(504,572);
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, s3*s0*s2*s1*s2*s3*s1*s2*s0*s1*s2*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 
References : None.
to this polytope