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Polytope of Type {24,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,6,4}*1152c
if this polytope has a name.
Group : SmallGroup(1152,119768)
Rank : 4
Schlafli Type : {24,6,4}
Number of vertices, edges, etc : 24, 72, 12, 4
Order of s0s1s2s3 : 24
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 : {24,6,2}*576b, {12,6,4}*576b
   3-fold quotients : {24,2,4}*384
   4-fold quotients : {12,6,2}*288b, {6,6,4}*288c
   6-fold quotients : {12,2,4}*192, {24,2,2}*192
   8-fold quotients : {3,6,4}*144, {6,6,2}*144c
   9-fold quotients : {8,2,4}*128
   12-fold quotients : {12,2,2}*96, {6,2,4}*96
   16-fold quotients : {3,6,2}*72
   18-fold quotients : {4,2,4}*64, {8,2,2}*64
   24-fold quotients : {3,2,4}*48, {6,2,2}*48
   36-fold quotients : {2,2,4}*32, {4,2,2}*32
   48-fold quotients : {3,2,2}*24
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,289)(  2,291)(  3,290)(  4,295)(  5,297)(  6,296)(  7,292)(  8,294)
(  9,293)( 10,298)( 11,300)( 12,299)( 13,304)( 14,306)( 15,305)( 16,301)
( 17,303)( 18,302)( 19,307)( 20,309)( 21,308)( 22,313)( 23,315)( 24,314)
( 25,310)( 26,312)( 27,311)( 28,316)( 29,318)( 30,317)( 31,322)( 32,324)
( 33,323)( 34,319)( 35,321)( 36,320)( 37,334)( 38,336)( 39,335)( 40,340)
( 41,342)( 42,341)( 43,337)( 44,339)( 45,338)( 46,325)( 47,327)( 48,326)
( 49,331)( 50,333)( 51,332)( 52,328)( 53,330)( 54,329)( 55,352)( 56,354)
( 57,353)( 58,358)( 59,360)( 60,359)( 61,355)( 62,357)( 63,356)( 64,343)
( 65,345)( 66,344)( 67,349)( 68,351)( 69,350)( 70,346)( 71,348)( 72,347)
( 73,397)( 74,399)( 75,398)( 76,403)( 77,405)( 78,404)( 79,400)( 80,402)
( 81,401)( 82,406)( 83,408)( 84,407)( 85,412)( 86,414)( 87,413)( 88,409)
( 89,411)( 90,410)( 91,415)( 92,417)( 93,416)( 94,421)( 95,423)( 96,422)
( 97,418)( 98,420)( 99,419)(100,424)(101,426)(102,425)(103,430)(104,432)
(105,431)(106,427)(107,429)(108,428)(109,361)(110,363)(111,362)(112,367)
(113,369)(114,368)(115,364)(116,366)(117,365)(118,370)(119,372)(120,371)
(121,376)(122,378)(123,377)(124,373)(125,375)(126,374)(127,379)(128,381)
(129,380)(130,385)(131,387)(132,386)(133,382)(134,384)(135,383)(136,388)
(137,390)(138,389)(139,394)(140,396)(141,395)(142,391)(143,393)(144,392)
(145,433)(146,435)(147,434)(148,439)(149,441)(150,440)(151,436)(152,438)
(153,437)(154,442)(155,444)(156,443)(157,448)(158,450)(159,449)(160,445)
(161,447)(162,446)(163,451)(164,453)(165,452)(166,457)(167,459)(168,458)
(169,454)(170,456)(171,455)(172,460)(173,462)(174,461)(175,466)(176,468)
(177,467)(178,463)(179,465)(180,464)(181,478)(182,480)(183,479)(184,484)
(185,486)(186,485)(187,481)(188,483)(189,482)(190,469)(191,471)(192,470)
(193,475)(194,477)(195,476)(196,472)(197,474)(198,473)(199,496)(200,498)
(201,497)(202,502)(203,504)(204,503)(205,499)(206,501)(207,500)(208,487)
(209,489)(210,488)(211,493)(212,495)(213,494)(214,490)(215,492)(216,491)
(217,541)(218,543)(219,542)(220,547)(221,549)(222,548)(223,544)(224,546)
(225,545)(226,550)(227,552)(228,551)(229,556)(230,558)(231,557)(232,553)
(233,555)(234,554)(235,559)(236,561)(237,560)(238,565)(239,567)(240,566)
(241,562)(242,564)(243,563)(244,568)(245,570)(246,569)(247,574)(248,576)
(249,575)(250,571)(251,573)(252,572)(253,505)(254,507)(255,506)(256,511)
(257,513)(258,512)(259,508)(260,510)(261,509)(262,514)(263,516)(264,515)
(265,520)(266,522)(267,521)(268,517)(269,519)(270,518)(271,523)(272,525)
(273,524)(274,529)(275,531)(276,530)(277,526)(278,528)(279,527)(280,532)
(281,534)(282,533)(283,538)(284,540)(285,539)(286,535)(287,537)(288,536);;
s1 := (  1, 74)(  2, 73)(  3, 75)(  4, 80)(  5, 79)(  6, 81)(  7, 77)(  8, 76)
(  9, 78)( 10, 83)( 11, 82)( 12, 84)( 13, 89)( 14, 88)( 15, 90)( 16, 86)
( 17, 85)( 18, 87)( 19, 92)( 20, 91)( 21, 93)( 22, 98)( 23, 97)( 24, 99)
( 25, 95)( 26, 94)( 27, 96)( 28,101)( 29,100)( 30,102)( 31,107)( 32,106)
( 33,108)( 34,104)( 35,103)( 36,105)( 37,119)( 38,118)( 39,120)( 40,125)
( 41,124)( 42,126)( 43,122)( 44,121)( 45,123)( 46,110)( 47,109)( 48,111)
( 49,116)( 50,115)( 51,117)( 52,113)( 53,112)( 54,114)( 55,137)( 56,136)
( 57,138)( 58,143)( 59,142)( 60,144)( 61,140)( 62,139)( 63,141)( 64,128)
( 65,127)( 66,129)( 67,134)( 68,133)( 69,135)( 70,131)( 71,130)( 72,132)
(145,218)(146,217)(147,219)(148,224)(149,223)(150,225)(151,221)(152,220)
(153,222)(154,227)(155,226)(156,228)(157,233)(158,232)(159,234)(160,230)
(161,229)(162,231)(163,236)(164,235)(165,237)(166,242)(167,241)(168,243)
(169,239)(170,238)(171,240)(172,245)(173,244)(174,246)(175,251)(176,250)
(177,252)(178,248)(179,247)(180,249)(181,263)(182,262)(183,264)(184,269)
(185,268)(186,270)(187,266)(188,265)(189,267)(190,254)(191,253)(192,255)
(193,260)(194,259)(195,261)(196,257)(197,256)(198,258)(199,281)(200,280)
(201,282)(202,287)(203,286)(204,288)(205,284)(206,283)(207,285)(208,272)
(209,271)(210,273)(211,278)(212,277)(213,279)(214,275)(215,274)(216,276)
(289,362)(290,361)(291,363)(292,368)(293,367)(294,369)(295,365)(296,364)
(297,366)(298,371)(299,370)(300,372)(301,377)(302,376)(303,378)(304,374)
(305,373)(306,375)(307,380)(308,379)(309,381)(310,386)(311,385)(312,387)
(313,383)(314,382)(315,384)(316,389)(317,388)(318,390)(319,395)(320,394)
(321,396)(322,392)(323,391)(324,393)(325,407)(326,406)(327,408)(328,413)
(329,412)(330,414)(331,410)(332,409)(333,411)(334,398)(335,397)(336,399)
(337,404)(338,403)(339,405)(340,401)(341,400)(342,402)(343,425)(344,424)
(345,426)(346,431)(347,430)(348,432)(349,428)(350,427)(351,429)(352,416)
(353,415)(354,417)(355,422)(356,421)(357,423)(358,419)(359,418)(360,420)
(433,506)(434,505)(435,507)(436,512)(437,511)(438,513)(439,509)(440,508)
(441,510)(442,515)(443,514)(444,516)(445,521)(446,520)(447,522)(448,518)
(449,517)(450,519)(451,524)(452,523)(453,525)(454,530)(455,529)(456,531)
(457,527)(458,526)(459,528)(460,533)(461,532)(462,534)(463,539)(464,538)
(465,540)(466,536)(467,535)(468,537)(469,551)(470,550)(471,552)(472,557)
(473,556)(474,558)(475,554)(476,553)(477,555)(478,542)(479,541)(480,543)
(481,548)(482,547)(483,549)(484,545)(485,544)(486,546)(487,569)(488,568)
(489,570)(490,575)(491,574)(492,576)(493,572)(494,571)(495,573)(496,560)
(497,559)(498,561)(499,566)(500,565)(501,567)(502,563)(503,562)(504,564);;
s2 := (  1,109)(  2,116)(  3,114)(  4,115)(  5,113)(  6,111)(  7,112)(  8,110)
(  9,117)( 10,118)( 11,125)( 12,123)( 13,124)( 14,122)( 15,120)( 16,121)
( 17,119)( 18,126)( 19,127)( 20,134)( 21,132)( 22,133)( 23,131)( 24,129)
( 25,130)( 26,128)( 27,135)( 28,136)( 29,143)( 30,141)( 31,142)( 32,140)
( 33,138)( 34,139)( 35,137)( 36,144)( 37, 82)( 38, 89)( 39, 87)( 40, 88)
( 41, 86)( 42, 84)( 43, 85)( 44, 83)( 45, 90)( 46, 73)( 47, 80)( 48, 78)
( 49, 79)( 50, 77)( 51, 75)( 52, 76)( 53, 74)( 54, 81)( 55,100)( 56,107)
( 57,105)( 58,106)( 59,104)( 60,102)( 61,103)( 62,101)( 63,108)( 64, 91)
( 65, 98)( 66, 96)( 67, 97)( 68, 95)( 69, 93)( 70, 94)( 71, 92)( 72, 99)
(145,271)(146,278)(147,276)(148,277)(149,275)(150,273)(151,274)(152,272)
(153,279)(154,280)(155,287)(156,285)(157,286)(158,284)(159,282)(160,283)
(161,281)(162,288)(163,253)(164,260)(165,258)(166,259)(167,257)(168,255)
(169,256)(170,254)(171,261)(172,262)(173,269)(174,267)(175,268)(176,266)
(177,264)(178,265)(179,263)(180,270)(181,244)(182,251)(183,249)(184,250)
(185,248)(186,246)(187,247)(188,245)(189,252)(190,235)(191,242)(192,240)
(193,241)(194,239)(195,237)(196,238)(197,236)(198,243)(199,226)(200,233)
(201,231)(202,232)(203,230)(204,228)(205,229)(206,227)(207,234)(208,217)
(209,224)(210,222)(211,223)(212,221)(213,219)(214,220)(215,218)(216,225)
(289,361)(290,368)(291,366)(292,367)(293,365)(294,363)(295,364)(296,362)
(297,369)(298,370)(299,377)(300,375)(301,376)(302,374)(303,372)(304,373)
(305,371)(306,378)(307,379)(308,386)(309,384)(310,385)(311,383)(312,381)
(313,382)(314,380)(315,387)(316,388)(317,395)(318,393)(319,394)(320,392)
(321,390)(322,391)(323,389)(324,396)(325,397)(326,404)(327,402)(328,403)
(329,401)(330,399)(331,400)(332,398)(333,405)(334,406)(335,413)(336,411)
(337,412)(338,410)(339,408)(340,409)(341,407)(342,414)(343,415)(344,422)
(345,420)(346,421)(347,419)(348,417)(349,418)(350,416)(351,423)(352,424)
(353,431)(354,429)(355,430)(356,428)(357,426)(358,427)(359,425)(360,432)
(433,523)(434,530)(435,528)(436,529)(437,527)(438,525)(439,526)(440,524)
(441,531)(442,532)(443,539)(444,537)(445,538)(446,536)(447,534)(448,535)
(449,533)(450,540)(451,505)(452,512)(453,510)(454,511)(455,509)(456,507)
(457,508)(458,506)(459,513)(460,514)(461,521)(462,519)(463,520)(464,518)
(465,516)(466,517)(467,515)(468,522)(469,559)(470,566)(471,564)(472,565)
(473,563)(474,561)(475,562)(476,560)(477,567)(478,568)(479,575)(480,573)
(481,574)(482,572)(483,570)(484,571)(485,569)(486,576)(487,541)(488,548)
(489,546)(490,547)(491,545)(492,543)(493,544)(494,542)(495,549)(496,550)
(497,557)(498,555)(499,556)(500,554)(501,552)(502,553)(503,551)(504,558);;
s3 := (  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)( 37,181)( 38,182)( 39,183)( 40,184)
( 41,185)( 42,186)( 43,187)( 44,188)( 45,189)( 46,190)( 47,191)( 48,192)
( 49,193)( 50,194)( 51,195)( 52,196)( 53,197)( 54,198)( 55,199)( 56,200)
( 57,201)( 58,202)( 59,203)( 60,204)( 61,205)( 62,206)( 63,207)( 64,208)
( 65,209)( 66,210)( 67,211)( 68,212)( 69,213)( 70,214)( 71,215)( 72,216)
( 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)(109,253)(110,254)(111,255)(112,256)
(113,257)(114,258)(115,259)(116,260)(117,261)(118,262)(119,263)(120,264)
(121,265)(122,266)(123,267)(124,268)(125,269)(126,270)(127,271)(128,272)
(129,273)(130,274)(131,275)(132,276)(133,277)(134,278)(135,279)(136,280)
(137,281)(138,282)(139,283)(140,284)(141,285)(142,286)(143,287)(144,288)
(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)(325,469)(326,470)(327,471)(328,472)
(329,473)(330,474)(331,475)(332,476)(333,477)(334,478)(335,479)(336,480)
(337,481)(338,482)(339,483)(340,484)(341,485)(342,486)(343,487)(344,488)
(345,489)(346,490)(347,491)(348,492)(349,493)(350,494)(351,495)(352,496)
(353,497)(354,498)(355,499)(356,500)(357,501)(358,502)(359,503)(360,504)
(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)(397,541)(398,542)(399,543)(400,544)
(401,545)(402,546)(403,547)(404,548)(405,549)(406,550)(407,551)(408,552)
(409,553)(410,554)(411,555)(412,556)(413,557)(414,558)(415,559)(416,560)
(417,561)(418,562)(419,563)(420,564)(421,565)(422,566)(423,567)(424,568)
(425,569)(426,570)(427,571)(428,572)(429,573)(430,574)(431,575)(432,576);;
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, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(576)!(  1,289)(  2,291)(  3,290)(  4,295)(  5,297)(  6,296)(  7,292)
(  8,294)(  9,293)( 10,298)( 11,300)( 12,299)( 13,304)( 14,306)( 15,305)
( 16,301)( 17,303)( 18,302)( 19,307)( 20,309)( 21,308)( 22,313)( 23,315)
( 24,314)( 25,310)( 26,312)( 27,311)( 28,316)( 29,318)( 30,317)( 31,322)
( 32,324)( 33,323)( 34,319)( 35,321)( 36,320)( 37,334)( 38,336)( 39,335)
( 40,340)( 41,342)( 42,341)( 43,337)( 44,339)( 45,338)( 46,325)( 47,327)
( 48,326)( 49,331)( 50,333)( 51,332)( 52,328)( 53,330)( 54,329)( 55,352)
( 56,354)( 57,353)( 58,358)( 59,360)( 60,359)( 61,355)( 62,357)( 63,356)
( 64,343)( 65,345)( 66,344)( 67,349)( 68,351)( 69,350)( 70,346)( 71,348)
( 72,347)( 73,397)( 74,399)( 75,398)( 76,403)( 77,405)( 78,404)( 79,400)
( 80,402)( 81,401)( 82,406)( 83,408)( 84,407)( 85,412)( 86,414)( 87,413)
( 88,409)( 89,411)( 90,410)( 91,415)( 92,417)( 93,416)( 94,421)( 95,423)
( 96,422)( 97,418)( 98,420)( 99,419)(100,424)(101,426)(102,425)(103,430)
(104,432)(105,431)(106,427)(107,429)(108,428)(109,361)(110,363)(111,362)
(112,367)(113,369)(114,368)(115,364)(116,366)(117,365)(118,370)(119,372)
(120,371)(121,376)(122,378)(123,377)(124,373)(125,375)(126,374)(127,379)
(128,381)(129,380)(130,385)(131,387)(132,386)(133,382)(134,384)(135,383)
(136,388)(137,390)(138,389)(139,394)(140,396)(141,395)(142,391)(143,393)
(144,392)(145,433)(146,435)(147,434)(148,439)(149,441)(150,440)(151,436)
(152,438)(153,437)(154,442)(155,444)(156,443)(157,448)(158,450)(159,449)
(160,445)(161,447)(162,446)(163,451)(164,453)(165,452)(166,457)(167,459)
(168,458)(169,454)(170,456)(171,455)(172,460)(173,462)(174,461)(175,466)
(176,468)(177,467)(178,463)(179,465)(180,464)(181,478)(182,480)(183,479)
(184,484)(185,486)(186,485)(187,481)(188,483)(189,482)(190,469)(191,471)
(192,470)(193,475)(194,477)(195,476)(196,472)(197,474)(198,473)(199,496)
(200,498)(201,497)(202,502)(203,504)(204,503)(205,499)(206,501)(207,500)
(208,487)(209,489)(210,488)(211,493)(212,495)(213,494)(214,490)(215,492)
(216,491)(217,541)(218,543)(219,542)(220,547)(221,549)(222,548)(223,544)
(224,546)(225,545)(226,550)(227,552)(228,551)(229,556)(230,558)(231,557)
(232,553)(233,555)(234,554)(235,559)(236,561)(237,560)(238,565)(239,567)
(240,566)(241,562)(242,564)(243,563)(244,568)(245,570)(246,569)(247,574)
(248,576)(249,575)(250,571)(251,573)(252,572)(253,505)(254,507)(255,506)
(256,511)(257,513)(258,512)(259,508)(260,510)(261,509)(262,514)(263,516)
(264,515)(265,520)(266,522)(267,521)(268,517)(269,519)(270,518)(271,523)
(272,525)(273,524)(274,529)(275,531)(276,530)(277,526)(278,528)(279,527)
(280,532)(281,534)(282,533)(283,538)(284,540)(285,539)(286,535)(287,537)
(288,536);
s1 := Sym(576)!(  1, 74)(  2, 73)(  3, 75)(  4, 80)(  5, 79)(  6, 81)(  7, 77)
(  8, 76)(  9, 78)( 10, 83)( 11, 82)( 12, 84)( 13, 89)( 14, 88)( 15, 90)
( 16, 86)( 17, 85)( 18, 87)( 19, 92)( 20, 91)( 21, 93)( 22, 98)( 23, 97)
( 24, 99)( 25, 95)( 26, 94)( 27, 96)( 28,101)( 29,100)( 30,102)( 31,107)
( 32,106)( 33,108)( 34,104)( 35,103)( 36,105)( 37,119)( 38,118)( 39,120)
( 40,125)( 41,124)( 42,126)( 43,122)( 44,121)( 45,123)( 46,110)( 47,109)
( 48,111)( 49,116)( 50,115)( 51,117)( 52,113)( 53,112)( 54,114)( 55,137)
( 56,136)( 57,138)( 58,143)( 59,142)( 60,144)( 61,140)( 62,139)( 63,141)
( 64,128)( 65,127)( 66,129)( 67,134)( 68,133)( 69,135)( 70,131)( 71,130)
( 72,132)(145,218)(146,217)(147,219)(148,224)(149,223)(150,225)(151,221)
(152,220)(153,222)(154,227)(155,226)(156,228)(157,233)(158,232)(159,234)
(160,230)(161,229)(162,231)(163,236)(164,235)(165,237)(166,242)(167,241)
(168,243)(169,239)(170,238)(171,240)(172,245)(173,244)(174,246)(175,251)
(176,250)(177,252)(178,248)(179,247)(180,249)(181,263)(182,262)(183,264)
(184,269)(185,268)(186,270)(187,266)(188,265)(189,267)(190,254)(191,253)
(192,255)(193,260)(194,259)(195,261)(196,257)(197,256)(198,258)(199,281)
(200,280)(201,282)(202,287)(203,286)(204,288)(205,284)(206,283)(207,285)
(208,272)(209,271)(210,273)(211,278)(212,277)(213,279)(214,275)(215,274)
(216,276)(289,362)(290,361)(291,363)(292,368)(293,367)(294,369)(295,365)
(296,364)(297,366)(298,371)(299,370)(300,372)(301,377)(302,376)(303,378)
(304,374)(305,373)(306,375)(307,380)(308,379)(309,381)(310,386)(311,385)
(312,387)(313,383)(314,382)(315,384)(316,389)(317,388)(318,390)(319,395)
(320,394)(321,396)(322,392)(323,391)(324,393)(325,407)(326,406)(327,408)
(328,413)(329,412)(330,414)(331,410)(332,409)(333,411)(334,398)(335,397)
(336,399)(337,404)(338,403)(339,405)(340,401)(341,400)(342,402)(343,425)
(344,424)(345,426)(346,431)(347,430)(348,432)(349,428)(350,427)(351,429)
(352,416)(353,415)(354,417)(355,422)(356,421)(357,423)(358,419)(359,418)
(360,420)(433,506)(434,505)(435,507)(436,512)(437,511)(438,513)(439,509)
(440,508)(441,510)(442,515)(443,514)(444,516)(445,521)(446,520)(447,522)
(448,518)(449,517)(450,519)(451,524)(452,523)(453,525)(454,530)(455,529)
(456,531)(457,527)(458,526)(459,528)(460,533)(461,532)(462,534)(463,539)
(464,538)(465,540)(466,536)(467,535)(468,537)(469,551)(470,550)(471,552)
(472,557)(473,556)(474,558)(475,554)(476,553)(477,555)(478,542)(479,541)
(480,543)(481,548)(482,547)(483,549)(484,545)(485,544)(486,546)(487,569)
(488,568)(489,570)(490,575)(491,574)(492,576)(493,572)(494,571)(495,573)
(496,560)(497,559)(498,561)(499,566)(500,565)(501,567)(502,563)(503,562)
(504,564);
s2 := Sym(576)!(  1,109)(  2,116)(  3,114)(  4,115)(  5,113)(  6,111)(  7,112)
(  8,110)(  9,117)( 10,118)( 11,125)( 12,123)( 13,124)( 14,122)( 15,120)
( 16,121)( 17,119)( 18,126)( 19,127)( 20,134)( 21,132)( 22,133)( 23,131)
( 24,129)( 25,130)( 26,128)( 27,135)( 28,136)( 29,143)( 30,141)( 31,142)
( 32,140)( 33,138)( 34,139)( 35,137)( 36,144)( 37, 82)( 38, 89)( 39, 87)
( 40, 88)( 41, 86)( 42, 84)( 43, 85)( 44, 83)( 45, 90)( 46, 73)( 47, 80)
( 48, 78)( 49, 79)( 50, 77)( 51, 75)( 52, 76)( 53, 74)( 54, 81)( 55,100)
( 56,107)( 57,105)( 58,106)( 59,104)( 60,102)( 61,103)( 62,101)( 63,108)
( 64, 91)( 65, 98)( 66, 96)( 67, 97)( 68, 95)( 69, 93)( 70, 94)( 71, 92)
( 72, 99)(145,271)(146,278)(147,276)(148,277)(149,275)(150,273)(151,274)
(152,272)(153,279)(154,280)(155,287)(156,285)(157,286)(158,284)(159,282)
(160,283)(161,281)(162,288)(163,253)(164,260)(165,258)(166,259)(167,257)
(168,255)(169,256)(170,254)(171,261)(172,262)(173,269)(174,267)(175,268)
(176,266)(177,264)(178,265)(179,263)(180,270)(181,244)(182,251)(183,249)
(184,250)(185,248)(186,246)(187,247)(188,245)(189,252)(190,235)(191,242)
(192,240)(193,241)(194,239)(195,237)(196,238)(197,236)(198,243)(199,226)
(200,233)(201,231)(202,232)(203,230)(204,228)(205,229)(206,227)(207,234)
(208,217)(209,224)(210,222)(211,223)(212,221)(213,219)(214,220)(215,218)
(216,225)(289,361)(290,368)(291,366)(292,367)(293,365)(294,363)(295,364)
(296,362)(297,369)(298,370)(299,377)(300,375)(301,376)(302,374)(303,372)
(304,373)(305,371)(306,378)(307,379)(308,386)(309,384)(310,385)(311,383)
(312,381)(313,382)(314,380)(315,387)(316,388)(317,395)(318,393)(319,394)
(320,392)(321,390)(322,391)(323,389)(324,396)(325,397)(326,404)(327,402)
(328,403)(329,401)(330,399)(331,400)(332,398)(333,405)(334,406)(335,413)
(336,411)(337,412)(338,410)(339,408)(340,409)(341,407)(342,414)(343,415)
(344,422)(345,420)(346,421)(347,419)(348,417)(349,418)(350,416)(351,423)
(352,424)(353,431)(354,429)(355,430)(356,428)(357,426)(358,427)(359,425)
(360,432)(433,523)(434,530)(435,528)(436,529)(437,527)(438,525)(439,526)
(440,524)(441,531)(442,532)(443,539)(444,537)(445,538)(446,536)(447,534)
(448,535)(449,533)(450,540)(451,505)(452,512)(453,510)(454,511)(455,509)
(456,507)(457,508)(458,506)(459,513)(460,514)(461,521)(462,519)(463,520)
(464,518)(465,516)(466,517)(467,515)(468,522)(469,559)(470,566)(471,564)
(472,565)(473,563)(474,561)(475,562)(476,560)(477,567)(478,568)(479,575)
(480,573)(481,574)(482,572)(483,570)(484,571)(485,569)(486,576)(487,541)
(488,548)(489,546)(490,547)(491,545)(492,543)(493,544)(494,542)(495,549)
(496,550)(497,557)(498,555)(499,556)(500,554)(501,552)(502,553)(503,551)
(504,558);
s3 := 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)( 37,181)( 38,182)( 39,183)
( 40,184)( 41,185)( 42,186)( 43,187)( 44,188)( 45,189)( 46,190)( 47,191)
( 48,192)( 49,193)( 50,194)( 51,195)( 52,196)( 53,197)( 54,198)( 55,199)
( 56,200)( 57,201)( 58,202)( 59,203)( 60,204)( 61,205)( 62,206)( 63,207)
( 64,208)( 65,209)( 66,210)( 67,211)( 68,212)( 69,213)( 70,214)( 71,215)
( 72,216)( 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)(109,253)(110,254)(111,255)
(112,256)(113,257)(114,258)(115,259)(116,260)(117,261)(118,262)(119,263)
(120,264)(121,265)(122,266)(123,267)(124,268)(125,269)(126,270)(127,271)
(128,272)(129,273)(130,274)(131,275)(132,276)(133,277)(134,278)(135,279)
(136,280)(137,281)(138,282)(139,283)(140,284)(141,285)(142,286)(143,287)
(144,288)(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)(325,469)(326,470)(327,471)
(328,472)(329,473)(330,474)(331,475)(332,476)(333,477)(334,478)(335,479)
(336,480)(337,481)(338,482)(339,483)(340,484)(341,485)(342,486)(343,487)
(344,488)(345,489)(346,490)(347,491)(348,492)(349,493)(350,494)(351,495)
(352,496)(353,497)(354,498)(355,499)(356,500)(357,501)(358,502)(359,503)
(360,504)(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)(397,541)(398,542)(399,543)
(400,544)(401,545)(402,546)(403,547)(404,548)(405,549)(406,550)(407,551)
(408,552)(409,553)(410,554)(411,555)(412,556)(413,557)(414,558)(415,559)
(416,560)(417,561)(418,562)(419,563)(420,564)(421,565)(422,566)(423,567)
(424,568)(425,569)(426,570)(427,571)(428,572)(429,573)(430,574)(431,575)
(432,576);
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, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s2*s1*s0*s1*s0*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope