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Polytope of Type {24,4,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,4,6}*1152a
Also Known As : {{24,4|2},{4,6|2}}. if this polytope has another name.
Group : SmallGroup(1152,97537)
Rank : 4
Schlafli Type : {24,4,6}
Number of vertices, edges, etc : 24, 48, 12, 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 : {12,4,6}*576, {24,2,6}*576
   3-fold quotients : {24,4,2}*384a, {8,4,6}*384a
   4-fold quotients : {24,2,3}*288, {12,2,6}*288, {6,4,6}*288
   6-fold quotients : {12,4,2}*192a, {4,4,6}*192, {24,2,2}*192, {8,2,6}*192
   8-fold quotients : {12,2,3}*144, {6,2,6}*144
   9-fold quotients : {8,4,2}*128a
   12-fold quotients : {8,2,3}*96, {12,2,2}*96, {2,4,6}*96a, {4,2,6}*96, {6,4,2}*96a
   16-fold quotients : {3,2,6}*72, {6,2,3}*72
   18-fold quotients : {4,4,2}*64, {8,2,2}*64
   24-fold quotients : {4,2,3}*48, {2,2,6}*48, {6,2,2}*48
   32-fold quotients : {3,2,3}*36
   36-fold quotients : {2,4,2}*32, {4,2,2}*32
   48-fold quotients : {2,2,3}*24, {3,2,2}*24
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,361)(  2,368)(  3,366)(  4,367)(  5,365)(  6,363)(  7,364)(  8,362)
(  9,369)( 10,370)( 11,377)( 12,375)( 13,376)( 14,374)( 15,372)( 16,373)
( 17,371)( 18,378)( 19,379)( 20,386)( 21,384)( 22,385)( 23,383)( 24,381)
( 25,382)( 26,380)( 27,387)( 28,388)( 29,395)( 30,393)( 31,394)( 32,392)
( 33,390)( 34,391)( 35,389)( 36,396)( 37,406)( 38,413)( 39,411)( 40,412)
( 41,410)( 42,408)( 43,409)( 44,407)( 45,414)( 46,397)( 47,404)( 48,402)
( 49,403)( 50,401)( 51,399)( 52,400)( 53,398)( 54,405)( 55,424)( 56,431)
( 57,429)( 58,430)( 59,428)( 60,426)( 61,427)( 62,425)( 63,432)( 64,415)
( 65,422)( 66,420)( 67,421)( 68,419)( 69,417)( 70,418)( 71,416)( 72,423)
( 73,289)( 74,296)( 75,294)( 76,295)( 77,293)( 78,291)( 79,292)( 80,290)
( 81,297)( 82,298)( 83,305)( 84,303)( 85,304)( 86,302)( 87,300)( 88,301)
( 89,299)( 90,306)( 91,307)( 92,314)( 93,312)( 94,313)( 95,311)( 96,309)
( 97,310)( 98,308)( 99,315)(100,316)(101,323)(102,321)(103,322)(104,320)
(105,318)(106,319)(107,317)(108,324)(109,334)(110,341)(111,339)(112,340)
(113,338)(114,336)(115,337)(116,335)(117,342)(118,325)(119,332)(120,330)
(121,331)(122,329)(123,327)(124,328)(125,326)(126,333)(127,352)(128,359)
(129,357)(130,358)(131,356)(132,354)(133,355)(134,353)(135,360)(136,343)
(137,350)(138,348)(139,349)(140,347)(141,345)(142,346)(143,344)(144,351)
(145,505)(146,512)(147,510)(148,511)(149,509)(150,507)(151,508)(152,506)
(153,513)(154,514)(155,521)(156,519)(157,520)(158,518)(159,516)(160,517)
(161,515)(162,522)(163,523)(164,530)(165,528)(166,529)(167,527)(168,525)
(169,526)(170,524)(171,531)(172,532)(173,539)(174,537)(175,538)(176,536)
(177,534)(178,535)(179,533)(180,540)(181,550)(182,557)(183,555)(184,556)
(185,554)(186,552)(187,553)(188,551)(189,558)(190,541)(191,548)(192,546)
(193,547)(194,545)(195,543)(196,544)(197,542)(198,549)(199,568)(200,575)
(201,573)(202,574)(203,572)(204,570)(205,571)(206,569)(207,576)(208,559)
(209,566)(210,564)(211,565)(212,563)(213,561)(214,562)(215,560)(216,567)
(217,433)(218,440)(219,438)(220,439)(221,437)(222,435)(223,436)(224,434)
(225,441)(226,442)(227,449)(228,447)(229,448)(230,446)(231,444)(232,445)
(233,443)(234,450)(235,451)(236,458)(237,456)(238,457)(239,455)(240,453)
(241,454)(242,452)(243,459)(244,460)(245,467)(246,465)(247,466)(248,464)
(249,462)(250,463)(251,461)(252,468)(253,478)(254,485)(255,483)(256,484)
(257,482)(258,480)(259,481)(260,479)(261,486)(262,469)(263,476)(264,474)
(265,475)(266,473)(267,471)(268,472)(269,470)(270,477)(271,496)(272,503)
(273,501)(274,502)(275,500)(276,498)(277,499)(278,497)(279,504)(280,487)
(281,494)(282,492)(283,493)(284,491)(285,489)(286,490)(287,488)(288,495);;
s1 := (  1, 76)(  2, 74)(  3, 81)(  4, 73)(  5, 80)(  6, 78)(  7, 79)(  8, 77)
(  9, 75)( 10, 85)( 11, 83)( 12, 90)( 13, 82)( 14, 89)( 15, 87)( 16, 88)
( 17, 86)( 18, 84)( 19, 94)( 20, 92)( 21, 99)( 22, 91)( 23, 98)( 24, 96)
( 25, 97)( 26, 95)( 27, 93)( 28,103)( 29,101)( 30,108)( 31,100)( 32,107)
( 33,105)( 34,106)( 35,104)( 36,102)( 37,121)( 38,119)( 39,126)( 40,118)
( 41,125)( 42,123)( 43,124)( 44,122)( 45,120)( 46,112)( 47,110)( 48,117)
( 49,109)( 50,116)( 51,114)( 52,115)( 53,113)( 54,111)( 55,139)( 56,137)
( 57,144)( 58,136)( 59,143)( 60,141)( 61,142)( 62,140)( 63,138)( 64,130)
( 65,128)( 66,135)( 67,127)( 68,134)( 69,132)( 70,133)( 71,131)( 72,129)
(145,238)(146,236)(147,243)(148,235)(149,242)(150,240)(151,241)(152,239)
(153,237)(154,247)(155,245)(156,252)(157,244)(158,251)(159,249)(160,250)
(161,248)(162,246)(163,220)(164,218)(165,225)(166,217)(167,224)(168,222)
(169,223)(170,221)(171,219)(172,229)(173,227)(174,234)(175,226)(176,233)
(177,231)(178,232)(179,230)(180,228)(181,283)(182,281)(183,288)(184,280)
(185,287)(186,285)(187,286)(188,284)(189,282)(190,274)(191,272)(192,279)
(193,271)(194,278)(195,276)(196,277)(197,275)(198,273)(199,265)(200,263)
(201,270)(202,262)(203,269)(204,267)(205,268)(206,266)(207,264)(208,256)
(209,254)(210,261)(211,253)(212,260)(213,258)(214,259)(215,257)(216,255)
(289,400)(290,398)(291,405)(292,397)(293,404)(294,402)(295,403)(296,401)
(297,399)(298,409)(299,407)(300,414)(301,406)(302,413)(303,411)(304,412)
(305,410)(306,408)(307,418)(308,416)(309,423)(310,415)(311,422)(312,420)
(313,421)(314,419)(315,417)(316,427)(317,425)(318,432)(319,424)(320,431)
(321,429)(322,430)(323,428)(324,426)(325,364)(326,362)(327,369)(328,361)
(329,368)(330,366)(331,367)(332,365)(333,363)(334,373)(335,371)(336,378)
(337,370)(338,377)(339,375)(340,376)(341,374)(342,372)(343,382)(344,380)
(345,387)(346,379)(347,386)(348,384)(349,385)(350,383)(351,381)(352,391)
(353,389)(354,396)(355,388)(356,395)(357,393)(358,394)(359,392)(360,390)
(433,562)(434,560)(435,567)(436,559)(437,566)(438,564)(439,565)(440,563)
(441,561)(442,571)(443,569)(444,576)(445,568)(446,575)(447,573)(448,574)
(449,572)(450,570)(451,544)(452,542)(453,549)(454,541)(455,548)(456,546)
(457,547)(458,545)(459,543)(460,553)(461,551)(462,558)(463,550)(464,557)
(465,555)(466,556)(467,554)(468,552)(469,526)(470,524)(471,531)(472,523)
(473,530)(474,528)(475,529)(476,527)(477,525)(478,535)(479,533)(480,540)
(481,532)(482,539)(483,537)(484,538)(485,536)(486,534)(487,508)(488,506)
(489,513)(490,505)(491,512)(492,510)(493,511)(494,509)(495,507)(496,517)
(497,515)(498,522)(499,514)(500,521)(501,519)(502,520)(503,518)(504,516);;
s2 := (  1,217)(  2,222)(  3,224)(  4,220)(  5,225)(  6,218)(  7,223)(  8,219)
(  9,221)( 10,226)( 11,231)( 12,233)( 13,229)( 14,234)( 15,227)( 16,232)
( 17,228)( 18,230)( 19,235)( 20,240)( 21,242)( 22,238)( 23,243)( 24,236)
( 25,241)( 26,237)( 27,239)( 28,244)( 29,249)( 30,251)( 31,247)( 32,252)
( 33,245)( 34,250)( 35,246)( 36,248)( 37,253)( 38,258)( 39,260)( 40,256)
( 41,261)( 42,254)( 43,259)( 44,255)( 45,257)( 46,262)( 47,267)( 48,269)
( 49,265)( 50,270)( 51,263)( 52,268)( 53,264)( 54,266)( 55,271)( 56,276)
( 57,278)( 58,274)( 59,279)( 60,272)( 61,277)( 62,273)( 63,275)( 64,280)
( 65,285)( 66,287)( 67,283)( 68,288)( 69,281)( 70,286)( 71,282)( 72,284)
( 73,145)( 74,150)( 75,152)( 76,148)( 77,153)( 78,146)( 79,151)( 80,147)
( 81,149)( 82,154)( 83,159)( 84,161)( 85,157)( 86,162)( 87,155)( 88,160)
( 89,156)( 90,158)( 91,163)( 92,168)( 93,170)( 94,166)( 95,171)( 96,164)
( 97,169)( 98,165)( 99,167)(100,172)(101,177)(102,179)(103,175)(104,180)
(105,173)(106,178)(107,174)(108,176)(109,181)(110,186)(111,188)(112,184)
(113,189)(114,182)(115,187)(116,183)(117,185)(118,190)(119,195)(120,197)
(121,193)(122,198)(123,191)(124,196)(125,192)(126,194)(127,199)(128,204)
(129,206)(130,202)(131,207)(132,200)(133,205)(134,201)(135,203)(136,208)
(137,213)(138,215)(139,211)(140,216)(141,209)(142,214)(143,210)(144,212)
(289,505)(290,510)(291,512)(292,508)(293,513)(294,506)(295,511)(296,507)
(297,509)(298,514)(299,519)(300,521)(301,517)(302,522)(303,515)(304,520)
(305,516)(306,518)(307,523)(308,528)(309,530)(310,526)(311,531)(312,524)
(313,529)(314,525)(315,527)(316,532)(317,537)(318,539)(319,535)(320,540)
(321,533)(322,538)(323,534)(324,536)(325,541)(326,546)(327,548)(328,544)
(329,549)(330,542)(331,547)(332,543)(333,545)(334,550)(335,555)(336,557)
(337,553)(338,558)(339,551)(340,556)(341,552)(342,554)(343,559)(344,564)
(345,566)(346,562)(347,567)(348,560)(349,565)(350,561)(351,563)(352,568)
(353,573)(354,575)(355,571)(356,576)(357,569)(358,574)(359,570)(360,572)
(361,433)(362,438)(363,440)(364,436)(365,441)(366,434)(367,439)(368,435)
(369,437)(370,442)(371,447)(372,449)(373,445)(374,450)(375,443)(376,448)
(377,444)(378,446)(379,451)(380,456)(381,458)(382,454)(383,459)(384,452)
(385,457)(386,453)(387,455)(388,460)(389,465)(390,467)(391,463)(392,468)
(393,461)(394,466)(395,462)(396,464)(397,469)(398,474)(399,476)(400,472)
(401,477)(402,470)(403,475)(404,471)(405,473)(406,478)(407,483)(408,485)
(409,481)(410,486)(411,479)(412,484)(413,480)(414,482)(415,487)(416,492)
(417,494)(418,490)(419,495)(420,488)(421,493)(422,489)(423,491)(424,496)
(425,501)(426,503)(427,499)(428,504)(429,497)(430,502)(431,498)(432,500);;
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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)!(  1,361)(  2,368)(  3,366)(  4,367)(  5,365)(  6,363)(  7,364)
(  8,362)(  9,369)( 10,370)( 11,377)( 12,375)( 13,376)( 14,374)( 15,372)
( 16,373)( 17,371)( 18,378)( 19,379)( 20,386)( 21,384)( 22,385)( 23,383)
( 24,381)( 25,382)( 26,380)( 27,387)( 28,388)( 29,395)( 30,393)( 31,394)
( 32,392)( 33,390)( 34,391)( 35,389)( 36,396)( 37,406)( 38,413)( 39,411)
( 40,412)( 41,410)( 42,408)( 43,409)( 44,407)( 45,414)( 46,397)( 47,404)
( 48,402)( 49,403)( 50,401)( 51,399)( 52,400)( 53,398)( 54,405)( 55,424)
( 56,431)( 57,429)( 58,430)( 59,428)( 60,426)( 61,427)( 62,425)( 63,432)
( 64,415)( 65,422)( 66,420)( 67,421)( 68,419)( 69,417)( 70,418)( 71,416)
( 72,423)( 73,289)( 74,296)( 75,294)( 76,295)( 77,293)( 78,291)( 79,292)
( 80,290)( 81,297)( 82,298)( 83,305)( 84,303)( 85,304)( 86,302)( 87,300)
( 88,301)( 89,299)( 90,306)( 91,307)( 92,314)( 93,312)( 94,313)( 95,311)
( 96,309)( 97,310)( 98,308)( 99,315)(100,316)(101,323)(102,321)(103,322)
(104,320)(105,318)(106,319)(107,317)(108,324)(109,334)(110,341)(111,339)
(112,340)(113,338)(114,336)(115,337)(116,335)(117,342)(118,325)(119,332)
(120,330)(121,331)(122,329)(123,327)(124,328)(125,326)(126,333)(127,352)
(128,359)(129,357)(130,358)(131,356)(132,354)(133,355)(134,353)(135,360)
(136,343)(137,350)(138,348)(139,349)(140,347)(141,345)(142,346)(143,344)
(144,351)(145,505)(146,512)(147,510)(148,511)(149,509)(150,507)(151,508)
(152,506)(153,513)(154,514)(155,521)(156,519)(157,520)(158,518)(159,516)
(160,517)(161,515)(162,522)(163,523)(164,530)(165,528)(166,529)(167,527)
(168,525)(169,526)(170,524)(171,531)(172,532)(173,539)(174,537)(175,538)
(176,536)(177,534)(178,535)(179,533)(180,540)(181,550)(182,557)(183,555)
(184,556)(185,554)(186,552)(187,553)(188,551)(189,558)(190,541)(191,548)
(192,546)(193,547)(194,545)(195,543)(196,544)(197,542)(198,549)(199,568)
(200,575)(201,573)(202,574)(203,572)(204,570)(205,571)(206,569)(207,576)
(208,559)(209,566)(210,564)(211,565)(212,563)(213,561)(214,562)(215,560)
(216,567)(217,433)(218,440)(219,438)(220,439)(221,437)(222,435)(223,436)
(224,434)(225,441)(226,442)(227,449)(228,447)(229,448)(230,446)(231,444)
(232,445)(233,443)(234,450)(235,451)(236,458)(237,456)(238,457)(239,455)
(240,453)(241,454)(242,452)(243,459)(244,460)(245,467)(246,465)(247,466)
(248,464)(249,462)(250,463)(251,461)(252,468)(253,478)(254,485)(255,483)
(256,484)(257,482)(258,480)(259,481)(260,479)(261,486)(262,469)(263,476)
(264,474)(265,475)(266,473)(267,471)(268,472)(269,470)(270,477)(271,496)
(272,503)(273,501)(274,502)(275,500)(276,498)(277,499)(278,497)(279,504)
(280,487)(281,494)(282,492)(283,493)(284,491)(285,489)(286,490)(287,488)
(288,495);
s1 := Sym(576)!(  1, 76)(  2, 74)(  3, 81)(  4, 73)(  5, 80)(  6, 78)(  7, 79)
(  8, 77)(  9, 75)( 10, 85)( 11, 83)( 12, 90)( 13, 82)( 14, 89)( 15, 87)
( 16, 88)( 17, 86)( 18, 84)( 19, 94)( 20, 92)( 21, 99)( 22, 91)( 23, 98)
( 24, 96)( 25, 97)( 26, 95)( 27, 93)( 28,103)( 29,101)( 30,108)( 31,100)
( 32,107)( 33,105)( 34,106)( 35,104)( 36,102)( 37,121)( 38,119)( 39,126)
( 40,118)( 41,125)( 42,123)( 43,124)( 44,122)( 45,120)( 46,112)( 47,110)
( 48,117)( 49,109)( 50,116)( 51,114)( 52,115)( 53,113)( 54,111)( 55,139)
( 56,137)( 57,144)( 58,136)( 59,143)( 60,141)( 61,142)( 62,140)( 63,138)
( 64,130)( 65,128)( 66,135)( 67,127)( 68,134)( 69,132)( 70,133)( 71,131)
( 72,129)(145,238)(146,236)(147,243)(148,235)(149,242)(150,240)(151,241)
(152,239)(153,237)(154,247)(155,245)(156,252)(157,244)(158,251)(159,249)
(160,250)(161,248)(162,246)(163,220)(164,218)(165,225)(166,217)(167,224)
(168,222)(169,223)(170,221)(171,219)(172,229)(173,227)(174,234)(175,226)
(176,233)(177,231)(178,232)(179,230)(180,228)(181,283)(182,281)(183,288)
(184,280)(185,287)(186,285)(187,286)(188,284)(189,282)(190,274)(191,272)
(192,279)(193,271)(194,278)(195,276)(196,277)(197,275)(198,273)(199,265)
(200,263)(201,270)(202,262)(203,269)(204,267)(205,268)(206,266)(207,264)
(208,256)(209,254)(210,261)(211,253)(212,260)(213,258)(214,259)(215,257)
(216,255)(289,400)(290,398)(291,405)(292,397)(293,404)(294,402)(295,403)
(296,401)(297,399)(298,409)(299,407)(300,414)(301,406)(302,413)(303,411)
(304,412)(305,410)(306,408)(307,418)(308,416)(309,423)(310,415)(311,422)
(312,420)(313,421)(314,419)(315,417)(316,427)(317,425)(318,432)(319,424)
(320,431)(321,429)(322,430)(323,428)(324,426)(325,364)(326,362)(327,369)
(328,361)(329,368)(330,366)(331,367)(332,365)(333,363)(334,373)(335,371)
(336,378)(337,370)(338,377)(339,375)(340,376)(341,374)(342,372)(343,382)
(344,380)(345,387)(346,379)(347,386)(348,384)(349,385)(350,383)(351,381)
(352,391)(353,389)(354,396)(355,388)(356,395)(357,393)(358,394)(359,392)
(360,390)(433,562)(434,560)(435,567)(436,559)(437,566)(438,564)(439,565)
(440,563)(441,561)(442,571)(443,569)(444,576)(445,568)(446,575)(447,573)
(448,574)(449,572)(450,570)(451,544)(452,542)(453,549)(454,541)(455,548)
(456,546)(457,547)(458,545)(459,543)(460,553)(461,551)(462,558)(463,550)
(464,557)(465,555)(466,556)(467,554)(468,552)(469,526)(470,524)(471,531)
(472,523)(473,530)(474,528)(475,529)(476,527)(477,525)(478,535)(479,533)
(480,540)(481,532)(482,539)(483,537)(484,538)(485,536)(486,534)(487,508)
(488,506)(489,513)(490,505)(491,512)(492,510)(493,511)(494,509)(495,507)
(496,517)(497,515)(498,522)(499,514)(500,521)(501,519)(502,520)(503,518)
(504,516);
s2 := Sym(576)!(  1,217)(  2,222)(  3,224)(  4,220)(  5,225)(  6,218)(  7,223)
(  8,219)(  9,221)( 10,226)( 11,231)( 12,233)( 13,229)( 14,234)( 15,227)
( 16,232)( 17,228)( 18,230)( 19,235)( 20,240)( 21,242)( 22,238)( 23,243)
( 24,236)( 25,241)( 26,237)( 27,239)( 28,244)( 29,249)( 30,251)( 31,247)
( 32,252)( 33,245)( 34,250)( 35,246)( 36,248)( 37,253)( 38,258)( 39,260)
( 40,256)( 41,261)( 42,254)( 43,259)( 44,255)( 45,257)( 46,262)( 47,267)
( 48,269)( 49,265)( 50,270)( 51,263)( 52,268)( 53,264)( 54,266)( 55,271)
( 56,276)( 57,278)( 58,274)( 59,279)( 60,272)( 61,277)( 62,273)( 63,275)
( 64,280)( 65,285)( 66,287)( 67,283)( 68,288)( 69,281)( 70,286)( 71,282)
( 72,284)( 73,145)( 74,150)( 75,152)( 76,148)( 77,153)( 78,146)( 79,151)
( 80,147)( 81,149)( 82,154)( 83,159)( 84,161)( 85,157)( 86,162)( 87,155)
( 88,160)( 89,156)( 90,158)( 91,163)( 92,168)( 93,170)( 94,166)( 95,171)
( 96,164)( 97,169)( 98,165)( 99,167)(100,172)(101,177)(102,179)(103,175)
(104,180)(105,173)(106,178)(107,174)(108,176)(109,181)(110,186)(111,188)
(112,184)(113,189)(114,182)(115,187)(116,183)(117,185)(118,190)(119,195)
(120,197)(121,193)(122,198)(123,191)(124,196)(125,192)(126,194)(127,199)
(128,204)(129,206)(130,202)(131,207)(132,200)(133,205)(134,201)(135,203)
(136,208)(137,213)(138,215)(139,211)(140,216)(141,209)(142,214)(143,210)
(144,212)(289,505)(290,510)(291,512)(292,508)(293,513)(294,506)(295,511)
(296,507)(297,509)(298,514)(299,519)(300,521)(301,517)(302,522)(303,515)
(304,520)(305,516)(306,518)(307,523)(308,528)(309,530)(310,526)(311,531)
(312,524)(313,529)(314,525)(315,527)(316,532)(317,537)(318,539)(319,535)
(320,540)(321,533)(322,538)(323,534)(324,536)(325,541)(326,546)(327,548)
(328,544)(329,549)(330,542)(331,547)(332,543)(333,545)(334,550)(335,555)
(336,557)(337,553)(338,558)(339,551)(340,556)(341,552)(342,554)(343,559)
(344,564)(345,566)(346,562)(347,567)(348,560)(349,565)(350,561)(351,563)
(352,568)(353,573)(354,575)(355,571)(356,576)(357,569)(358,574)(359,570)
(360,572)(361,433)(362,438)(363,440)(364,436)(365,441)(366,434)(367,439)
(368,435)(369,437)(370,442)(371,447)(372,449)(373,445)(374,450)(375,443)
(376,448)(377,444)(378,446)(379,451)(380,456)(381,458)(382,454)(383,459)
(384,452)(385,457)(386,453)(387,455)(388,460)(389,465)(390,467)(391,463)
(392,468)(393,461)(394,466)(395,462)(396,464)(397,469)(398,474)(399,476)
(400,472)(401,477)(402,470)(403,475)(404,471)(405,473)(406,478)(407,483)
(408,485)(409,481)(410,486)(411,479)(412,484)(413,480)(414,482)(415,487)
(416,492)(417,494)(418,490)(419,495)(420,488)(421,493)(422,489)(423,491)
(424,496)(425,501)(426,503)(427,499)(428,504)(429,497)(430,502)(431,498)
(432,500);
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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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