Part of the Atlas of Small Regular Polytopes

Polytope of Type {12,8,6}

Atlas Canonical Name {12,8,6}*1152b

Overview

Group
SmallGroup(1152,98785)
Rank
4
Schläfli Type
{12,8,6}
Vertices, edges, …
12, 48, 24, 6
Order of s0s1s2s3
24
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

3-fold

4-fold

6-fold

8-fold

9-fold

12-fold

16-fold

18-fold

24-fold

32-fold

36-fold

48-fold

72-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

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

References

None.

to this polytope.