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Polytope of Type {4,4,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,12}*1152
if this polytope has a name.
Group : SmallGroup(1152,43029)
Rank : 4
Schlafli Type : {4,4,12}
Number of vertices, edges, etc : 4, 24, 72, 36
Order of s0s1s2s3 : 4
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 : {4,4,6}*576, {2,4,12}*576
   4-fold quotients : {4,4,6}*288, {2,4,6}*288
   8-fold quotients : {2,4,6}*144
   9-fold quotients : {4,4,4}*128
   18-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64
   36-fold quotients : {2,2,4}*32, {2,4,2}*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, 73)(  2, 74)(  3, 75)(  4, 76)(  5, 77)(  6, 78)(  7, 79)(  8, 80)
(  9, 81)( 10, 82)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)( 16, 88)
( 17, 89)( 18, 90)( 19, 91)( 20, 92)( 21, 93)( 22, 94)( 23, 95)( 24, 96)
( 25, 97)( 26, 98)( 27, 99)( 28,100)( 29,101)( 30,102)( 31,103)( 32,104)
( 33,105)( 34,106)( 35,107)( 36,108)( 37,109)( 38,110)( 39,111)( 40,112)
( 41,113)( 42,114)( 43,115)( 44,116)( 45,117)( 46,118)( 47,119)( 48,120)
( 49,121)( 50,122)( 51,123)( 52,124)( 53,125)( 54,126)( 55,127)( 56,128)
( 57,129)( 58,130)( 59,131)( 60,132)( 61,133)( 62,134)( 63,135)( 64,136)
( 65,137)( 66,138)( 67,139)( 68,140)( 69,141)( 70,142)( 71,143)( 72,144)
(145,217)(146,218)(147,219)(148,220)(149,221)(150,222)(151,223)(152,224)
(153,225)(154,226)(155,227)(156,228)(157,229)(158,230)(159,231)(160,232)
(161,233)(162,234)(163,235)(164,236)(165,237)(166,238)(167,239)(168,240)
(169,241)(170,242)(171,243)(172,244)(173,245)(174,246)(175,247)(176,248)
(177,249)(178,250)(179,251)(180,252)(181,253)(182,254)(183,255)(184,256)
(185,257)(186,258)(187,259)(188,260)(189,261)(190,262)(191,263)(192,264)
(193,265)(194,266)(195,267)(196,268)(197,269)(198,270)(199,271)(200,272)
(201,273)(202,274)(203,275)(204,276)(205,277)(206,278)(207,279)(208,280)
(209,281)(210,282)(211,283)(212,284)(213,285)(214,286)(215,287)(216,288)
(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)(307,379)(308,380)(309,381)(310,382)(311,383)(312,384)
(313,385)(314,386)(315,387)(316,388)(317,389)(318,390)(319,391)(320,392)
(321,393)(322,394)(323,395)(324,396)(325,397)(326,398)(327,399)(328,400)
(329,401)(330,402)(331,403)(332,404)(333,405)(334,406)(335,407)(336,408)
(337,409)(338,410)(339,411)(340,412)(341,413)(342,414)(343,415)(344,416)
(345,417)(346,418)(347,419)(348,420)(349,421)(350,422)(351,423)(352,424)
(353,425)(354,426)(355,427)(356,428)(357,429)(358,430)(359,431)(360,432)
(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)(451,523)(452,524)(453,525)(454,526)(455,527)(456,528)
(457,529)(458,530)(459,531)(460,532)(461,533)(462,534)(463,535)(464,536)
(465,537)(466,538)(467,539)(468,540)(469,541)(470,542)(471,543)(472,544)
(473,545)(474,546)(475,547)(476,548)(477,549)(478,550)(479,551)(480,552)
(481,553)(482,554)(483,555)(484,556)(485,557)(486,558)(487,559)(488,560)
(489,561)(490,562)(491,563)(492,564)(493,565)(494,566)(495,567)(496,568)
(497,569)(498,570)(499,571)(500,572)(501,573)(502,574)(503,575)(504,576);;
s1 := (  2,  6)(  3,  8)(  5,  9)( 11, 15)( 12, 17)( 14, 18)( 20, 24)( 21, 26)
( 23, 27)( 29, 33)( 30, 35)( 32, 36)( 38, 42)( 39, 44)( 41, 45)( 47, 51)
( 48, 53)( 50, 54)( 56, 60)( 57, 62)( 59, 63)( 65, 69)( 66, 71)( 68, 72)
( 73,109)( 74,114)( 75,116)( 76,112)( 77,117)( 78,110)( 79,115)( 80,111)
( 81,113)( 82,118)( 83,123)( 84,125)( 85,121)( 86,126)( 87,119)( 88,124)
( 89,120)( 90,122)( 91,127)( 92,132)( 93,134)( 94,130)( 95,135)( 96,128)
( 97,133)( 98,129)( 99,131)(100,136)(101,141)(102,143)(103,139)(104,144)
(105,137)(106,142)(107,138)(108,140)(145,163)(146,168)(147,170)(148,166)
(149,171)(150,164)(151,169)(152,165)(153,167)(154,172)(155,177)(156,179)
(157,175)(158,180)(159,173)(160,178)(161,174)(162,176)(181,199)(182,204)
(183,206)(184,202)(185,207)(186,200)(187,205)(188,201)(189,203)(190,208)
(191,213)(192,215)(193,211)(194,216)(195,209)(196,214)(197,210)(198,212)
(217,271)(218,276)(219,278)(220,274)(221,279)(222,272)(223,277)(224,273)
(225,275)(226,280)(227,285)(228,287)(229,283)(230,288)(231,281)(232,286)
(233,282)(234,284)(235,253)(236,258)(237,260)(238,256)(239,261)(240,254)
(241,259)(242,255)(243,257)(244,262)(245,267)(246,269)(247,265)(248,270)
(249,263)(250,268)(251,264)(252,266)(289,325)(290,330)(291,332)(292,328)
(293,333)(294,326)(295,331)(296,327)(297,329)(298,334)(299,339)(300,341)
(301,337)(302,342)(303,335)(304,340)(305,336)(306,338)(307,343)(308,348)
(309,350)(310,346)(311,351)(312,344)(313,349)(314,345)(315,347)(316,352)
(317,357)(318,359)(319,355)(320,360)(321,353)(322,358)(323,354)(324,356)
(362,366)(363,368)(365,369)(371,375)(372,377)(374,378)(380,384)(381,386)
(383,387)(389,393)(390,395)(392,396)(398,402)(399,404)(401,405)(407,411)
(408,413)(410,414)(416,420)(417,422)(419,423)(425,429)(426,431)(428,432)
(433,487)(434,492)(435,494)(436,490)(437,495)(438,488)(439,493)(440,489)
(441,491)(442,496)(443,501)(444,503)(445,499)(446,504)(447,497)(448,502)
(449,498)(450,500)(451,469)(452,474)(453,476)(454,472)(455,477)(456,470)
(457,475)(458,471)(459,473)(460,478)(461,483)(462,485)(463,481)(464,486)
(465,479)(466,484)(467,480)(468,482)(505,523)(506,528)(507,530)(508,526)
(509,531)(510,524)(511,529)(512,525)(513,527)(514,532)(515,537)(516,539)
(517,535)(518,540)(519,533)(520,538)(521,534)(522,536)(541,559)(542,564)
(543,566)(544,562)(545,567)(546,560)(547,565)(548,561)(549,563)(550,568)
(551,573)(552,575)(553,571)(554,576)(555,569)(556,574)(557,570)(558,572);;
s2 := (  1,145)(  2,147)(  3,146)(  4,149)(  5,148)(  6,150)(  7,153)(  8,152)
(  9,151)( 10,154)( 11,156)( 12,155)( 13,158)( 14,157)( 15,159)( 16,162)
( 17,161)( 18,160)( 19,163)( 20,165)( 21,164)( 22,167)( 23,166)( 24,168)
( 25,171)( 26,170)( 27,169)( 28,172)( 29,174)( 30,173)( 31,176)( 32,175)
( 33,177)( 34,180)( 35,179)( 36,178)( 37,181)( 38,183)( 39,182)( 40,185)
( 41,184)( 42,186)( 43,189)( 44,188)( 45,187)( 46,190)( 47,192)( 48,191)
( 49,194)( 50,193)( 51,195)( 52,198)( 53,197)( 54,196)( 55,199)( 56,201)
( 57,200)( 58,203)( 59,202)( 60,204)( 61,207)( 62,206)( 63,205)( 64,208)
( 65,210)( 66,209)( 67,212)( 68,211)( 69,213)( 70,216)( 71,215)( 72,214)
( 73,217)( 74,219)( 75,218)( 76,221)( 77,220)( 78,222)( 79,225)( 80,224)
( 81,223)( 82,226)( 83,228)( 84,227)( 85,230)( 86,229)( 87,231)( 88,234)
( 89,233)( 90,232)( 91,235)( 92,237)( 93,236)( 94,239)( 95,238)( 96,240)
( 97,243)( 98,242)( 99,241)(100,244)(101,246)(102,245)(103,248)(104,247)
(105,249)(106,252)(107,251)(108,250)(109,253)(110,255)(111,254)(112,257)
(113,256)(114,258)(115,261)(116,260)(117,259)(118,262)(119,264)(120,263)
(121,266)(122,265)(123,267)(124,270)(125,269)(126,268)(127,271)(128,273)
(129,272)(130,275)(131,274)(132,276)(133,279)(134,278)(135,277)(136,280)
(137,282)(138,281)(139,284)(140,283)(141,285)(142,288)(143,287)(144,286)
(289,433)(290,435)(291,434)(292,437)(293,436)(294,438)(295,441)(296,440)
(297,439)(298,442)(299,444)(300,443)(301,446)(302,445)(303,447)(304,450)
(305,449)(306,448)(307,451)(308,453)(309,452)(310,455)(311,454)(312,456)
(313,459)(314,458)(315,457)(316,460)(317,462)(318,461)(319,464)(320,463)
(321,465)(322,468)(323,467)(324,466)(325,469)(326,471)(327,470)(328,473)
(329,472)(330,474)(331,477)(332,476)(333,475)(334,478)(335,480)(336,479)
(337,482)(338,481)(339,483)(340,486)(341,485)(342,484)(343,487)(344,489)
(345,488)(346,491)(347,490)(348,492)(349,495)(350,494)(351,493)(352,496)
(353,498)(354,497)(355,500)(356,499)(357,501)(358,504)(359,503)(360,502)
(361,505)(362,507)(363,506)(364,509)(365,508)(366,510)(367,513)(368,512)
(369,511)(370,514)(371,516)(372,515)(373,518)(374,517)(375,519)(376,522)
(377,521)(378,520)(379,523)(380,525)(381,524)(382,527)(383,526)(384,528)
(385,531)(386,530)(387,529)(388,532)(389,534)(390,533)(391,536)(392,535)
(393,537)(394,540)(395,539)(396,538)(397,541)(398,543)(399,542)(400,545)
(401,544)(402,546)(403,549)(404,548)(405,547)(406,550)(407,552)(408,551)
(409,554)(410,553)(411,555)(412,558)(413,557)(414,556)(415,559)(416,561)
(417,560)(418,563)(419,562)(420,564)(421,567)(422,566)(423,565)(424,568)
(425,570)(426,569)(427,572)(428,571)(429,573)(430,576)(431,575)(432,574);;
s3 := (  1,382)(  2,384)(  3,383)(  4,379)(  5,381)(  6,380)(  7,385)(  8,387)
(  9,386)( 10,391)( 11,393)( 12,392)( 13,388)( 14,390)( 15,389)( 16,394)
( 17,396)( 18,395)( 19,364)( 20,366)( 21,365)( 22,361)( 23,363)( 24,362)
( 25,367)( 26,369)( 27,368)( 28,373)( 29,375)( 30,374)( 31,370)( 32,372)
( 33,371)( 34,376)( 35,378)( 36,377)( 37,418)( 38,420)( 39,419)( 40,415)
( 41,417)( 42,416)( 43,421)( 44,423)( 45,422)( 46,427)( 47,429)( 48,428)
( 49,424)( 50,426)( 51,425)( 52,430)( 53,432)( 54,431)( 55,400)( 56,402)
( 57,401)( 58,397)( 59,399)( 60,398)( 61,403)( 62,405)( 63,404)( 64,409)
( 65,411)( 66,410)( 67,406)( 68,408)( 69,407)( 70,412)( 71,414)( 72,413)
( 73,310)( 74,312)( 75,311)( 76,307)( 77,309)( 78,308)( 79,313)( 80,315)
( 81,314)( 82,319)( 83,321)( 84,320)( 85,316)( 86,318)( 87,317)( 88,322)
( 89,324)( 90,323)( 91,292)( 92,294)( 93,293)( 94,289)( 95,291)( 96,290)
( 97,295)( 98,297)( 99,296)(100,301)(101,303)(102,302)(103,298)(104,300)
(105,299)(106,304)(107,306)(108,305)(109,346)(110,348)(111,347)(112,343)
(113,345)(114,344)(115,349)(116,351)(117,350)(118,355)(119,357)(120,356)
(121,352)(122,354)(123,353)(124,358)(125,360)(126,359)(127,328)(128,330)
(129,329)(130,325)(131,327)(132,326)(133,331)(134,333)(135,332)(136,337)
(137,339)(138,338)(139,334)(140,336)(141,335)(142,340)(143,342)(144,341)
(145,535)(146,537)(147,536)(148,532)(149,534)(150,533)(151,538)(152,540)
(153,539)(154,526)(155,528)(156,527)(157,523)(158,525)(159,524)(160,529)
(161,531)(162,530)(163,517)(164,519)(165,518)(166,514)(167,516)(168,515)
(169,520)(170,522)(171,521)(172,508)(173,510)(174,509)(175,505)(176,507)
(177,506)(178,511)(179,513)(180,512)(181,571)(182,573)(183,572)(184,568)
(185,570)(186,569)(187,574)(188,576)(189,575)(190,562)(191,564)(192,563)
(193,559)(194,561)(195,560)(196,565)(197,567)(198,566)(199,553)(200,555)
(201,554)(202,550)(203,552)(204,551)(205,556)(206,558)(207,557)(208,544)
(209,546)(210,545)(211,541)(212,543)(213,542)(214,547)(215,549)(216,548)
(217,463)(218,465)(219,464)(220,460)(221,462)(222,461)(223,466)(224,468)
(225,467)(226,454)(227,456)(228,455)(229,451)(230,453)(231,452)(232,457)
(233,459)(234,458)(235,445)(236,447)(237,446)(238,442)(239,444)(240,443)
(241,448)(242,450)(243,449)(244,436)(245,438)(246,437)(247,433)(248,435)
(249,434)(250,439)(251,441)(252,440)(253,499)(254,501)(255,500)(256,496)
(257,498)(258,497)(259,502)(260,504)(261,503)(262,490)(263,492)(264,491)
(265,487)(266,489)(267,488)(268,493)(269,495)(270,494)(271,481)(272,483)
(273,482)(274,478)(275,480)(276,479)(277,484)(278,486)(279,485)(280,472)
(281,474)(282,473)(283,469)(284,471)(285,470)(286,475)(287,477)(288,476);;
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*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(576)!(  1, 73)(  2, 74)(  3, 75)(  4, 76)(  5, 77)(  6, 78)(  7, 79)
(  8, 80)(  9, 81)( 10, 82)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)
( 16, 88)( 17, 89)( 18, 90)( 19, 91)( 20, 92)( 21, 93)( 22, 94)( 23, 95)
( 24, 96)( 25, 97)( 26, 98)( 27, 99)( 28,100)( 29,101)( 30,102)( 31,103)
( 32,104)( 33,105)( 34,106)( 35,107)( 36,108)( 37,109)( 38,110)( 39,111)
( 40,112)( 41,113)( 42,114)( 43,115)( 44,116)( 45,117)( 46,118)( 47,119)
( 48,120)( 49,121)( 50,122)( 51,123)( 52,124)( 53,125)( 54,126)( 55,127)
( 56,128)( 57,129)( 58,130)( 59,131)( 60,132)( 61,133)( 62,134)( 63,135)
( 64,136)( 65,137)( 66,138)( 67,139)( 68,140)( 69,141)( 70,142)( 71,143)
( 72,144)(145,217)(146,218)(147,219)(148,220)(149,221)(150,222)(151,223)
(152,224)(153,225)(154,226)(155,227)(156,228)(157,229)(158,230)(159,231)
(160,232)(161,233)(162,234)(163,235)(164,236)(165,237)(166,238)(167,239)
(168,240)(169,241)(170,242)(171,243)(172,244)(173,245)(174,246)(175,247)
(176,248)(177,249)(178,250)(179,251)(180,252)(181,253)(182,254)(183,255)
(184,256)(185,257)(186,258)(187,259)(188,260)(189,261)(190,262)(191,263)
(192,264)(193,265)(194,266)(195,267)(196,268)(197,269)(198,270)(199,271)
(200,272)(201,273)(202,274)(203,275)(204,276)(205,277)(206,278)(207,279)
(208,280)(209,281)(210,282)(211,283)(212,284)(213,285)(214,286)(215,287)
(216,288)(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)(307,379)(308,380)(309,381)(310,382)(311,383)
(312,384)(313,385)(314,386)(315,387)(316,388)(317,389)(318,390)(319,391)
(320,392)(321,393)(322,394)(323,395)(324,396)(325,397)(326,398)(327,399)
(328,400)(329,401)(330,402)(331,403)(332,404)(333,405)(334,406)(335,407)
(336,408)(337,409)(338,410)(339,411)(340,412)(341,413)(342,414)(343,415)
(344,416)(345,417)(346,418)(347,419)(348,420)(349,421)(350,422)(351,423)
(352,424)(353,425)(354,426)(355,427)(356,428)(357,429)(358,430)(359,431)
(360,432)(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)(451,523)(452,524)(453,525)(454,526)(455,527)
(456,528)(457,529)(458,530)(459,531)(460,532)(461,533)(462,534)(463,535)
(464,536)(465,537)(466,538)(467,539)(468,540)(469,541)(470,542)(471,543)
(472,544)(473,545)(474,546)(475,547)(476,548)(477,549)(478,550)(479,551)
(480,552)(481,553)(482,554)(483,555)(484,556)(485,557)(486,558)(487,559)
(488,560)(489,561)(490,562)(491,563)(492,564)(493,565)(494,566)(495,567)
(496,568)(497,569)(498,570)(499,571)(500,572)(501,573)(502,574)(503,575)
(504,576);
s1 := Sym(576)!(  2,  6)(  3,  8)(  5,  9)( 11, 15)( 12, 17)( 14, 18)( 20, 24)
( 21, 26)( 23, 27)( 29, 33)( 30, 35)( 32, 36)( 38, 42)( 39, 44)( 41, 45)
( 47, 51)( 48, 53)( 50, 54)( 56, 60)( 57, 62)( 59, 63)( 65, 69)( 66, 71)
( 68, 72)( 73,109)( 74,114)( 75,116)( 76,112)( 77,117)( 78,110)( 79,115)
( 80,111)( 81,113)( 82,118)( 83,123)( 84,125)( 85,121)( 86,126)( 87,119)
( 88,124)( 89,120)( 90,122)( 91,127)( 92,132)( 93,134)( 94,130)( 95,135)
( 96,128)( 97,133)( 98,129)( 99,131)(100,136)(101,141)(102,143)(103,139)
(104,144)(105,137)(106,142)(107,138)(108,140)(145,163)(146,168)(147,170)
(148,166)(149,171)(150,164)(151,169)(152,165)(153,167)(154,172)(155,177)
(156,179)(157,175)(158,180)(159,173)(160,178)(161,174)(162,176)(181,199)
(182,204)(183,206)(184,202)(185,207)(186,200)(187,205)(188,201)(189,203)
(190,208)(191,213)(192,215)(193,211)(194,216)(195,209)(196,214)(197,210)
(198,212)(217,271)(218,276)(219,278)(220,274)(221,279)(222,272)(223,277)
(224,273)(225,275)(226,280)(227,285)(228,287)(229,283)(230,288)(231,281)
(232,286)(233,282)(234,284)(235,253)(236,258)(237,260)(238,256)(239,261)
(240,254)(241,259)(242,255)(243,257)(244,262)(245,267)(246,269)(247,265)
(248,270)(249,263)(250,268)(251,264)(252,266)(289,325)(290,330)(291,332)
(292,328)(293,333)(294,326)(295,331)(296,327)(297,329)(298,334)(299,339)
(300,341)(301,337)(302,342)(303,335)(304,340)(305,336)(306,338)(307,343)
(308,348)(309,350)(310,346)(311,351)(312,344)(313,349)(314,345)(315,347)
(316,352)(317,357)(318,359)(319,355)(320,360)(321,353)(322,358)(323,354)
(324,356)(362,366)(363,368)(365,369)(371,375)(372,377)(374,378)(380,384)
(381,386)(383,387)(389,393)(390,395)(392,396)(398,402)(399,404)(401,405)
(407,411)(408,413)(410,414)(416,420)(417,422)(419,423)(425,429)(426,431)
(428,432)(433,487)(434,492)(435,494)(436,490)(437,495)(438,488)(439,493)
(440,489)(441,491)(442,496)(443,501)(444,503)(445,499)(446,504)(447,497)
(448,502)(449,498)(450,500)(451,469)(452,474)(453,476)(454,472)(455,477)
(456,470)(457,475)(458,471)(459,473)(460,478)(461,483)(462,485)(463,481)
(464,486)(465,479)(466,484)(467,480)(468,482)(505,523)(506,528)(507,530)
(508,526)(509,531)(510,524)(511,529)(512,525)(513,527)(514,532)(515,537)
(516,539)(517,535)(518,540)(519,533)(520,538)(521,534)(522,536)(541,559)
(542,564)(543,566)(544,562)(545,567)(546,560)(547,565)(548,561)(549,563)
(550,568)(551,573)(552,575)(553,571)(554,576)(555,569)(556,574)(557,570)
(558,572);
s2 := Sym(576)!(  1,145)(  2,147)(  3,146)(  4,149)(  5,148)(  6,150)(  7,153)
(  8,152)(  9,151)( 10,154)( 11,156)( 12,155)( 13,158)( 14,157)( 15,159)
( 16,162)( 17,161)( 18,160)( 19,163)( 20,165)( 21,164)( 22,167)( 23,166)
( 24,168)( 25,171)( 26,170)( 27,169)( 28,172)( 29,174)( 30,173)( 31,176)
( 32,175)( 33,177)( 34,180)( 35,179)( 36,178)( 37,181)( 38,183)( 39,182)
( 40,185)( 41,184)( 42,186)( 43,189)( 44,188)( 45,187)( 46,190)( 47,192)
( 48,191)( 49,194)( 50,193)( 51,195)( 52,198)( 53,197)( 54,196)( 55,199)
( 56,201)( 57,200)( 58,203)( 59,202)( 60,204)( 61,207)( 62,206)( 63,205)
( 64,208)( 65,210)( 66,209)( 67,212)( 68,211)( 69,213)( 70,216)( 71,215)
( 72,214)( 73,217)( 74,219)( 75,218)( 76,221)( 77,220)( 78,222)( 79,225)
( 80,224)( 81,223)( 82,226)( 83,228)( 84,227)( 85,230)( 86,229)( 87,231)
( 88,234)( 89,233)( 90,232)( 91,235)( 92,237)( 93,236)( 94,239)( 95,238)
( 96,240)( 97,243)( 98,242)( 99,241)(100,244)(101,246)(102,245)(103,248)
(104,247)(105,249)(106,252)(107,251)(108,250)(109,253)(110,255)(111,254)
(112,257)(113,256)(114,258)(115,261)(116,260)(117,259)(118,262)(119,264)
(120,263)(121,266)(122,265)(123,267)(124,270)(125,269)(126,268)(127,271)
(128,273)(129,272)(130,275)(131,274)(132,276)(133,279)(134,278)(135,277)
(136,280)(137,282)(138,281)(139,284)(140,283)(141,285)(142,288)(143,287)
(144,286)(289,433)(290,435)(291,434)(292,437)(293,436)(294,438)(295,441)
(296,440)(297,439)(298,442)(299,444)(300,443)(301,446)(302,445)(303,447)
(304,450)(305,449)(306,448)(307,451)(308,453)(309,452)(310,455)(311,454)
(312,456)(313,459)(314,458)(315,457)(316,460)(317,462)(318,461)(319,464)
(320,463)(321,465)(322,468)(323,467)(324,466)(325,469)(326,471)(327,470)
(328,473)(329,472)(330,474)(331,477)(332,476)(333,475)(334,478)(335,480)
(336,479)(337,482)(338,481)(339,483)(340,486)(341,485)(342,484)(343,487)
(344,489)(345,488)(346,491)(347,490)(348,492)(349,495)(350,494)(351,493)
(352,496)(353,498)(354,497)(355,500)(356,499)(357,501)(358,504)(359,503)
(360,502)(361,505)(362,507)(363,506)(364,509)(365,508)(366,510)(367,513)
(368,512)(369,511)(370,514)(371,516)(372,515)(373,518)(374,517)(375,519)
(376,522)(377,521)(378,520)(379,523)(380,525)(381,524)(382,527)(383,526)
(384,528)(385,531)(386,530)(387,529)(388,532)(389,534)(390,533)(391,536)
(392,535)(393,537)(394,540)(395,539)(396,538)(397,541)(398,543)(399,542)
(400,545)(401,544)(402,546)(403,549)(404,548)(405,547)(406,550)(407,552)
(408,551)(409,554)(410,553)(411,555)(412,558)(413,557)(414,556)(415,559)
(416,561)(417,560)(418,563)(419,562)(420,564)(421,567)(422,566)(423,565)
(424,568)(425,570)(426,569)(427,572)(428,571)(429,573)(430,576)(431,575)
(432,574);
s3 := Sym(576)!(  1,382)(  2,384)(  3,383)(  4,379)(  5,381)(  6,380)(  7,385)
(  8,387)(  9,386)( 10,391)( 11,393)( 12,392)( 13,388)( 14,390)( 15,389)
( 16,394)( 17,396)( 18,395)( 19,364)( 20,366)( 21,365)( 22,361)( 23,363)
( 24,362)( 25,367)( 26,369)( 27,368)( 28,373)( 29,375)( 30,374)( 31,370)
( 32,372)( 33,371)( 34,376)( 35,378)( 36,377)( 37,418)( 38,420)( 39,419)
( 40,415)( 41,417)( 42,416)( 43,421)( 44,423)( 45,422)( 46,427)( 47,429)
( 48,428)( 49,424)( 50,426)( 51,425)( 52,430)( 53,432)( 54,431)( 55,400)
( 56,402)( 57,401)( 58,397)( 59,399)( 60,398)( 61,403)( 62,405)( 63,404)
( 64,409)( 65,411)( 66,410)( 67,406)( 68,408)( 69,407)( 70,412)( 71,414)
( 72,413)( 73,310)( 74,312)( 75,311)( 76,307)( 77,309)( 78,308)( 79,313)
( 80,315)( 81,314)( 82,319)( 83,321)( 84,320)( 85,316)( 86,318)( 87,317)
( 88,322)( 89,324)( 90,323)( 91,292)( 92,294)( 93,293)( 94,289)( 95,291)
( 96,290)( 97,295)( 98,297)( 99,296)(100,301)(101,303)(102,302)(103,298)
(104,300)(105,299)(106,304)(107,306)(108,305)(109,346)(110,348)(111,347)
(112,343)(113,345)(114,344)(115,349)(116,351)(117,350)(118,355)(119,357)
(120,356)(121,352)(122,354)(123,353)(124,358)(125,360)(126,359)(127,328)
(128,330)(129,329)(130,325)(131,327)(132,326)(133,331)(134,333)(135,332)
(136,337)(137,339)(138,338)(139,334)(140,336)(141,335)(142,340)(143,342)
(144,341)(145,535)(146,537)(147,536)(148,532)(149,534)(150,533)(151,538)
(152,540)(153,539)(154,526)(155,528)(156,527)(157,523)(158,525)(159,524)
(160,529)(161,531)(162,530)(163,517)(164,519)(165,518)(166,514)(167,516)
(168,515)(169,520)(170,522)(171,521)(172,508)(173,510)(174,509)(175,505)
(176,507)(177,506)(178,511)(179,513)(180,512)(181,571)(182,573)(183,572)
(184,568)(185,570)(186,569)(187,574)(188,576)(189,575)(190,562)(191,564)
(192,563)(193,559)(194,561)(195,560)(196,565)(197,567)(198,566)(199,553)
(200,555)(201,554)(202,550)(203,552)(204,551)(205,556)(206,558)(207,557)
(208,544)(209,546)(210,545)(211,541)(212,543)(213,542)(214,547)(215,549)
(216,548)(217,463)(218,465)(219,464)(220,460)(221,462)(222,461)(223,466)
(224,468)(225,467)(226,454)(227,456)(228,455)(229,451)(230,453)(231,452)
(232,457)(233,459)(234,458)(235,445)(236,447)(237,446)(238,442)(239,444)
(240,443)(241,448)(242,450)(243,449)(244,436)(245,438)(246,437)(247,433)
(248,435)(249,434)(250,439)(251,441)(252,440)(253,499)(254,501)(255,500)
(256,496)(257,498)(258,497)(259,502)(260,504)(261,503)(262,490)(263,492)
(264,491)(265,487)(266,489)(267,488)(268,493)(269,495)(270,494)(271,481)
(272,483)(273,482)(274,478)(275,480)(276,479)(277,484)(278,486)(279,485)
(280,472)(281,474)(282,473)(283,469)(284,471)(285,470)(286,475)(287,477)
(288,476);
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*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 >; 
 
References : None.
to this polytope