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Polytope of Type {3,6,32}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,32}*1152
if this polytope has a name.
Group : SmallGroup(1152,34514)
Rank : 4
Schlafli Type : {3,6,32}
Number of vertices, edges, etc : 3, 9, 96, 32
Order of s0s1s2s3 : 96
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 : {3,6,16}*576
   3-fold quotients : {3,2,32}*384
   4-fold quotients : {3,6,8}*288
   6-fold quotients : {3,2,16}*192
   8-fold quotients : {3,6,4}*144
   12-fold quotients : {3,2,8}*96
   16-fold quotients : {3,6,2}*72
   24-fold quotients : {3,2,4}*48
   48-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,145)(  2,147)(  3,146)(  4,151)(  5,153)(  6,152)(  7,148)(  8,150)
(  9,149)( 10,154)( 11,156)( 12,155)( 13,160)( 14,162)( 15,161)( 16,157)
( 17,159)( 18,158)( 19,163)( 20,165)( 21,164)( 22,169)( 23,171)( 24,170)
( 25,166)( 26,168)( 27,167)( 28,172)( 29,174)( 30,173)( 31,178)( 32,180)
( 33,179)( 34,175)( 35,177)( 36,176)( 37,181)( 38,183)( 39,182)( 40,187)
( 41,189)( 42,188)( 43,184)( 44,186)( 45,185)( 46,190)( 47,192)( 48,191)
( 49,196)( 50,198)( 51,197)( 52,193)( 53,195)( 54,194)( 55,199)( 56,201)
( 57,200)( 58,205)( 59,207)( 60,206)( 61,202)( 62,204)( 63,203)( 64,208)
( 65,210)( 66,209)( 67,214)( 68,216)( 69,215)( 70,211)( 71,213)( 72,212)
( 73,217)( 74,219)( 75,218)( 76,223)( 77,225)( 78,224)( 79,220)( 80,222)
( 81,221)( 82,226)( 83,228)( 84,227)( 85,232)( 86,234)( 87,233)( 88,229)
( 89,231)( 90,230)( 91,235)( 92,237)( 93,236)( 94,241)( 95,243)( 96,242)
( 97,238)( 98,240)( 99,239)(100,244)(101,246)(102,245)(103,250)(104,252)
(105,251)(106,247)(107,249)(108,248)(109,253)(110,255)(111,254)(112,259)
(113,261)(114,260)(115,256)(116,258)(117,257)(118,262)(119,264)(120,263)
(121,268)(122,270)(123,269)(124,265)(125,267)(126,266)(127,271)(128,273)
(129,272)(130,277)(131,279)(132,278)(133,274)(134,276)(135,275)(136,280)
(137,282)(138,281)(139,286)(140,288)(141,287)(142,283)(143,285)(144,284)
(289,433)(290,435)(291,434)(292,439)(293,441)(294,440)(295,436)(296,438)
(297,437)(298,442)(299,444)(300,443)(301,448)(302,450)(303,449)(304,445)
(305,447)(306,446)(307,451)(308,453)(309,452)(310,457)(311,459)(312,458)
(313,454)(314,456)(315,455)(316,460)(317,462)(318,461)(319,466)(320,468)
(321,467)(322,463)(323,465)(324,464)(325,469)(326,471)(327,470)(328,475)
(329,477)(330,476)(331,472)(332,474)(333,473)(334,478)(335,480)(336,479)
(337,484)(338,486)(339,485)(340,481)(341,483)(342,482)(343,487)(344,489)
(345,488)(346,493)(347,495)(348,494)(349,490)(350,492)(351,491)(352,496)
(353,498)(354,497)(355,502)(356,504)(357,503)(358,499)(359,501)(360,500)
(361,505)(362,507)(363,506)(364,511)(365,513)(366,512)(367,508)(368,510)
(369,509)(370,514)(371,516)(372,515)(373,520)(374,522)(375,521)(376,517)
(377,519)(378,518)(379,523)(380,525)(381,524)(382,529)(383,531)(384,530)
(385,526)(386,528)(387,527)(388,532)(389,534)(390,533)(391,538)(392,540)
(393,539)(394,535)(395,537)(396,536)(397,541)(398,543)(399,542)(400,547)
(401,549)(402,548)(403,544)(404,546)(405,545)(406,550)(407,552)(408,551)
(409,556)(410,558)(411,557)(412,553)(413,555)(414,554)(415,559)(416,561)
(417,560)(418,565)(419,567)(420,566)(421,562)(422,564)(423,563)(424,568)
(425,570)(426,569)(427,574)(428,576)(429,575)(430,571)(431,573)(432,572);;
s1 := (  1,146)(  2,145)(  3,147)(  4,152)(  5,151)(  6,153)(  7,149)(  8,148)
(  9,150)( 10,155)( 11,154)( 12,156)( 13,161)( 14,160)( 15,162)( 16,158)
( 17,157)( 18,159)( 19,164)( 20,163)( 21,165)( 22,170)( 23,169)( 24,171)
( 25,167)( 26,166)( 27,168)( 28,173)( 29,172)( 30,174)( 31,179)( 32,178)
( 33,180)( 34,176)( 35,175)( 36,177)( 37,182)( 38,181)( 39,183)( 40,188)
( 41,187)( 42,189)( 43,185)( 44,184)( 45,186)( 46,191)( 47,190)( 48,192)
( 49,197)( 50,196)( 51,198)( 52,194)( 53,193)( 54,195)( 55,200)( 56,199)
( 57,201)( 58,206)( 59,205)( 60,207)( 61,203)( 62,202)( 63,204)( 64,209)
( 65,208)( 66,210)( 67,215)( 68,214)( 69,216)( 70,212)( 71,211)( 72,213)
( 73,218)( 74,217)( 75,219)( 76,224)( 77,223)( 78,225)( 79,221)( 80,220)
( 81,222)( 82,227)( 83,226)( 84,228)( 85,233)( 86,232)( 87,234)( 88,230)
( 89,229)( 90,231)( 91,236)( 92,235)( 93,237)( 94,242)( 95,241)( 96,243)
( 97,239)( 98,238)( 99,240)(100,245)(101,244)(102,246)(103,251)(104,250)
(105,252)(106,248)(107,247)(108,249)(109,254)(110,253)(111,255)(112,260)
(113,259)(114,261)(115,257)(116,256)(117,258)(118,263)(119,262)(120,264)
(121,269)(122,268)(123,270)(124,266)(125,265)(126,267)(127,272)(128,271)
(129,273)(130,278)(131,277)(132,279)(133,275)(134,274)(135,276)(136,281)
(137,280)(138,282)(139,287)(140,286)(141,288)(142,284)(143,283)(144,285)
(289,434)(290,433)(291,435)(292,440)(293,439)(294,441)(295,437)(296,436)
(297,438)(298,443)(299,442)(300,444)(301,449)(302,448)(303,450)(304,446)
(305,445)(306,447)(307,452)(308,451)(309,453)(310,458)(311,457)(312,459)
(313,455)(314,454)(315,456)(316,461)(317,460)(318,462)(319,467)(320,466)
(321,468)(322,464)(323,463)(324,465)(325,470)(326,469)(327,471)(328,476)
(329,475)(330,477)(331,473)(332,472)(333,474)(334,479)(335,478)(336,480)
(337,485)(338,484)(339,486)(340,482)(341,481)(342,483)(343,488)(344,487)
(345,489)(346,494)(347,493)(348,495)(349,491)(350,490)(351,492)(352,497)
(353,496)(354,498)(355,503)(356,502)(357,504)(358,500)(359,499)(360,501)
(361,506)(362,505)(363,507)(364,512)(365,511)(366,513)(367,509)(368,508)
(369,510)(370,515)(371,514)(372,516)(373,521)(374,520)(375,522)(376,518)
(377,517)(378,519)(379,524)(380,523)(381,525)(382,530)(383,529)(384,531)
(385,527)(386,526)(387,528)(388,533)(389,532)(390,534)(391,539)(392,538)
(393,540)(394,536)(395,535)(396,537)(397,542)(398,541)(399,543)(400,548)
(401,547)(402,549)(403,545)(404,544)(405,546)(406,551)(407,550)(408,552)
(409,557)(410,556)(411,558)(412,554)(413,553)(414,555)(415,560)(416,559)
(417,561)(418,566)(419,565)(420,567)(421,563)(422,562)(423,564)(424,569)
(425,568)(426,570)(427,575)(428,574)(429,576)(430,572)(431,571)(432,573);;
s2 := (  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)( 19,316)( 20,321)( 21,323)( 22,319)( 23,324)( 24,317)
( 25,322)( 26,318)( 27,320)( 28,307)( 29,312)( 30,314)( 31,310)( 32,315)
( 33,308)( 34,313)( 35,309)( 36,311)( 37,343)( 38,348)( 39,350)( 40,346)
( 41,351)( 42,344)( 43,349)( 44,345)( 45,347)( 46,352)( 47,357)( 48,359)
( 49,355)( 50,360)( 51,353)( 52,358)( 53,354)( 54,356)( 55,325)( 56,330)
( 57,332)( 58,328)( 59,333)( 60,326)( 61,331)( 62,327)( 63,329)( 64,334)
( 65,339)( 66,341)( 67,337)( 68,342)( 69,335)( 70,340)( 71,336)( 72,338)
( 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)( 91,424)( 92,429)( 93,431)( 94,427)( 95,432)( 96,425)
( 97,430)( 98,426)( 99,428)(100,415)(101,420)(102,422)(103,418)(104,423)
(105,416)(106,421)(107,417)(108,419)(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)(127,388)(128,393)
(129,395)(130,391)(131,396)(132,389)(133,394)(134,390)(135,392)(136,379)
(137,384)(138,386)(139,382)(140,387)(141,380)(142,385)(143,381)(144,383)
(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)(163,460)(164,465)(165,467)(166,463)(167,468)(168,461)
(169,466)(170,462)(171,464)(172,451)(173,456)(174,458)(175,454)(176,459)
(177,452)(178,457)(179,453)(180,455)(181,487)(182,492)(183,494)(184,490)
(185,495)(186,488)(187,493)(188,489)(189,491)(190,496)(191,501)(192,503)
(193,499)(194,504)(195,497)(196,502)(197,498)(198,500)(199,469)(200,474)
(201,476)(202,472)(203,477)(204,470)(205,475)(206,471)(207,473)(208,478)
(209,483)(210,485)(211,481)(212,486)(213,479)(214,484)(215,480)(216,482)
(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)(235,568)(236,573)(237,575)(238,571)(239,576)(240,569)
(241,574)(242,570)(243,572)(244,559)(245,564)(246,566)(247,562)(248,567)
(249,560)(250,565)(251,561)(252,563)(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)(271,532)(272,537)
(273,539)(274,535)(275,540)(276,533)(277,538)(278,534)(279,536)(280,523)
(281,528)(282,530)(283,526)(284,531)(285,524)(286,529)(287,525)(288,527);;
s3 := ( 19, 28)( 20, 29)( 21, 30)( 22, 31)( 23, 32)( 24, 33)( 25, 34)( 26, 35)
( 27, 36)( 37, 55)( 38, 56)( 39, 57)( 40, 58)( 41, 59)( 42, 60)( 43, 61)
( 44, 62)( 45, 63)( 46, 64)( 47, 65)( 48, 66)( 49, 67)( 50, 68)( 51, 69)
( 52, 70)( 53, 71)( 54, 72)( 73,109)( 74,110)( 75,111)( 76,112)( 77,113)
( 78,114)( 79,115)( 80,116)( 81,117)( 82,118)( 83,119)( 84,120)( 85,121)
( 86,122)( 87,123)( 88,124)( 89,125)( 90,126)( 91,136)( 92,137)( 93,138)
( 94,139)( 95,140)( 96,141)( 97,142)( 98,143)( 99,144)(100,127)(101,128)
(102,129)(103,130)(104,131)(105,132)(106,133)(107,134)(108,135)(163,172)
(164,173)(165,174)(166,175)(167,176)(168,177)(169,178)(170,179)(171,180)
(181,199)(182,200)(183,201)(184,202)(185,203)(186,204)(187,205)(188,206)
(189,207)(190,208)(191,209)(192,210)(193,211)(194,212)(195,213)(196,214)
(197,215)(198,216)(217,253)(218,254)(219,255)(220,256)(221,257)(222,258)
(223,259)(224,260)(225,261)(226,262)(227,263)(228,264)(229,265)(230,266)
(231,267)(232,268)(233,269)(234,270)(235,280)(236,281)(237,282)(238,283)
(239,284)(240,285)(241,286)(242,287)(243,288)(244,271)(245,272)(246,273)
(247,274)(248,275)(249,276)(250,277)(251,278)(252,279)(289,361)(290,362)
(291,363)(292,364)(293,365)(294,366)(295,367)(296,368)(297,369)(298,370)
(299,371)(300,372)(301,373)(302,374)(303,375)(304,376)(305,377)(306,378)
(307,388)(308,389)(309,390)(310,391)(311,392)(312,393)(313,394)(314,395)
(315,396)(316,379)(317,380)(318,381)(319,382)(320,383)(321,384)(322,385)
(323,386)(324,387)(325,415)(326,416)(327,417)(328,418)(329,419)(330,420)
(331,421)(332,422)(333,423)(334,424)(335,425)(336,426)(337,427)(338,428)
(339,429)(340,430)(341,431)(342,432)(343,397)(344,398)(345,399)(346,400)
(347,401)(348,402)(349,403)(350,404)(351,405)(352,406)(353,407)(354,408)
(355,409)(356,410)(357,411)(358,412)(359,413)(360,414)(433,505)(434,506)
(435,507)(436,508)(437,509)(438,510)(439,511)(440,512)(441,513)(442,514)
(443,515)(444,516)(445,517)(446,518)(447,519)(448,520)(449,521)(450,522)
(451,532)(452,533)(453,534)(454,535)(455,536)(456,537)(457,538)(458,539)
(459,540)(460,523)(461,524)(462,525)(463,526)(464,527)(465,528)(466,529)
(467,530)(468,531)(469,559)(470,560)(471,561)(472,562)(473,563)(474,564)
(475,565)(476,566)(477,567)(478,568)(479,569)(480,570)(481,571)(482,572)
(483,573)(484,574)(485,575)(486,576)(487,541)(488,542)(489,543)(490,544)
(491,545)(492,546)(493,547)(494,548)(495,549)(496,550)(497,551)(498,552)
(499,553)(500,554)(501,555)(502,556)(503,557)(504,558);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*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*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)!(  1,145)(  2,147)(  3,146)(  4,151)(  5,153)(  6,152)(  7,148)
(  8,150)(  9,149)( 10,154)( 11,156)( 12,155)( 13,160)( 14,162)( 15,161)
( 16,157)( 17,159)( 18,158)( 19,163)( 20,165)( 21,164)( 22,169)( 23,171)
( 24,170)( 25,166)( 26,168)( 27,167)( 28,172)( 29,174)( 30,173)( 31,178)
( 32,180)( 33,179)( 34,175)( 35,177)( 36,176)( 37,181)( 38,183)( 39,182)
( 40,187)( 41,189)( 42,188)( 43,184)( 44,186)( 45,185)( 46,190)( 47,192)
( 48,191)( 49,196)( 50,198)( 51,197)( 52,193)( 53,195)( 54,194)( 55,199)
( 56,201)( 57,200)( 58,205)( 59,207)( 60,206)( 61,202)( 62,204)( 63,203)
( 64,208)( 65,210)( 66,209)( 67,214)( 68,216)( 69,215)( 70,211)( 71,213)
( 72,212)( 73,217)( 74,219)( 75,218)( 76,223)( 77,225)( 78,224)( 79,220)
( 80,222)( 81,221)( 82,226)( 83,228)( 84,227)( 85,232)( 86,234)( 87,233)
( 88,229)( 89,231)( 90,230)( 91,235)( 92,237)( 93,236)( 94,241)( 95,243)
( 96,242)( 97,238)( 98,240)( 99,239)(100,244)(101,246)(102,245)(103,250)
(104,252)(105,251)(106,247)(107,249)(108,248)(109,253)(110,255)(111,254)
(112,259)(113,261)(114,260)(115,256)(116,258)(117,257)(118,262)(119,264)
(120,263)(121,268)(122,270)(123,269)(124,265)(125,267)(126,266)(127,271)
(128,273)(129,272)(130,277)(131,279)(132,278)(133,274)(134,276)(135,275)
(136,280)(137,282)(138,281)(139,286)(140,288)(141,287)(142,283)(143,285)
(144,284)(289,433)(290,435)(291,434)(292,439)(293,441)(294,440)(295,436)
(296,438)(297,437)(298,442)(299,444)(300,443)(301,448)(302,450)(303,449)
(304,445)(305,447)(306,446)(307,451)(308,453)(309,452)(310,457)(311,459)
(312,458)(313,454)(314,456)(315,455)(316,460)(317,462)(318,461)(319,466)
(320,468)(321,467)(322,463)(323,465)(324,464)(325,469)(326,471)(327,470)
(328,475)(329,477)(330,476)(331,472)(332,474)(333,473)(334,478)(335,480)
(336,479)(337,484)(338,486)(339,485)(340,481)(341,483)(342,482)(343,487)
(344,489)(345,488)(346,493)(347,495)(348,494)(349,490)(350,492)(351,491)
(352,496)(353,498)(354,497)(355,502)(356,504)(357,503)(358,499)(359,501)
(360,500)(361,505)(362,507)(363,506)(364,511)(365,513)(366,512)(367,508)
(368,510)(369,509)(370,514)(371,516)(372,515)(373,520)(374,522)(375,521)
(376,517)(377,519)(378,518)(379,523)(380,525)(381,524)(382,529)(383,531)
(384,530)(385,526)(386,528)(387,527)(388,532)(389,534)(390,533)(391,538)
(392,540)(393,539)(394,535)(395,537)(396,536)(397,541)(398,543)(399,542)
(400,547)(401,549)(402,548)(403,544)(404,546)(405,545)(406,550)(407,552)
(408,551)(409,556)(410,558)(411,557)(412,553)(413,555)(414,554)(415,559)
(416,561)(417,560)(418,565)(419,567)(420,566)(421,562)(422,564)(423,563)
(424,568)(425,570)(426,569)(427,574)(428,576)(429,575)(430,571)(431,573)
(432,572);
s1 := Sym(576)!(  1,146)(  2,145)(  3,147)(  4,152)(  5,151)(  6,153)(  7,149)
(  8,148)(  9,150)( 10,155)( 11,154)( 12,156)( 13,161)( 14,160)( 15,162)
( 16,158)( 17,157)( 18,159)( 19,164)( 20,163)( 21,165)( 22,170)( 23,169)
( 24,171)( 25,167)( 26,166)( 27,168)( 28,173)( 29,172)( 30,174)( 31,179)
( 32,178)( 33,180)( 34,176)( 35,175)( 36,177)( 37,182)( 38,181)( 39,183)
( 40,188)( 41,187)( 42,189)( 43,185)( 44,184)( 45,186)( 46,191)( 47,190)
( 48,192)( 49,197)( 50,196)( 51,198)( 52,194)( 53,193)( 54,195)( 55,200)
( 56,199)( 57,201)( 58,206)( 59,205)( 60,207)( 61,203)( 62,202)( 63,204)
( 64,209)( 65,208)( 66,210)( 67,215)( 68,214)( 69,216)( 70,212)( 71,211)
( 72,213)( 73,218)( 74,217)( 75,219)( 76,224)( 77,223)( 78,225)( 79,221)
( 80,220)( 81,222)( 82,227)( 83,226)( 84,228)( 85,233)( 86,232)( 87,234)
( 88,230)( 89,229)( 90,231)( 91,236)( 92,235)( 93,237)( 94,242)( 95,241)
( 96,243)( 97,239)( 98,238)( 99,240)(100,245)(101,244)(102,246)(103,251)
(104,250)(105,252)(106,248)(107,247)(108,249)(109,254)(110,253)(111,255)
(112,260)(113,259)(114,261)(115,257)(116,256)(117,258)(118,263)(119,262)
(120,264)(121,269)(122,268)(123,270)(124,266)(125,265)(126,267)(127,272)
(128,271)(129,273)(130,278)(131,277)(132,279)(133,275)(134,274)(135,276)
(136,281)(137,280)(138,282)(139,287)(140,286)(141,288)(142,284)(143,283)
(144,285)(289,434)(290,433)(291,435)(292,440)(293,439)(294,441)(295,437)
(296,436)(297,438)(298,443)(299,442)(300,444)(301,449)(302,448)(303,450)
(304,446)(305,445)(306,447)(307,452)(308,451)(309,453)(310,458)(311,457)
(312,459)(313,455)(314,454)(315,456)(316,461)(317,460)(318,462)(319,467)
(320,466)(321,468)(322,464)(323,463)(324,465)(325,470)(326,469)(327,471)
(328,476)(329,475)(330,477)(331,473)(332,472)(333,474)(334,479)(335,478)
(336,480)(337,485)(338,484)(339,486)(340,482)(341,481)(342,483)(343,488)
(344,487)(345,489)(346,494)(347,493)(348,495)(349,491)(350,490)(351,492)
(352,497)(353,496)(354,498)(355,503)(356,502)(357,504)(358,500)(359,499)
(360,501)(361,506)(362,505)(363,507)(364,512)(365,511)(366,513)(367,509)
(368,508)(369,510)(370,515)(371,514)(372,516)(373,521)(374,520)(375,522)
(376,518)(377,517)(378,519)(379,524)(380,523)(381,525)(382,530)(383,529)
(384,531)(385,527)(386,526)(387,528)(388,533)(389,532)(390,534)(391,539)
(392,538)(393,540)(394,536)(395,535)(396,537)(397,542)(398,541)(399,543)
(400,548)(401,547)(402,549)(403,545)(404,544)(405,546)(406,551)(407,550)
(408,552)(409,557)(410,556)(411,558)(412,554)(413,553)(414,555)(415,560)
(416,559)(417,561)(418,566)(419,565)(420,567)(421,563)(422,562)(423,564)
(424,569)(425,568)(426,570)(427,575)(428,574)(429,576)(430,572)(431,571)
(432,573);
s2 := 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)( 19,316)( 20,321)( 21,323)( 22,319)( 23,324)
( 24,317)( 25,322)( 26,318)( 27,320)( 28,307)( 29,312)( 30,314)( 31,310)
( 32,315)( 33,308)( 34,313)( 35,309)( 36,311)( 37,343)( 38,348)( 39,350)
( 40,346)( 41,351)( 42,344)( 43,349)( 44,345)( 45,347)( 46,352)( 47,357)
( 48,359)( 49,355)( 50,360)( 51,353)( 52,358)( 53,354)( 54,356)( 55,325)
( 56,330)( 57,332)( 58,328)( 59,333)( 60,326)( 61,331)( 62,327)( 63,329)
( 64,334)( 65,339)( 66,341)( 67,337)( 68,342)( 69,335)( 70,340)( 71,336)
( 72,338)( 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)( 91,424)( 92,429)( 93,431)( 94,427)( 95,432)
( 96,425)( 97,430)( 98,426)( 99,428)(100,415)(101,420)(102,422)(103,418)
(104,423)(105,416)(106,421)(107,417)(108,419)(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)(127,388)
(128,393)(129,395)(130,391)(131,396)(132,389)(133,394)(134,390)(135,392)
(136,379)(137,384)(138,386)(139,382)(140,387)(141,380)(142,385)(143,381)
(144,383)(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)(163,460)(164,465)(165,467)(166,463)(167,468)
(168,461)(169,466)(170,462)(171,464)(172,451)(173,456)(174,458)(175,454)
(176,459)(177,452)(178,457)(179,453)(180,455)(181,487)(182,492)(183,494)
(184,490)(185,495)(186,488)(187,493)(188,489)(189,491)(190,496)(191,501)
(192,503)(193,499)(194,504)(195,497)(196,502)(197,498)(198,500)(199,469)
(200,474)(201,476)(202,472)(203,477)(204,470)(205,475)(206,471)(207,473)
(208,478)(209,483)(210,485)(211,481)(212,486)(213,479)(214,484)(215,480)
(216,482)(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)(235,568)(236,573)(237,575)(238,571)(239,576)
(240,569)(241,574)(242,570)(243,572)(244,559)(245,564)(246,566)(247,562)
(248,567)(249,560)(250,565)(251,561)(252,563)(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)(271,532)
(272,537)(273,539)(274,535)(275,540)(276,533)(277,538)(278,534)(279,536)
(280,523)(281,528)(282,530)(283,526)(284,531)(285,524)(286,529)(287,525)
(288,527);
s3 := Sym(576)!( 19, 28)( 20, 29)( 21, 30)( 22, 31)( 23, 32)( 24, 33)( 25, 34)
( 26, 35)( 27, 36)( 37, 55)( 38, 56)( 39, 57)( 40, 58)( 41, 59)( 42, 60)
( 43, 61)( 44, 62)( 45, 63)( 46, 64)( 47, 65)( 48, 66)( 49, 67)( 50, 68)
( 51, 69)( 52, 70)( 53, 71)( 54, 72)( 73,109)( 74,110)( 75,111)( 76,112)
( 77,113)( 78,114)( 79,115)( 80,116)( 81,117)( 82,118)( 83,119)( 84,120)
( 85,121)( 86,122)( 87,123)( 88,124)( 89,125)( 90,126)( 91,136)( 92,137)
( 93,138)( 94,139)( 95,140)( 96,141)( 97,142)( 98,143)( 99,144)(100,127)
(101,128)(102,129)(103,130)(104,131)(105,132)(106,133)(107,134)(108,135)
(163,172)(164,173)(165,174)(166,175)(167,176)(168,177)(169,178)(170,179)
(171,180)(181,199)(182,200)(183,201)(184,202)(185,203)(186,204)(187,205)
(188,206)(189,207)(190,208)(191,209)(192,210)(193,211)(194,212)(195,213)
(196,214)(197,215)(198,216)(217,253)(218,254)(219,255)(220,256)(221,257)
(222,258)(223,259)(224,260)(225,261)(226,262)(227,263)(228,264)(229,265)
(230,266)(231,267)(232,268)(233,269)(234,270)(235,280)(236,281)(237,282)
(238,283)(239,284)(240,285)(241,286)(242,287)(243,288)(244,271)(245,272)
(246,273)(247,274)(248,275)(249,276)(250,277)(251,278)(252,279)(289,361)
(290,362)(291,363)(292,364)(293,365)(294,366)(295,367)(296,368)(297,369)
(298,370)(299,371)(300,372)(301,373)(302,374)(303,375)(304,376)(305,377)
(306,378)(307,388)(308,389)(309,390)(310,391)(311,392)(312,393)(313,394)
(314,395)(315,396)(316,379)(317,380)(318,381)(319,382)(320,383)(321,384)
(322,385)(323,386)(324,387)(325,415)(326,416)(327,417)(328,418)(329,419)
(330,420)(331,421)(332,422)(333,423)(334,424)(335,425)(336,426)(337,427)
(338,428)(339,429)(340,430)(341,431)(342,432)(343,397)(344,398)(345,399)
(346,400)(347,401)(348,402)(349,403)(350,404)(351,405)(352,406)(353,407)
(354,408)(355,409)(356,410)(357,411)(358,412)(359,413)(360,414)(433,505)
(434,506)(435,507)(436,508)(437,509)(438,510)(439,511)(440,512)(441,513)
(442,514)(443,515)(444,516)(445,517)(446,518)(447,519)(448,520)(449,521)
(450,522)(451,532)(452,533)(453,534)(454,535)(455,536)(456,537)(457,538)
(458,539)(459,540)(460,523)(461,524)(462,525)(463,526)(464,527)(465,528)
(466,529)(467,530)(468,531)(469,559)(470,560)(471,561)(472,562)(473,563)
(474,564)(475,565)(476,566)(477,567)(478,568)(479,569)(480,570)(481,571)
(482,572)(483,573)(484,574)(485,575)(486,576)(487,541)(488,542)(489,543)
(490,544)(491,545)(492,546)(493,547)(494,548)(495,549)(496,550)(497,551)
(498,552)(499,553)(500,554)(501,555)(502,556)(503,557)(504,558);
poly := sub<Sym(576)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 
References : None.
to this polytope