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Polytope of Type {8,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6,4}*1152b
if this polytope has a name.
Group : SmallGroup(1152,119791)
Rank : 4
Schlafli Type : {8,6,4}
Number of vertices, edges, etc : 24, 72, 36, 4
Order of s0s1s2s3 : 8
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 : {8,6,2}*576, {4,6,4}*576a
   4-fold quotients : {4,6,2}*288
   8-fold quotients : {4,6,2}*144
   9-fold quotients : {8,2,4}*128
   18-fold quotients : {4,2,4}*64, {8,2,2}*64
   36-fold quotients : {2,2,4}*32, {4,2,2}*32
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,289)(  2,294)(  3,296)(  4,292)(  5,297)(  6,290)(  7,295)(  8,291)
(  9,293)( 10,298)( 11,303)( 12,305)( 13,301)( 14,306)( 15,299)( 16,304)
( 17,300)( 18,302)( 19,307)( 20,312)( 21,314)( 22,310)( 23,315)( 24,308)
( 25,313)( 26,309)( 27,311)( 28,316)( 29,321)( 30,323)( 31,319)( 32,324)
( 33,317)( 34,322)( 35,318)( 36,320)( 37,334)( 38,339)( 39,341)( 40,337)
( 41,342)( 42,335)( 43,340)( 44,336)( 45,338)( 46,325)( 47,330)( 48,332)
( 49,328)( 50,333)( 51,326)( 52,331)( 53,327)( 54,329)( 55,352)( 56,357)
( 57,359)( 58,355)( 59,360)( 60,353)( 61,358)( 62,354)( 63,356)( 64,343)
( 65,348)( 66,350)( 67,346)( 68,351)( 69,344)( 70,349)( 71,345)( 72,347)
( 73,397)( 74,402)( 75,404)( 76,400)( 77,405)( 78,398)( 79,403)( 80,399)
( 81,401)( 82,406)( 83,411)( 84,413)( 85,409)( 86,414)( 87,407)( 88,412)
( 89,408)( 90,410)( 91,415)( 92,420)( 93,422)( 94,418)( 95,423)( 96,416)
( 97,421)( 98,417)( 99,419)(100,424)(101,429)(102,431)(103,427)(104,432)
(105,425)(106,430)(107,426)(108,428)(109,361)(110,366)(111,368)(112,364)
(113,369)(114,362)(115,367)(116,363)(117,365)(118,370)(119,375)(120,377)
(121,373)(122,378)(123,371)(124,376)(125,372)(126,374)(127,379)(128,384)
(129,386)(130,382)(131,387)(132,380)(133,385)(134,381)(135,383)(136,388)
(137,393)(138,395)(139,391)(140,396)(141,389)(142,394)(143,390)(144,392)
(145,433)(146,438)(147,440)(148,436)(149,441)(150,434)(151,439)(152,435)
(153,437)(154,442)(155,447)(156,449)(157,445)(158,450)(159,443)(160,448)
(161,444)(162,446)(163,451)(164,456)(165,458)(166,454)(167,459)(168,452)
(169,457)(170,453)(171,455)(172,460)(173,465)(174,467)(175,463)(176,468)
(177,461)(178,466)(179,462)(180,464)(181,478)(182,483)(183,485)(184,481)
(185,486)(186,479)(187,484)(188,480)(189,482)(190,469)(191,474)(192,476)
(193,472)(194,477)(195,470)(196,475)(197,471)(198,473)(199,496)(200,501)
(201,503)(202,499)(203,504)(204,497)(205,502)(206,498)(207,500)(208,487)
(209,492)(210,494)(211,490)(212,495)(213,488)(214,493)(215,489)(216,491)
(217,541)(218,546)(219,548)(220,544)(221,549)(222,542)(223,547)(224,543)
(225,545)(226,550)(227,555)(228,557)(229,553)(230,558)(231,551)(232,556)
(233,552)(234,554)(235,559)(236,564)(237,566)(238,562)(239,567)(240,560)
(241,565)(242,561)(243,563)(244,568)(245,573)(246,575)(247,571)(248,576)
(249,569)(250,574)(251,570)(252,572)(253,505)(254,510)(255,512)(256,508)
(257,513)(258,506)(259,511)(260,507)(261,509)(262,514)(263,519)(264,521)
(265,517)(266,522)(267,515)(268,520)(269,516)(270,518)(271,523)(272,528)
(273,530)(274,526)(275,531)(276,524)(277,529)(278,525)(279,527)(280,532)
(281,537)(282,539)(283,535)(284,540)(285,533)(286,538)(287,534)(288,536);;
s1 := (  1, 73)(  2, 75)(  3, 74)(  4, 77)(  5, 76)(  6, 78)(  7, 81)(  8, 80)
(  9, 79)( 10, 82)( 11, 84)( 12, 83)( 13, 86)( 14, 85)( 15, 87)( 16, 90)
( 17, 89)( 18, 88)( 19, 91)( 20, 93)( 21, 92)( 22, 95)( 23, 94)( 24, 96)
( 25, 99)( 26, 98)( 27, 97)( 28,100)( 29,102)( 30,101)( 31,104)( 32,103)
( 33,105)( 34,108)( 35,107)( 36,106)( 37,118)( 38,120)( 39,119)( 40,122)
( 41,121)( 42,123)( 43,126)( 44,125)( 45,124)( 46,109)( 47,111)( 48,110)
( 49,113)( 50,112)( 51,114)( 52,117)( 53,116)( 54,115)( 55,136)( 56,138)
( 57,137)( 58,140)( 59,139)( 60,141)( 61,144)( 62,143)( 63,142)( 64,127)
( 65,129)( 66,128)( 67,131)( 68,130)( 69,132)( 70,135)( 71,134)( 72,133)
(145,217)(146,219)(147,218)(148,221)(149,220)(150,222)(151,225)(152,224)
(153,223)(154,226)(155,228)(156,227)(157,230)(158,229)(159,231)(160,234)
(161,233)(162,232)(163,235)(164,237)(165,236)(166,239)(167,238)(168,240)
(169,243)(170,242)(171,241)(172,244)(173,246)(174,245)(175,248)(176,247)
(177,249)(178,252)(179,251)(180,250)(181,262)(182,264)(183,263)(184,266)
(185,265)(186,267)(187,270)(188,269)(189,268)(190,253)(191,255)(192,254)
(193,257)(194,256)(195,258)(196,261)(197,260)(198,259)(199,280)(200,282)
(201,281)(202,284)(203,283)(204,285)(205,288)(206,287)(207,286)(208,271)
(209,273)(210,272)(211,275)(212,274)(213,276)(214,279)(215,278)(216,277)
(289,361)(290,363)(291,362)(292,365)(293,364)(294,366)(295,369)(296,368)
(297,367)(298,370)(299,372)(300,371)(301,374)(302,373)(303,375)(304,378)
(305,377)(306,376)(307,379)(308,381)(309,380)(310,383)(311,382)(312,384)
(313,387)(314,386)(315,385)(316,388)(317,390)(318,389)(319,392)(320,391)
(321,393)(322,396)(323,395)(324,394)(325,406)(326,408)(327,407)(328,410)
(329,409)(330,411)(331,414)(332,413)(333,412)(334,397)(335,399)(336,398)
(337,401)(338,400)(339,402)(340,405)(341,404)(342,403)(343,424)(344,426)
(345,425)(346,428)(347,427)(348,429)(349,432)(350,431)(351,430)(352,415)
(353,417)(354,416)(355,419)(356,418)(357,420)(358,423)(359,422)(360,421)
(433,505)(434,507)(435,506)(436,509)(437,508)(438,510)(439,513)(440,512)
(441,511)(442,514)(443,516)(444,515)(445,518)(446,517)(447,519)(448,522)
(449,521)(450,520)(451,523)(452,525)(453,524)(454,527)(455,526)(456,528)
(457,531)(458,530)(459,529)(460,532)(461,534)(462,533)(463,536)(464,535)
(465,537)(466,540)(467,539)(468,538)(469,550)(470,552)(471,551)(472,554)
(473,553)(474,555)(475,558)(476,557)(477,556)(478,541)(479,543)(480,542)
(481,545)(482,544)(483,546)(484,549)(485,548)(486,547)(487,568)(488,570)
(489,569)(490,572)(491,571)(492,573)(493,576)(494,575)(495,574)(496,559)
(497,561)(498,560)(499,563)(500,562)(501,564)(502,567)(503,566)(504,565);;
s2 := (  1,112)(  2,114)(  3,113)(  4,109)(  5,111)(  6,110)(  7,115)(  8,117)
(  9,116)( 10,121)( 11,123)( 12,122)( 13,118)( 14,120)( 15,119)( 16,124)
( 17,126)( 18,125)( 19,130)( 20,132)( 21,131)( 22,127)( 23,129)( 24,128)
( 25,133)( 26,135)( 27,134)( 28,139)( 29,141)( 30,140)( 31,136)( 32,138)
( 33,137)( 34,142)( 35,144)( 36,143)( 37, 85)( 38, 87)( 39, 86)( 40, 82)
( 41, 84)( 42, 83)( 43, 88)( 44, 90)( 45, 89)( 46, 76)( 47, 78)( 48, 77)
( 49, 73)( 50, 75)( 51, 74)( 52, 79)( 53, 81)( 54, 80)( 55,103)( 56,105)
( 57,104)( 58,100)( 59,102)( 60,101)( 61,106)( 62,108)( 63,107)( 64, 94)
( 65, 96)( 66, 95)( 67, 91)( 68, 93)( 69, 92)( 70, 97)( 71, 99)( 72, 98)
(145,274)(146,276)(147,275)(148,271)(149,273)(150,272)(151,277)(152,279)
(153,278)(154,283)(155,285)(156,284)(157,280)(158,282)(159,281)(160,286)
(161,288)(162,287)(163,256)(164,258)(165,257)(166,253)(167,255)(168,254)
(169,259)(170,261)(171,260)(172,265)(173,267)(174,266)(175,262)(176,264)
(177,263)(178,268)(179,270)(180,269)(181,247)(182,249)(183,248)(184,244)
(185,246)(186,245)(187,250)(188,252)(189,251)(190,238)(191,240)(192,239)
(193,235)(194,237)(195,236)(196,241)(197,243)(198,242)(199,229)(200,231)
(201,230)(202,226)(203,228)(204,227)(205,232)(206,234)(207,233)(208,220)
(209,222)(210,221)(211,217)(212,219)(213,218)(214,223)(215,225)(216,224)
(289,364)(290,366)(291,365)(292,361)(293,363)(294,362)(295,367)(296,369)
(297,368)(298,373)(299,375)(300,374)(301,370)(302,372)(303,371)(304,376)
(305,378)(306,377)(307,382)(308,384)(309,383)(310,379)(311,381)(312,380)
(313,385)(314,387)(315,386)(316,391)(317,393)(318,392)(319,388)(320,390)
(321,389)(322,394)(323,396)(324,395)(325,400)(326,402)(327,401)(328,397)
(329,399)(330,398)(331,403)(332,405)(333,404)(334,409)(335,411)(336,410)
(337,406)(338,408)(339,407)(340,412)(341,414)(342,413)(343,418)(344,420)
(345,419)(346,415)(347,417)(348,416)(349,421)(350,423)(351,422)(352,427)
(353,429)(354,428)(355,424)(356,426)(357,425)(358,430)(359,432)(360,431)
(433,526)(434,528)(435,527)(436,523)(437,525)(438,524)(439,529)(440,531)
(441,530)(442,535)(443,537)(444,536)(445,532)(446,534)(447,533)(448,538)
(449,540)(450,539)(451,508)(452,510)(453,509)(454,505)(455,507)(456,506)
(457,511)(458,513)(459,512)(460,517)(461,519)(462,518)(463,514)(464,516)
(465,515)(466,520)(467,522)(468,521)(469,562)(470,564)(471,563)(472,559)
(473,561)(474,560)(475,565)(476,567)(477,566)(478,571)(479,573)(480,572)
(481,568)(482,570)(483,569)(484,574)(485,576)(486,575)(487,544)(488,546)
(489,545)(490,541)(491,543)(492,542)(493,547)(494,549)(495,548)(496,553)
(497,555)(498,554)(499,550)(500,552)(501,551)(502,556)(503,558)(504,557);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(576)!(  1,289)(  2,294)(  3,296)(  4,292)(  5,297)(  6,290)(  7,295)
(  8,291)(  9,293)( 10,298)( 11,303)( 12,305)( 13,301)( 14,306)( 15,299)
( 16,304)( 17,300)( 18,302)( 19,307)( 20,312)( 21,314)( 22,310)( 23,315)
( 24,308)( 25,313)( 26,309)( 27,311)( 28,316)( 29,321)( 30,323)( 31,319)
( 32,324)( 33,317)( 34,322)( 35,318)( 36,320)( 37,334)( 38,339)( 39,341)
( 40,337)( 41,342)( 42,335)( 43,340)( 44,336)( 45,338)( 46,325)( 47,330)
( 48,332)( 49,328)( 50,333)( 51,326)( 52,331)( 53,327)( 54,329)( 55,352)
( 56,357)( 57,359)( 58,355)( 59,360)( 60,353)( 61,358)( 62,354)( 63,356)
( 64,343)( 65,348)( 66,350)( 67,346)( 68,351)( 69,344)( 70,349)( 71,345)
( 72,347)( 73,397)( 74,402)( 75,404)( 76,400)( 77,405)( 78,398)( 79,403)
( 80,399)( 81,401)( 82,406)( 83,411)( 84,413)( 85,409)( 86,414)( 87,407)
( 88,412)( 89,408)( 90,410)( 91,415)( 92,420)( 93,422)( 94,418)( 95,423)
( 96,416)( 97,421)( 98,417)( 99,419)(100,424)(101,429)(102,431)(103,427)
(104,432)(105,425)(106,430)(107,426)(108,428)(109,361)(110,366)(111,368)
(112,364)(113,369)(114,362)(115,367)(116,363)(117,365)(118,370)(119,375)
(120,377)(121,373)(122,378)(123,371)(124,376)(125,372)(126,374)(127,379)
(128,384)(129,386)(130,382)(131,387)(132,380)(133,385)(134,381)(135,383)
(136,388)(137,393)(138,395)(139,391)(140,396)(141,389)(142,394)(143,390)
(144,392)(145,433)(146,438)(147,440)(148,436)(149,441)(150,434)(151,439)
(152,435)(153,437)(154,442)(155,447)(156,449)(157,445)(158,450)(159,443)
(160,448)(161,444)(162,446)(163,451)(164,456)(165,458)(166,454)(167,459)
(168,452)(169,457)(170,453)(171,455)(172,460)(173,465)(174,467)(175,463)
(176,468)(177,461)(178,466)(179,462)(180,464)(181,478)(182,483)(183,485)
(184,481)(185,486)(186,479)(187,484)(188,480)(189,482)(190,469)(191,474)
(192,476)(193,472)(194,477)(195,470)(196,475)(197,471)(198,473)(199,496)
(200,501)(201,503)(202,499)(203,504)(204,497)(205,502)(206,498)(207,500)
(208,487)(209,492)(210,494)(211,490)(212,495)(213,488)(214,493)(215,489)
(216,491)(217,541)(218,546)(219,548)(220,544)(221,549)(222,542)(223,547)
(224,543)(225,545)(226,550)(227,555)(228,557)(229,553)(230,558)(231,551)
(232,556)(233,552)(234,554)(235,559)(236,564)(237,566)(238,562)(239,567)
(240,560)(241,565)(242,561)(243,563)(244,568)(245,573)(246,575)(247,571)
(248,576)(249,569)(250,574)(251,570)(252,572)(253,505)(254,510)(255,512)
(256,508)(257,513)(258,506)(259,511)(260,507)(261,509)(262,514)(263,519)
(264,521)(265,517)(266,522)(267,515)(268,520)(269,516)(270,518)(271,523)
(272,528)(273,530)(274,526)(275,531)(276,524)(277,529)(278,525)(279,527)
(280,532)(281,537)(282,539)(283,535)(284,540)(285,533)(286,538)(287,534)
(288,536);
s1 := Sym(576)!(  1, 73)(  2, 75)(  3, 74)(  4, 77)(  5, 76)(  6, 78)(  7, 81)
(  8, 80)(  9, 79)( 10, 82)( 11, 84)( 12, 83)( 13, 86)( 14, 85)( 15, 87)
( 16, 90)( 17, 89)( 18, 88)( 19, 91)( 20, 93)( 21, 92)( 22, 95)( 23, 94)
( 24, 96)( 25, 99)( 26, 98)( 27, 97)( 28,100)( 29,102)( 30,101)( 31,104)
( 32,103)( 33,105)( 34,108)( 35,107)( 36,106)( 37,118)( 38,120)( 39,119)
( 40,122)( 41,121)( 42,123)( 43,126)( 44,125)( 45,124)( 46,109)( 47,111)
( 48,110)( 49,113)( 50,112)( 51,114)( 52,117)( 53,116)( 54,115)( 55,136)
( 56,138)( 57,137)( 58,140)( 59,139)( 60,141)( 61,144)( 62,143)( 63,142)
( 64,127)( 65,129)( 66,128)( 67,131)( 68,130)( 69,132)( 70,135)( 71,134)
( 72,133)(145,217)(146,219)(147,218)(148,221)(149,220)(150,222)(151,225)
(152,224)(153,223)(154,226)(155,228)(156,227)(157,230)(158,229)(159,231)
(160,234)(161,233)(162,232)(163,235)(164,237)(165,236)(166,239)(167,238)
(168,240)(169,243)(170,242)(171,241)(172,244)(173,246)(174,245)(175,248)
(176,247)(177,249)(178,252)(179,251)(180,250)(181,262)(182,264)(183,263)
(184,266)(185,265)(186,267)(187,270)(188,269)(189,268)(190,253)(191,255)
(192,254)(193,257)(194,256)(195,258)(196,261)(197,260)(198,259)(199,280)
(200,282)(201,281)(202,284)(203,283)(204,285)(205,288)(206,287)(207,286)
(208,271)(209,273)(210,272)(211,275)(212,274)(213,276)(214,279)(215,278)
(216,277)(289,361)(290,363)(291,362)(292,365)(293,364)(294,366)(295,369)
(296,368)(297,367)(298,370)(299,372)(300,371)(301,374)(302,373)(303,375)
(304,378)(305,377)(306,376)(307,379)(308,381)(309,380)(310,383)(311,382)
(312,384)(313,387)(314,386)(315,385)(316,388)(317,390)(318,389)(319,392)
(320,391)(321,393)(322,396)(323,395)(324,394)(325,406)(326,408)(327,407)
(328,410)(329,409)(330,411)(331,414)(332,413)(333,412)(334,397)(335,399)
(336,398)(337,401)(338,400)(339,402)(340,405)(341,404)(342,403)(343,424)
(344,426)(345,425)(346,428)(347,427)(348,429)(349,432)(350,431)(351,430)
(352,415)(353,417)(354,416)(355,419)(356,418)(357,420)(358,423)(359,422)
(360,421)(433,505)(434,507)(435,506)(436,509)(437,508)(438,510)(439,513)
(440,512)(441,511)(442,514)(443,516)(444,515)(445,518)(446,517)(447,519)
(448,522)(449,521)(450,520)(451,523)(452,525)(453,524)(454,527)(455,526)
(456,528)(457,531)(458,530)(459,529)(460,532)(461,534)(462,533)(463,536)
(464,535)(465,537)(466,540)(467,539)(468,538)(469,550)(470,552)(471,551)
(472,554)(473,553)(474,555)(475,558)(476,557)(477,556)(478,541)(479,543)
(480,542)(481,545)(482,544)(483,546)(484,549)(485,548)(486,547)(487,568)
(488,570)(489,569)(490,572)(491,571)(492,573)(493,576)(494,575)(495,574)
(496,559)(497,561)(498,560)(499,563)(500,562)(501,564)(502,567)(503,566)
(504,565);
s2 := Sym(576)!(  1,112)(  2,114)(  3,113)(  4,109)(  5,111)(  6,110)(  7,115)
(  8,117)(  9,116)( 10,121)( 11,123)( 12,122)( 13,118)( 14,120)( 15,119)
( 16,124)( 17,126)( 18,125)( 19,130)( 20,132)( 21,131)( 22,127)( 23,129)
( 24,128)( 25,133)( 26,135)( 27,134)( 28,139)( 29,141)( 30,140)( 31,136)
( 32,138)( 33,137)( 34,142)( 35,144)( 36,143)( 37, 85)( 38, 87)( 39, 86)
( 40, 82)( 41, 84)( 42, 83)( 43, 88)( 44, 90)( 45, 89)( 46, 76)( 47, 78)
( 48, 77)( 49, 73)( 50, 75)( 51, 74)( 52, 79)( 53, 81)( 54, 80)( 55,103)
( 56,105)( 57,104)( 58,100)( 59,102)( 60,101)( 61,106)( 62,108)( 63,107)
( 64, 94)( 65, 96)( 66, 95)( 67, 91)( 68, 93)( 69, 92)( 70, 97)( 71, 99)
( 72, 98)(145,274)(146,276)(147,275)(148,271)(149,273)(150,272)(151,277)
(152,279)(153,278)(154,283)(155,285)(156,284)(157,280)(158,282)(159,281)
(160,286)(161,288)(162,287)(163,256)(164,258)(165,257)(166,253)(167,255)
(168,254)(169,259)(170,261)(171,260)(172,265)(173,267)(174,266)(175,262)
(176,264)(177,263)(178,268)(179,270)(180,269)(181,247)(182,249)(183,248)
(184,244)(185,246)(186,245)(187,250)(188,252)(189,251)(190,238)(191,240)
(192,239)(193,235)(194,237)(195,236)(196,241)(197,243)(198,242)(199,229)
(200,231)(201,230)(202,226)(203,228)(204,227)(205,232)(206,234)(207,233)
(208,220)(209,222)(210,221)(211,217)(212,219)(213,218)(214,223)(215,225)
(216,224)(289,364)(290,366)(291,365)(292,361)(293,363)(294,362)(295,367)
(296,369)(297,368)(298,373)(299,375)(300,374)(301,370)(302,372)(303,371)
(304,376)(305,378)(306,377)(307,382)(308,384)(309,383)(310,379)(311,381)
(312,380)(313,385)(314,387)(315,386)(316,391)(317,393)(318,392)(319,388)
(320,390)(321,389)(322,394)(323,396)(324,395)(325,400)(326,402)(327,401)
(328,397)(329,399)(330,398)(331,403)(332,405)(333,404)(334,409)(335,411)
(336,410)(337,406)(338,408)(339,407)(340,412)(341,414)(342,413)(343,418)
(344,420)(345,419)(346,415)(347,417)(348,416)(349,421)(350,423)(351,422)
(352,427)(353,429)(354,428)(355,424)(356,426)(357,425)(358,430)(359,432)
(360,431)(433,526)(434,528)(435,527)(436,523)(437,525)(438,524)(439,529)
(440,531)(441,530)(442,535)(443,537)(444,536)(445,532)(446,534)(447,533)
(448,538)(449,540)(450,539)(451,508)(452,510)(453,509)(454,505)(455,507)
(456,506)(457,511)(458,513)(459,512)(460,517)(461,519)(462,518)(463,514)
(464,516)(465,515)(466,520)(467,522)(468,521)(469,562)(470,564)(471,563)
(472,559)(473,561)(474,560)(475,565)(476,567)(477,566)(478,571)(479,573)
(480,572)(481,568)(482,570)(483,569)(484,574)(485,576)(486,575)(487,544)
(488,546)(489,545)(490,541)(491,543)(492,542)(493,547)(494,549)(495,548)
(496,553)(497,555)(498,554)(499,550)(500,552)(501,551)(502,556)(503,558)
(504,557);
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope