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Polytope of Type {6,24,4}

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