Polytope of Type {12,4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,4,4}*1152
if this polytope has a name.
Group : SmallGroup(1152,43029)
Rank : 4
Schlafli Type : {12,4,4}
Number of vertices, edges, etc : 36, 72, 24, 4
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 : {6,4,4}*576, {12,4,2}*576
   4-fold quotients : {6,4,4}*288, {6,4,2}*288
   8-fold quotients : {6,4,2}*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.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2> of order 2.
      4 facets:
         4 of 2-fold non-regular quotient of {12,4}*288
      18 vertex figures:
         18 of {4,4}*32
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1> of order 3.
      4 facets:
         4 of 3-fold non-regular quotient of {12,4}*288
      12 vertex figures:
         12 of {4,4}*32
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2> of order 3.
      4 facets:
         4 of 3-fold non-regular quotient of {12,4}*288
      12 vertex figures:
         12 of {4,4}*32

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