Polytope of Type {4,24,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,24,6}*1152f
if this polytope has a name.
Group : SmallGroup(1152,98791)
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 :
   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 : {4,12,6}*576a
   3-fold quotients : {4,24,2}*384b, {4,8,6}*384b
   4-fold quotients : {2,12,6}*288a, {4,6,6}*288a
   6-fold quotients : {4,12,2}*192a, {4,4,6}*192
   8-fold quotients : {2,6,6}*144a
   9-fold quotients : {4,8,2}*128b
   12-fold quotients : {2,12,2}*96, {2,4,6}*96a, {4,2,6}*96, {4,6,2}*96a
   18-fold quotients : {4,4,2}*64
   24-fold quotients : {4,2,3}*48, {2,2,6}*48, {2,6,2}*48
   36-fold quotients : {2,4,2}*32, {4,2,2}*32
   48-fold quotients : {2,2,3}*24, {2,3,2}*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 := (  1, 73)(  2, 80)(  3, 78)(  4, 79)(  5, 77)(  6, 75)(  7, 76)(  8, 74)
(  9, 81)( 10, 82)( 11, 89)( 12, 87)( 13, 88)( 14, 86)( 15, 84)( 16, 85)
( 17, 83)( 18, 90)( 19, 91)( 20, 98)( 21, 96)( 22, 97)( 23, 95)( 24, 93)
( 25, 94)( 26, 92)( 27, 99)( 28,100)( 29,107)( 30,105)( 31,106)( 32,104)
( 33,102)( 34,103)( 35,101)( 36,108)( 37,118)( 38,125)( 39,123)( 40,124)
( 41,122)( 42,120)( 43,121)( 44,119)( 45,126)( 46,109)( 47,116)( 48,114)
( 49,115)( 50,113)( 51,111)( 52,112)( 53,110)( 54,117)( 55,136)( 56,143)
( 57,141)( 58,142)( 59,140)( 60,138)( 61,139)( 62,137)( 63,144)( 64,127)
( 65,134)( 66,132)( 67,133)( 68,131)( 69,129)( 70,130)( 71,128)( 72,135)
(145,235)(146,242)(147,240)(148,241)(149,239)(150,237)(151,238)(152,236)
(153,243)(154,244)(155,251)(156,249)(157,250)(158,248)(159,246)(160,247)
(161,245)(162,252)(163,217)(164,224)(165,222)(166,223)(167,221)(168,219)
(169,220)(170,218)(171,225)(172,226)(173,233)(174,231)(175,232)(176,230)
(177,228)(178,229)(179,227)(180,234)(181,280)(182,287)(183,285)(184,286)
(185,284)(186,282)(187,283)(188,281)(189,288)(190,271)(191,278)(192,276)
(193,277)(194,275)(195,273)(196,274)(197,272)(198,279)(199,262)(200,269)
(201,267)(202,268)(203,266)(204,264)(205,265)(206,263)(207,270)(208,253)
(209,260)(210,258)(211,259)(212,257)(213,255)(214,256)(215,254)(216,261)
(289,397)(290,404)(291,402)(292,403)(293,401)(294,399)(295,400)(296,398)
(297,405)(298,406)(299,413)(300,411)(301,412)(302,410)(303,408)(304,409)
(305,407)(306,414)(307,415)(308,422)(309,420)(310,421)(311,419)(312,417)
(313,418)(314,416)(315,423)(316,424)(317,431)(318,429)(319,430)(320,428)
(321,426)(322,427)(323,425)(324,432)(325,361)(326,368)(327,366)(328,367)
(329,365)(330,363)(331,364)(332,362)(333,369)(334,370)(335,377)(336,375)
(337,376)(338,374)(339,372)(340,373)(341,371)(342,378)(343,379)(344,386)
(345,384)(346,385)(347,383)(348,381)(349,382)(350,380)(351,387)(352,388)
(353,395)(354,393)(355,394)(356,392)(357,390)(358,391)(359,389)(360,396)
(433,568)(434,575)(435,573)(436,574)(437,572)(438,570)(439,571)(440,569)
(441,576)(442,559)(443,566)(444,564)(445,565)(446,563)(447,561)(448,562)
(449,560)(450,567)(451,550)(452,557)(453,555)(454,556)(455,554)(456,552)
(457,553)(458,551)(459,558)(460,541)(461,548)(462,546)(463,547)(464,545)
(465,543)(466,544)(467,542)(468,549)(469,532)(470,539)(471,537)(472,538)
(473,536)(474,534)(475,535)(476,533)(477,540)(478,523)(479,530)(480,528)
(481,529)(482,527)(483,525)(484,526)(485,524)(486,531)(487,514)(488,521)
(489,519)(490,520)(491,518)(492,516)(493,517)(494,515)(495,522)(496,505)
(497,512)(498,510)(499,511)(500,509)(501,507)(502,508)(503,506)(504,513);;
s2 := (  1,292)(  2,294)(  3,293)(  4,289)(  5,291)(  6,290)(  7,295)(  8,297)
(  9,296)( 10,301)( 11,303)( 12,302)( 13,298)( 14,300)( 15,299)( 16,304)
( 17,306)( 18,305)( 19,319)( 20,321)( 21,320)( 22,316)( 23,318)( 24,317)
( 25,322)( 26,324)( 27,323)( 28,310)( 29,312)( 30,311)( 31,307)( 32,309)
( 33,308)( 34,313)( 35,315)( 36,314)( 37,337)( 38,339)( 39,338)( 40,334)
( 41,336)( 42,335)( 43,340)( 44,342)( 45,341)( 46,328)( 47,330)( 48,329)
( 49,325)( 50,327)( 51,326)( 52,331)( 53,333)( 54,332)( 55,346)( 56,348)
( 57,347)( 58,343)( 59,345)( 60,344)( 61,349)( 62,351)( 63,350)( 64,355)
( 65,357)( 66,356)( 67,352)( 68,354)( 69,353)( 70,358)( 71,360)( 72,359)
( 73,364)( 74,366)( 75,365)( 76,361)( 77,363)( 78,362)( 79,367)( 80,369)
( 81,368)( 82,373)( 83,375)( 84,374)( 85,370)( 86,372)( 87,371)( 88,376)
( 89,378)( 90,377)( 91,391)( 92,393)( 93,392)( 94,388)( 95,390)( 96,389)
( 97,394)( 98,396)( 99,395)(100,382)(101,384)(102,383)(103,379)(104,381)
(105,380)(106,385)(107,387)(108,386)(109,409)(110,411)(111,410)(112,406)
(113,408)(114,407)(115,412)(116,414)(117,413)(118,400)(119,402)(120,401)
(121,397)(122,399)(123,398)(124,403)(125,405)(126,404)(127,418)(128,420)
(129,419)(130,415)(131,417)(132,416)(133,421)(134,423)(135,422)(136,427)
(137,429)(138,428)(139,424)(140,426)(141,425)(142,430)(143,432)(144,431)
(145,436)(146,438)(147,437)(148,433)(149,435)(150,434)(151,439)(152,441)
(153,440)(154,445)(155,447)(156,446)(157,442)(158,444)(159,443)(160,448)
(161,450)(162,449)(163,463)(164,465)(165,464)(166,460)(167,462)(168,461)
(169,466)(170,468)(171,467)(172,454)(173,456)(174,455)(175,451)(176,453)
(177,452)(178,457)(179,459)(180,458)(181,481)(182,483)(183,482)(184,478)
(185,480)(186,479)(187,484)(188,486)(189,485)(190,472)(191,474)(192,473)
(193,469)(194,471)(195,470)(196,475)(197,477)(198,476)(199,490)(200,492)
(201,491)(202,487)(203,489)(204,488)(205,493)(206,495)(207,494)(208,499)
(209,501)(210,500)(211,496)(212,498)(213,497)(214,502)(215,504)(216,503)
(217,508)(218,510)(219,509)(220,505)(221,507)(222,506)(223,511)(224,513)
(225,512)(226,517)(227,519)(228,518)(229,514)(230,516)(231,515)(232,520)
(233,522)(234,521)(235,535)(236,537)(237,536)(238,532)(239,534)(240,533)
(241,538)(242,540)(243,539)(244,526)(245,528)(246,527)(247,523)(248,525)
(249,524)(250,529)(251,531)(252,530)(253,553)(254,555)(255,554)(256,550)
(257,552)(258,551)(259,556)(260,558)(261,557)(262,544)(263,546)(264,545)
(265,541)(266,543)(267,542)(268,547)(269,549)(270,548)(271,562)(272,564)
(273,563)(274,559)(275,561)(276,560)(277,565)(278,567)(279,566)(280,571)
(281,573)(282,572)(283,568)(284,570)(285,569)(286,574)(287,576)(288,575);;
s3 := (  1, 77)(  2, 79)(  3, 75)(  4, 80)(  5, 73)(  6, 78)(  7, 74)(  8, 76)
(  9, 81)( 10, 86)( 11, 88)( 12, 84)( 13, 89)( 14, 82)( 15, 87)( 16, 83)
( 17, 85)( 18, 90)( 19, 95)( 20, 97)( 21, 93)( 22, 98)( 23, 91)( 24, 96)
( 25, 92)( 26, 94)( 27, 99)( 28,104)( 29,106)( 30,102)( 31,107)( 32,100)
( 33,105)( 34,101)( 35,103)( 36,108)( 37,113)( 38,115)( 39,111)( 40,116)
( 41,109)( 42,114)( 43,110)( 44,112)( 45,117)( 46,122)( 47,124)( 48,120)
( 49,125)( 50,118)( 51,123)( 52,119)( 53,121)( 54,126)( 55,131)( 56,133)
( 57,129)( 58,134)( 59,127)( 60,132)( 61,128)( 62,130)( 63,135)( 64,140)
( 65,142)( 66,138)( 67,143)( 68,136)( 69,141)( 70,137)( 71,139)( 72,144)
(145,221)(146,223)(147,219)(148,224)(149,217)(150,222)(151,218)(152,220)
(153,225)(154,230)(155,232)(156,228)(157,233)(158,226)(159,231)(160,227)
(161,229)(162,234)(163,239)(164,241)(165,237)(166,242)(167,235)(168,240)
(169,236)(170,238)(171,243)(172,248)(173,250)(174,246)(175,251)(176,244)
(177,249)(178,245)(179,247)(180,252)(181,257)(182,259)(183,255)(184,260)
(185,253)(186,258)(187,254)(188,256)(189,261)(190,266)(191,268)(192,264)
(193,269)(194,262)(195,267)(196,263)(197,265)(198,270)(199,275)(200,277)
(201,273)(202,278)(203,271)(204,276)(205,272)(206,274)(207,279)(208,284)
(209,286)(210,282)(211,287)(212,280)(213,285)(214,281)(215,283)(216,288)
(289,365)(290,367)(291,363)(292,368)(293,361)(294,366)(295,362)(296,364)
(297,369)(298,374)(299,376)(300,372)(301,377)(302,370)(303,375)(304,371)
(305,373)(306,378)(307,383)(308,385)(309,381)(310,386)(311,379)(312,384)
(313,380)(314,382)(315,387)(316,392)(317,394)(318,390)(319,395)(320,388)
(321,393)(322,389)(323,391)(324,396)(325,401)(326,403)(327,399)(328,404)
(329,397)(330,402)(331,398)(332,400)(333,405)(334,410)(335,412)(336,408)
(337,413)(338,406)(339,411)(340,407)(341,409)(342,414)(343,419)(344,421)
(345,417)(346,422)(347,415)(348,420)(349,416)(350,418)(351,423)(352,428)
(353,430)(354,426)(355,431)(356,424)(357,429)(358,425)(359,427)(360,432)
(433,509)(434,511)(435,507)(436,512)(437,505)(438,510)(439,506)(440,508)
(441,513)(442,518)(443,520)(444,516)(445,521)(446,514)(447,519)(448,515)
(449,517)(450,522)(451,527)(452,529)(453,525)(454,530)(455,523)(456,528)
(457,524)(458,526)(459,531)(460,536)(461,538)(462,534)(463,539)(464,532)
(465,537)(466,533)(467,535)(468,540)(469,545)(470,547)(471,543)(472,548)
(473,541)(474,546)(475,542)(476,544)(477,549)(478,554)(479,556)(480,552)
(481,557)(482,550)(483,555)(484,551)(485,553)(486,558)(487,563)(488,565)
(489,561)(490,566)(491,559)(492,564)(493,560)(494,562)(495,567)(496,572)
(497,574)(498,570)(499,575)(500,568)(501,573)(502,569)(503,571)(504,576);;
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1, 
s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1 ];;
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)!(  1, 73)(  2, 80)(  3, 78)(  4, 79)(  5, 77)(  6, 75)(  7, 76)
(  8, 74)(  9, 81)( 10, 82)( 11, 89)( 12, 87)( 13, 88)( 14, 86)( 15, 84)
( 16, 85)( 17, 83)( 18, 90)( 19, 91)( 20, 98)( 21, 96)( 22, 97)( 23, 95)
( 24, 93)( 25, 94)( 26, 92)( 27, 99)( 28,100)( 29,107)( 30,105)( 31,106)
( 32,104)( 33,102)( 34,103)( 35,101)( 36,108)( 37,118)( 38,125)( 39,123)
( 40,124)( 41,122)( 42,120)( 43,121)( 44,119)( 45,126)( 46,109)( 47,116)
( 48,114)( 49,115)( 50,113)( 51,111)( 52,112)( 53,110)( 54,117)( 55,136)
( 56,143)( 57,141)( 58,142)( 59,140)( 60,138)( 61,139)( 62,137)( 63,144)
( 64,127)( 65,134)( 66,132)( 67,133)( 68,131)( 69,129)( 70,130)( 71,128)
( 72,135)(145,235)(146,242)(147,240)(148,241)(149,239)(150,237)(151,238)
(152,236)(153,243)(154,244)(155,251)(156,249)(157,250)(158,248)(159,246)
(160,247)(161,245)(162,252)(163,217)(164,224)(165,222)(166,223)(167,221)
(168,219)(169,220)(170,218)(171,225)(172,226)(173,233)(174,231)(175,232)
(176,230)(177,228)(178,229)(179,227)(180,234)(181,280)(182,287)(183,285)
(184,286)(185,284)(186,282)(187,283)(188,281)(189,288)(190,271)(191,278)
(192,276)(193,277)(194,275)(195,273)(196,274)(197,272)(198,279)(199,262)
(200,269)(201,267)(202,268)(203,266)(204,264)(205,265)(206,263)(207,270)
(208,253)(209,260)(210,258)(211,259)(212,257)(213,255)(214,256)(215,254)
(216,261)(289,397)(290,404)(291,402)(292,403)(293,401)(294,399)(295,400)
(296,398)(297,405)(298,406)(299,413)(300,411)(301,412)(302,410)(303,408)
(304,409)(305,407)(306,414)(307,415)(308,422)(309,420)(310,421)(311,419)
(312,417)(313,418)(314,416)(315,423)(316,424)(317,431)(318,429)(319,430)
(320,428)(321,426)(322,427)(323,425)(324,432)(325,361)(326,368)(327,366)
(328,367)(329,365)(330,363)(331,364)(332,362)(333,369)(334,370)(335,377)
(336,375)(337,376)(338,374)(339,372)(340,373)(341,371)(342,378)(343,379)
(344,386)(345,384)(346,385)(347,383)(348,381)(349,382)(350,380)(351,387)
(352,388)(353,395)(354,393)(355,394)(356,392)(357,390)(358,391)(359,389)
(360,396)(433,568)(434,575)(435,573)(436,574)(437,572)(438,570)(439,571)
(440,569)(441,576)(442,559)(443,566)(444,564)(445,565)(446,563)(447,561)
(448,562)(449,560)(450,567)(451,550)(452,557)(453,555)(454,556)(455,554)
(456,552)(457,553)(458,551)(459,558)(460,541)(461,548)(462,546)(463,547)
(464,545)(465,543)(466,544)(467,542)(468,549)(469,532)(470,539)(471,537)
(472,538)(473,536)(474,534)(475,535)(476,533)(477,540)(478,523)(479,530)
(480,528)(481,529)(482,527)(483,525)(484,526)(485,524)(486,531)(487,514)
(488,521)(489,519)(490,520)(491,518)(492,516)(493,517)(494,515)(495,522)
(496,505)(497,512)(498,510)(499,511)(500,509)(501,507)(502,508)(503,506)
(504,513);
s2 := Sym(576)!(  1,292)(  2,294)(  3,293)(  4,289)(  5,291)(  6,290)(  7,295)
(  8,297)(  9,296)( 10,301)( 11,303)( 12,302)( 13,298)( 14,300)( 15,299)
( 16,304)( 17,306)( 18,305)( 19,319)( 20,321)( 21,320)( 22,316)( 23,318)
( 24,317)( 25,322)( 26,324)( 27,323)( 28,310)( 29,312)( 30,311)( 31,307)
( 32,309)( 33,308)( 34,313)( 35,315)( 36,314)( 37,337)( 38,339)( 39,338)
( 40,334)( 41,336)( 42,335)( 43,340)( 44,342)( 45,341)( 46,328)( 47,330)
( 48,329)( 49,325)( 50,327)( 51,326)( 52,331)( 53,333)( 54,332)( 55,346)
( 56,348)( 57,347)( 58,343)( 59,345)( 60,344)( 61,349)( 62,351)( 63,350)
( 64,355)( 65,357)( 66,356)( 67,352)( 68,354)( 69,353)( 70,358)( 71,360)
( 72,359)( 73,364)( 74,366)( 75,365)( 76,361)( 77,363)( 78,362)( 79,367)
( 80,369)( 81,368)( 82,373)( 83,375)( 84,374)( 85,370)( 86,372)( 87,371)
( 88,376)( 89,378)( 90,377)( 91,391)( 92,393)( 93,392)( 94,388)( 95,390)
( 96,389)( 97,394)( 98,396)( 99,395)(100,382)(101,384)(102,383)(103,379)
(104,381)(105,380)(106,385)(107,387)(108,386)(109,409)(110,411)(111,410)
(112,406)(113,408)(114,407)(115,412)(116,414)(117,413)(118,400)(119,402)
(120,401)(121,397)(122,399)(123,398)(124,403)(125,405)(126,404)(127,418)
(128,420)(129,419)(130,415)(131,417)(132,416)(133,421)(134,423)(135,422)
(136,427)(137,429)(138,428)(139,424)(140,426)(141,425)(142,430)(143,432)
(144,431)(145,436)(146,438)(147,437)(148,433)(149,435)(150,434)(151,439)
(152,441)(153,440)(154,445)(155,447)(156,446)(157,442)(158,444)(159,443)
(160,448)(161,450)(162,449)(163,463)(164,465)(165,464)(166,460)(167,462)
(168,461)(169,466)(170,468)(171,467)(172,454)(173,456)(174,455)(175,451)
(176,453)(177,452)(178,457)(179,459)(180,458)(181,481)(182,483)(183,482)
(184,478)(185,480)(186,479)(187,484)(188,486)(189,485)(190,472)(191,474)
(192,473)(193,469)(194,471)(195,470)(196,475)(197,477)(198,476)(199,490)
(200,492)(201,491)(202,487)(203,489)(204,488)(205,493)(206,495)(207,494)
(208,499)(209,501)(210,500)(211,496)(212,498)(213,497)(214,502)(215,504)
(216,503)(217,508)(218,510)(219,509)(220,505)(221,507)(222,506)(223,511)
(224,513)(225,512)(226,517)(227,519)(228,518)(229,514)(230,516)(231,515)
(232,520)(233,522)(234,521)(235,535)(236,537)(237,536)(238,532)(239,534)
(240,533)(241,538)(242,540)(243,539)(244,526)(245,528)(246,527)(247,523)
(248,525)(249,524)(250,529)(251,531)(252,530)(253,553)(254,555)(255,554)
(256,550)(257,552)(258,551)(259,556)(260,558)(261,557)(262,544)(263,546)
(264,545)(265,541)(266,543)(267,542)(268,547)(269,549)(270,548)(271,562)
(272,564)(273,563)(274,559)(275,561)(276,560)(277,565)(278,567)(279,566)
(280,571)(281,573)(282,572)(283,568)(284,570)(285,569)(286,574)(287,576)
(288,575);
s3 := Sym(576)!(  1, 77)(  2, 79)(  3, 75)(  4, 80)(  5, 73)(  6, 78)(  7, 74)
(  8, 76)(  9, 81)( 10, 86)( 11, 88)( 12, 84)( 13, 89)( 14, 82)( 15, 87)
( 16, 83)( 17, 85)( 18, 90)( 19, 95)( 20, 97)( 21, 93)( 22, 98)( 23, 91)
( 24, 96)( 25, 92)( 26, 94)( 27, 99)( 28,104)( 29,106)( 30,102)( 31,107)
( 32,100)( 33,105)( 34,101)( 35,103)( 36,108)( 37,113)( 38,115)( 39,111)
( 40,116)( 41,109)( 42,114)( 43,110)( 44,112)( 45,117)( 46,122)( 47,124)
( 48,120)( 49,125)( 50,118)( 51,123)( 52,119)( 53,121)( 54,126)( 55,131)
( 56,133)( 57,129)( 58,134)( 59,127)( 60,132)( 61,128)( 62,130)( 63,135)
( 64,140)( 65,142)( 66,138)( 67,143)( 68,136)( 69,141)( 70,137)( 71,139)
( 72,144)(145,221)(146,223)(147,219)(148,224)(149,217)(150,222)(151,218)
(152,220)(153,225)(154,230)(155,232)(156,228)(157,233)(158,226)(159,231)
(160,227)(161,229)(162,234)(163,239)(164,241)(165,237)(166,242)(167,235)
(168,240)(169,236)(170,238)(171,243)(172,248)(173,250)(174,246)(175,251)
(176,244)(177,249)(178,245)(179,247)(180,252)(181,257)(182,259)(183,255)
(184,260)(185,253)(186,258)(187,254)(188,256)(189,261)(190,266)(191,268)
(192,264)(193,269)(194,262)(195,267)(196,263)(197,265)(198,270)(199,275)
(200,277)(201,273)(202,278)(203,271)(204,276)(205,272)(206,274)(207,279)
(208,284)(209,286)(210,282)(211,287)(212,280)(213,285)(214,281)(215,283)
(216,288)(289,365)(290,367)(291,363)(292,368)(293,361)(294,366)(295,362)
(296,364)(297,369)(298,374)(299,376)(300,372)(301,377)(302,370)(303,375)
(304,371)(305,373)(306,378)(307,383)(308,385)(309,381)(310,386)(311,379)
(312,384)(313,380)(314,382)(315,387)(316,392)(317,394)(318,390)(319,395)
(320,388)(321,393)(322,389)(323,391)(324,396)(325,401)(326,403)(327,399)
(328,404)(329,397)(330,402)(331,398)(332,400)(333,405)(334,410)(335,412)
(336,408)(337,413)(338,406)(339,411)(340,407)(341,409)(342,414)(343,419)
(344,421)(345,417)(346,422)(347,415)(348,420)(349,416)(350,418)(351,423)
(352,428)(353,430)(354,426)(355,431)(356,424)(357,429)(358,425)(359,427)
(360,432)(433,509)(434,511)(435,507)(436,512)(437,505)(438,510)(439,506)
(440,508)(441,513)(442,518)(443,520)(444,516)(445,521)(446,514)(447,519)
(448,515)(449,517)(450,522)(451,527)(452,529)(453,525)(454,530)(455,523)
(456,528)(457,524)(458,526)(459,531)(460,536)(461,538)(462,534)(463,539)
(464,532)(465,537)(466,533)(467,535)(468,540)(469,545)(470,547)(471,543)
(472,548)(473,541)(474,546)(475,542)(476,544)(477,549)(478,554)(479,556)
(480,552)(481,557)(482,550)(483,555)(484,551)(485,553)(486,558)(487,563)
(488,565)(489,561)(490,566)(491,559)(492,564)(493,560)(494,562)(495,567)
(496,572)(497,574)(498,570)(499,575)(500,568)(501,573)(502,569)(503,571)
(504,576);
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, 
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1, 
s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1 >;
References : None.
to this polytope