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Polytope of Type {6,4,24}

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