Polytope of Type {6,12,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12,8}*1152f
if this polytope has a name.
Group : SmallGroup(1152,98790)
Rank : 4
Schlafli Type : {6,12,8}
Number of vertices, edges, etc : 6, 36, 48, 8
Order of s0s1s2s3 : 24
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 : {6,12,4}*576c
3-fold quotients : {6,4,8}*384b
4-fold quotients : {6,6,4}*288c, {6,12,2}*288c
6-fold quotients : {6,4,4}*192
8-fold quotients : {3,6,4}*144, {6,6,2}*144c
9-fold quotients : {2,4,8}*128b
12-fold quotients : {6,2,4}*96, {6,4,2}*96a
16-fold quotients : {3,6,2}*72
18-fold quotients : {2,4,4}*64
24-fold quotients : {3,2,4}*48, {6,2,2}*48
36-fold quotients : {2,2,4}*32, {2,4,2}*32
48-fold quotients : {3,2,2}*24
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):
None.
Permutation Representation (GAP) :
s0 := ( 1, 73)( 2, 75)( 3, 74)( 4, 79)( 5, 81)( 6, 80)( 7, 76)( 8, 78)( 9, 77)( 10, 82)( 11, 84)( 12, 83)( 13, 88)( 14, 90)( 15, 89)( 16, 85)( 17, 87)( 18, 86)( 19, 91)( 20, 93)( 21, 92)( 22, 97)( 23, 99)( 24, 98)( 25, 94)( 26, 96)( 27, 95)( 28,100)( 29,102)( 30,101)( 31,106)( 32,108)( 33,107)( 34,103)( 35,105)( 36,104)( 37,109)( 38,111)( 39,110)( 40,115)( 41,117)( 42,116)( 43,112)( 44,114)( 45,113)( 46,118)( 47,120)( 48,119)( 49,124)( 50,126)( 51,125)( 52,121)( 53,123)( 54,122)( 55,127)( 56,129)( 57,128)( 58,133)( 59,135)( 60,134)( 61,130)( 62,132)( 63,131)( 64,136)( 65,138)( 66,137)( 67,142)( 68,144)( 69,143)( 70,139)( 71,141)( 72,140)(145,217)(146,219)(147,218)(148,223)(149,225)(150,224)(151,220)(152,222)(153,221)(154,226)(155,228)(156,227)(157,232)(158,234)(159,233)(160,229)(161,231)(162,230)(163,235)(164,237)(165,236)(166,241)(167,243)(168,242)(169,238)(170,240)(171,239)(172,244)(173,246)(174,245)(175,250)(176,252)(177,251)(178,247)(179,249)(180,248)(181,253)(182,255)(183,254)(184,259)(185,261)(186,260)(187,256)(188,258)(189,257)(190,262)(191,264)(192,263)(193,268)(194,270)(195,269)(196,265)(197,267)(198,266)(199,271)(200,273)(201,272)(202,277)(203,279)(204,278)(205,274)(206,276)(207,275)(208,280)(209,282)(210,281)(211,286)(212,288)(213,287)(214,283)(215,285)(216,284)(289,361)(290,363)(291,362)(292,367)(293,369)(294,368)(295,364)(296,366)(297,365)(298,370)(299,372)(300,371)(301,376)(302,378)(303,377)(304,373)(305,375)(306,374)(307,379)(308,381)(309,380)(310,385)(311,387)(312,386)(313,382)(314,384)(315,383)(316,388)(317,390)(318,389)(319,394)(320,396)(321,395)(322,391)(323,393)(324,392)(325,397)(326,399)(327,398)(328,403)(329,405)(330,404)(331,400)(332,402)(333,401)(334,406)(335,408)(336,407)(337,412)(338,414)(339,413)(340,409)(341,411)(342,410)(343,415)(344,417)(345,416)(346,421)(347,423)(348,422)(349,418)(350,420)(351,419)(352,424)(353,426)(354,425)(355,430)(356,432)(357,431)(358,427)(359,429)(360,428)(433,505)(434,507)(435,506)(436,511)(437,513)(438,512)(439,508)(440,510)(441,509)(442,514)(443,516)(444,515)(445,520)(446,522)(447,521)(448,517)(449,519)(450,518)(451,523)(452,525)(453,524)(454,529)(455,531)(456,530)(457,526)(458,528)(459,527)(460,532)(461,534)(462,533)(463,538)(464,540)(465,539)(466,535)(467,537)(468,536)(469,541)(470,543)(471,542)(472,547)(473,549)(474,548)(475,544)(476,546)(477,545)(478,550)(479,552)(480,551)(481,556)(482,558)(483,557)(484,553)(485,555)(486,554)(487,559)(488,561)(489,560)(490,565)(491,567)(492,566)(493,562)(494,564)(495,563)(496,568)(497,570)(498,569)(499,574)(500,576)(501,575)(502,571)(503,573)(504,572);;
s1 := ( 1,218)( 2,217)( 3,219)( 4,224)( 5,223)( 6,225)( 7,221)( 8,220)( 9,222)( 10,227)( 11,226)( 12,228)( 13,233)( 14,232)( 15,234)( 16,230)( 17,229)( 18,231)( 19,236)( 20,235)( 21,237)( 22,242)( 23,241)( 24,243)( 25,239)( 26,238)( 27,240)( 28,245)( 29,244)( 30,246)( 31,251)( 32,250)( 33,252)( 34,248)( 35,247)( 36,249)( 37,263)( 38,262)( 39,264)( 40,269)( 41,268)( 42,270)( 43,266)( 44,265)( 45,267)( 46,254)( 47,253)( 48,255)( 49,260)( 50,259)( 51,261)( 52,257)( 53,256)( 54,258)( 55,281)( 56,280)( 57,282)( 58,287)( 59,286)( 60,288)( 61,284)( 62,283)( 63,285)( 64,272)( 65,271)( 66,273)( 67,278)( 68,277)( 69,279)( 70,275)( 71,274)( 72,276)( 73,146)( 74,145)( 75,147)( 76,152)( 77,151)( 78,153)( 79,149)( 80,148)( 81,150)( 82,155)( 83,154)( 84,156)( 85,161)( 86,160)( 87,162)( 88,158)( 89,157)( 90,159)( 91,164)( 92,163)( 93,165)( 94,170)( 95,169)( 96,171)( 97,167)( 98,166)( 99,168)(100,173)(101,172)(102,174)(103,179)(104,178)(105,180)(106,176)(107,175)(108,177)(109,191)(110,190)(111,192)(112,197)(113,196)(114,198)(115,194)(116,193)(117,195)(118,182)(119,181)(120,183)(121,188)(122,187)(123,189)(124,185)(125,184)(126,186)(127,209)(128,208)(129,210)(130,215)(131,214)(132,216)(133,212)(134,211)(135,213)(136,200)(137,199)(138,201)(139,206)(140,205)(141,207)(142,203)(143,202)(144,204)(289,506)(290,505)(291,507)(292,512)(293,511)(294,513)(295,509)(296,508)(297,510)(298,515)(299,514)(300,516)(301,521)(302,520)(303,522)(304,518)(305,517)(306,519)(307,524)(308,523)(309,525)(310,530)(311,529)(312,531)(313,527)(314,526)(315,528)(316,533)(317,532)(318,534)(319,539)(320,538)(321,540)(322,536)(323,535)(324,537)(325,551)(326,550)(327,552)(328,557)(329,556)(330,558)(331,554)(332,553)(333,555)(334,542)(335,541)(336,543)(337,548)(338,547)(339,549)(340,545)(341,544)(342,546)(343,569)(344,568)(345,570)(346,575)(347,574)(348,576)(349,572)(350,571)(351,573)(352,560)(353,559)(354,561)(355,566)(356,565)(357,567)(358,563)(359,562)(360,564)(361,434)(362,433)(363,435)(364,440)(365,439)(366,441)(367,437)(368,436)(369,438)(370,443)(371,442)(372,444)(373,449)(374,448)(375,450)(376,446)(377,445)(378,447)(379,452)(380,451)(381,453)(382,458)(383,457)(384,459)(385,455)(386,454)(387,456)(388,461)(389,460)(390,462)(391,467)(392,466)(393,468)(394,464)(395,463)(396,465)(397,479)(398,478)(399,480)(400,485)(401,484)(402,486)(403,482)(404,481)(405,483)(406,470)(407,469)(408,471)(409,476)(410,475)(411,477)(412,473)(413,472)(414,474)(415,497)(416,496)(417,498)(418,503)(419,502)(420,504)(421,500)(422,499)(423,501)(424,488)(425,487)(426,489)(427,494)(428,493)(429,495)(430,491)(431,490)(432,492);;
s2 := ( 2, 6)( 3, 8)( 5, 9)( 11, 15)( 12, 17)( 14, 18)( 20, 24)( 21, 26)( 23, 27)( 29, 33)( 30, 35)( 32, 36)( 37, 46)( 38, 51)( 39, 53)( 40, 49)( 41, 54)( 42, 47)( 43, 52)( 44, 48)( 45, 50)( 55, 64)( 56, 69)( 57, 71)( 58, 67)( 59, 72)( 60, 65)( 61, 70)( 62, 66)( 63, 68)( 74, 78)( 75, 80)( 77, 81)( 83, 87)( 84, 89)( 86, 90)( 92, 96)( 93, 98)( 95, 99)(101,105)(102,107)(104,108)(109,118)(110,123)(111,125)(112,121)(113,126)(114,119)(115,124)(116,120)(117,122)(127,136)(128,141)(129,143)(130,139)(131,144)(132,137)(133,142)(134,138)(135,140)(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)(181,208)(182,213)(183,215)(184,211)(185,216)(186,209)(187,214)(188,210)(189,212)(190,199)(191,204)(192,206)(193,202)(194,207)(195,200)(196,205)(197,201)(198,203)(217,235)(218,240)(219,242)(220,238)(221,243)(222,236)(223,241)(224,237)(225,239)(226,244)(227,249)(228,251)(229,247)(230,252)(231,245)(232,250)(233,246)(234,248)(253,280)(254,285)(255,287)(256,283)(257,288)(258,281)(259,286)(260,282)(261,284)(262,271)(263,276)(264,278)(265,274)(266,279)(267,272)(268,277)(269,273)(270,275)(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)(361,397)(362,402)(363,404)(364,400)(365,405)(366,398)(367,403)(368,399)(369,401)(370,406)(371,411)(372,413)(373,409)(374,414)(375,407)(376,412)(377,408)(378,410)(379,415)(380,420)(381,422)(382,418)(383,423)(384,416)(385,421)(386,417)(387,419)(388,424)(389,429)(390,431)(391,427)(392,432)(393,425)(394,430)(395,426)(396,428)(433,496)(434,501)(435,503)(436,499)(437,504)(438,497)(439,502)(440,498)(441,500)(442,487)(443,492)(444,494)(445,490)(446,495)(447,488)(448,493)(449,489)(450,491)(451,478)(452,483)(453,485)(454,481)(455,486)(456,479)(457,484)(458,480)(459,482)(460,469)(461,474)(462,476)(463,472)(464,477)(465,470)(466,475)(467,471)(468,473)(505,568)(506,573)(507,575)(508,571)(509,576)(510,569)(511,574)(512,570)(513,572)(514,559)(515,564)(516,566)(517,562)(518,567)(519,560)(520,565)(521,561)(522,563)(523,550)(524,555)(525,557)(526,553)(527,558)(528,551)(529,556)(530,552)(531,554)(532,541)(533,546)(534,548)(535,544)(536,549)(537,542)(538,547)(539,543)(540,545);;
s3 := ( 1,289)( 2,290)( 3,291)( 4,292)( 5,293)( 6,294)( 7,295)( 8,296)( 9,297)( 10,298)( 11,299)( 12,300)( 13,301)( 14,302)( 15,303)( 16,304)( 17,305)( 18,306)( 19,316)( 20,317)( 21,318)( 22,319)( 23,320)( 24,321)( 25,322)( 26,323)( 27,324)( 28,307)( 29,308)( 30,309)( 31,310)( 32,311)( 33,312)( 34,313)( 35,314)( 36,315)( 37,334)( 38,335)( 39,336)( 40,337)( 41,338)( 42,339)( 43,340)( 44,341)( 45,342)( 46,325)( 47,326)( 48,327)( 49,328)( 50,329)( 51,330)( 52,331)( 53,332)( 54,333)( 55,343)( 56,344)( 57,345)( 58,346)( 59,347)( 60,348)( 61,349)( 62,350)( 63,351)( 64,352)( 65,353)( 66,354)( 67,355)( 68,356)( 69,357)( 70,358)( 71,359)( 72,360)( 73,361)( 74,362)( 75,363)( 76,364)( 77,365)( 78,366)( 79,367)( 80,368)( 81,369)( 82,370)( 83,371)( 84,372)( 85,373)( 86,374)( 87,375)( 88,376)( 89,377)( 90,378)( 91,388)( 92,389)( 93,390)( 94,391)( 95,392)( 96,393)( 97,394)( 98,395)( 99,396)(100,379)(101,380)(102,381)(103,382)(104,383)(105,384)(106,385)(107,386)(108,387)(109,406)(110,407)(111,408)(112,409)(113,410)(114,411)(115,412)(116,413)(117,414)(118,397)(119,398)(120,399)(121,400)(122,401)(123,402)(124,403)(125,404)(126,405)(127,415)(128,416)(129,417)(130,418)(131,419)(132,420)(133,421)(134,422)(135,423)(136,424)(137,425)(138,426)(139,427)(140,428)(141,429)(142,430)(143,431)(144,432)(145,433)(146,434)(147,435)(148,436)(149,437)(150,438)(151,439)(152,440)(153,441)(154,442)(155,443)(156,444)(157,445)(158,446)(159,447)(160,448)(161,449)(162,450)(163,460)(164,461)(165,462)(166,463)(167,464)(168,465)(169,466)(170,467)(171,468)(172,451)(173,452)(174,453)(175,454)(176,455)(177,456)(178,457)(179,458)(180,459)(181,478)(182,479)(183,480)(184,481)(185,482)(186,483)(187,484)(188,485)(189,486)(190,469)(191,470)(192,471)(193,472)(194,473)(195,474)(196,475)(197,476)(198,477)(199,487)(200,488)(201,489)(202,490)(203,491)(204,492)(205,493)(206,494)(207,495)(208,496)(209,497)(210,498)(211,499)(212,500)(213,501)(214,502)(215,503)(216,504)(217,505)(218,506)(219,507)(220,508)(221,509)(222,510)(223,511)(224,512)(225,513)(226,514)(227,515)(228,516)(229,517)(230,518)(231,519)(232,520)(233,521)(234,522)(235,532)(236,533)(237,534)(238,535)(239,536)(240,537)(241,538)(242,539)(243,540)(244,523)(245,524)(246,525)(247,526)(248,527)(249,528)(250,529)(251,530)(252,531)(253,550)(254,551)(255,552)(256,553)(257,554)(258,555)(259,556)(260,557)(261,558)(262,541)(263,542)(264,543)(265,544)(266,545)(267,546)(268,547)(269,548)(270,549)(271,559)(272,560)(273,561)(274,562)(275,563)(276,564)(277,565)(278,566)(279,567)(280,568)(281,569)(282,570)(283,571)(284,572)(285,573)(286,574)(287,575)(288,576);;
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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(576)!( 1, 73)( 2, 75)( 3, 74)( 4, 79)( 5, 81)( 6, 80)( 7, 76)( 8, 78)( 9, 77)( 10, 82)( 11, 84)( 12, 83)( 13, 88)( 14, 90)( 15, 89)( 16, 85)( 17, 87)( 18, 86)( 19, 91)( 20, 93)( 21, 92)( 22, 97)( 23, 99)( 24, 98)( 25, 94)( 26, 96)( 27, 95)( 28,100)( 29,102)( 30,101)( 31,106)( 32,108)( 33,107)( 34,103)( 35,105)( 36,104)( 37,109)( 38,111)( 39,110)( 40,115)( 41,117)( 42,116)( 43,112)( 44,114)( 45,113)( 46,118)( 47,120)( 48,119)( 49,124)( 50,126)( 51,125)( 52,121)( 53,123)( 54,122)( 55,127)( 56,129)( 57,128)( 58,133)( 59,135)( 60,134)( 61,130)( 62,132)( 63,131)( 64,136)( 65,138)( 66,137)( 67,142)( 68,144)( 69,143)( 70,139)( 71,141)( 72,140)(145,217)(146,219)(147,218)(148,223)(149,225)(150,224)(151,220)(152,222)(153,221)(154,226)(155,228)(156,227)(157,232)(158,234)(159,233)(160,229)(161,231)(162,230)(163,235)(164,237)(165,236)(166,241)(167,243)(168,242)(169,238)(170,240)(171,239)(172,244)(173,246)(174,245)(175,250)(176,252)(177,251)(178,247)(179,249)(180,248)(181,253)(182,255)(183,254)(184,259)(185,261)(186,260)(187,256)(188,258)(189,257)(190,262)(191,264)(192,263)(193,268)(194,270)(195,269)(196,265)(197,267)(198,266)(199,271)(200,273)(201,272)(202,277)(203,279)(204,278)(205,274)(206,276)(207,275)(208,280)(209,282)(210,281)(211,286)(212,288)(213,287)(214,283)(215,285)(216,284)(289,361)(290,363)(291,362)(292,367)(293,369)(294,368)(295,364)(296,366)(297,365)(298,370)(299,372)(300,371)(301,376)(302,378)(303,377)(304,373)(305,375)(306,374)(307,379)(308,381)(309,380)(310,385)(311,387)(312,386)(313,382)(314,384)(315,383)(316,388)(317,390)(318,389)(319,394)(320,396)(321,395)(322,391)(323,393)(324,392)(325,397)(326,399)(327,398)(328,403)(329,405)(330,404)(331,400)(332,402)(333,401)(334,406)(335,408)(336,407)(337,412)(338,414)(339,413)(340,409)(341,411)(342,410)(343,415)(344,417)(345,416)(346,421)(347,423)(348,422)(349,418)(350,420)(351,419)(352,424)(353,426)(354,425)(355,430)(356,432)(357,431)(358,427)(359,429)(360,428)(433,505)(434,507)(435,506)(436,511)(437,513)(438,512)(439,508)(440,510)(441,509)(442,514)(443,516)(444,515)(445,520)(446,522)(447,521)(448,517)(449,519)(450,518)(451,523)(452,525)(453,524)(454,529)(455,531)(456,530)(457,526)(458,528)(459,527)(460,532)(461,534)(462,533)(463,538)(464,540)(465,539)(466,535)(467,537)(468,536)(469,541)(470,543)(471,542)(472,547)(473,549)(474,548)(475,544)(476,546)(477,545)(478,550)(479,552)(480,551)(481,556)(482,558)(483,557)(484,553)(485,555)(486,554)(487,559)(488,561)(489,560)(490,565)(491,567)(492,566)(493,562)(494,564)(495,563)(496,568)(497,570)(498,569)(499,574)(500,576)(501,575)(502,571)(503,573)(504,572);
s1 := Sym(576)!( 1,218)( 2,217)( 3,219)( 4,224)( 5,223)( 6,225)( 7,221)( 8,220)( 9,222)( 10,227)( 11,226)( 12,228)( 13,233)( 14,232)( 15,234)( 16,230)( 17,229)( 18,231)( 19,236)( 20,235)( 21,237)( 22,242)( 23,241)( 24,243)( 25,239)( 26,238)( 27,240)( 28,245)( 29,244)( 30,246)( 31,251)( 32,250)( 33,252)( 34,248)( 35,247)( 36,249)( 37,263)( 38,262)( 39,264)( 40,269)( 41,268)( 42,270)( 43,266)( 44,265)( 45,267)( 46,254)( 47,253)( 48,255)( 49,260)( 50,259)( 51,261)( 52,257)( 53,256)( 54,258)( 55,281)( 56,280)( 57,282)( 58,287)( 59,286)( 60,288)( 61,284)( 62,283)( 63,285)( 64,272)( 65,271)( 66,273)( 67,278)( 68,277)( 69,279)( 70,275)( 71,274)( 72,276)( 73,146)( 74,145)( 75,147)( 76,152)( 77,151)( 78,153)( 79,149)( 80,148)( 81,150)( 82,155)( 83,154)( 84,156)( 85,161)( 86,160)( 87,162)( 88,158)( 89,157)( 90,159)( 91,164)( 92,163)( 93,165)( 94,170)( 95,169)( 96,171)( 97,167)( 98,166)( 99,168)(100,173)(101,172)(102,174)(103,179)(104,178)(105,180)(106,176)(107,175)(108,177)(109,191)(110,190)(111,192)(112,197)(113,196)(114,198)(115,194)(116,193)(117,195)(118,182)(119,181)(120,183)(121,188)(122,187)(123,189)(124,185)(125,184)(126,186)(127,209)(128,208)(129,210)(130,215)(131,214)(132,216)(133,212)(134,211)(135,213)(136,200)(137,199)(138,201)(139,206)(140,205)(141,207)(142,203)(143,202)(144,204)(289,506)(290,505)(291,507)(292,512)(293,511)(294,513)(295,509)(296,508)(297,510)(298,515)(299,514)(300,516)(301,521)(302,520)(303,522)(304,518)(305,517)(306,519)(307,524)(308,523)(309,525)(310,530)(311,529)(312,531)(313,527)(314,526)(315,528)(316,533)(317,532)(318,534)(319,539)(320,538)(321,540)(322,536)(323,535)(324,537)(325,551)(326,550)(327,552)(328,557)(329,556)(330,558)(331,554)(332,553)(333,555)(334,542)(335,541)(336,543)(337,548)(338,547)(339,549)(340,545)(341,544)(342,546)(343,569)(344,568)(345,570)(346,575)(347,574)(348,576)(349,572)(350,571)(351,573)(352,560)(353,559)(354,561)(355,566)(356,565)(357,567)(358,563)(359,562)(360,564)(361,434)(362,433)(363,435)(364,440)(365,439)(366,441)(367,437)(368,436)(369,438)(370,443)(371,442)(372,444)(373,449)(374,448)(375,450)(376,446)(377,445)(378,447)(379,452)(380,451)(381,453)(382,458)(383,457)(384,459)(385,455)(386,454)(387,456)(388,461)(389,460)(390,462)(391,467)(392,466)(393,468)(394,464)(395,463)(396,465)(397,479)(398,478)(399,480)(400,485)(401,484)(402,486)(403,482)(404,481)(405,483)(406,470)(407,469)(408,471)(409,476)(410,475)(411,477)(412,473)(413,472)(414,474)(415,497)(416,496)(417,498)(418,503)(419,502)(420,504)(421,500)(422,499)(423,501)(424,488)(425,487)(426,489)(427,494)(428,493)(429,495)(430,491)(431,490)(432,492);
s2 := 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)( 37, 46)( 38, 51)( 39, 53)( 40, 49)( 41, 54)( 42, 47)( 43, 52)( 44, 48)( 45, 50)( 55, 64)( 56, 69)( 57, 71)( 58, 67)( 59, 72)( 60, 65)( 61, 70)( 62, 66)( 63, 68)( 74, 78)( 75, 80)( 77, 81)( 83, 87)( 84, 89)( 86, 90)( 92, 96)( 93, 98)( 95, 99)(101,105)(102,107)(104,108)(109,118)(110,123)(111,125)(112,121)(113,126)(114,119)(115,124)(116,120)(117,122)(127,136)(128,141)(129,143)(130,139)(131,144)(132,137)(133,142)(134,138)(135,140)(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)(181,208)(182,213)(183,215)(184,211)(185,216)(186,209)(187,214)(188,210)(189,212)(190,199)(191,204)(192,206)(193,202)(194,207)(195,200)(196,205)(197,201)(198,203)(217,235)(218,240)(219,242)(220,238)(221,243)(222,236)(223,241)(224,237)(225,239)(226,244)(227,249)(228,251)(229,247)(230,252)(231,245)(232,250)(233,246)(234,248)(253,280)(254,285)(255,287)(256,283)(257,288)(258,281)(259,286)(260,282)(261,284)(262,271)(263,276)(264,278)(265,274)(266,279)(267,272)(268,277)(269,273)(270,275)(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)(361,397)(362,402)(363,404)(364,400)(365,405)(366,398)(367,403)(368,399)(369,401)(370,406)(371,411)(372,413)(373,409)(374,414)(375,407)(376,412)(377,408)(378,410)(379,415)(380,420)(381,422)(382,418)(383,423)(384,416)(385,421)(386,417)(387,419)(388,424)(389,429)(390,431)(391,427)(392,432)(393,425)(394,430)(395,426)(396,428)(433,496)(434,501)(435,503)(436,499)(437,504)(438,497)(439,502)(440,498)(441,500)(442,487)(443,492)(444,494)(445,490)(446,495)(447,488)(448,493)(449,489)(450,491)(451,478)(452,483)(453,485)(454,481)(455,486)(456,479)(457,484)(458,480)(459,482)(460,469)(461,474)(462,476)(463,472)(464,477)(465,470)(466,475)(467,471)(468,473)(505,568)(506,573)(507,575)(508,571)(509,576)(510,569)(511,574)(512,570)(513,572)(514,559)(515,564)(516,566)(517,562)(518,567)(519,560)(520,565)(521,561)(522,563)(523,550)(524,555)(525,557)(526,553)(527,558)(528,551)(529,556)(530,552)(531,554)(532,541)(533,546)(534,548)(535,544)(536,549)(537,542)(538,547)(539,543)(540,545);
s3 := Sym(576)!( 1,289)( 2,290)( 3,291)( 4,292)( 5,293)( 6,294)( 7,295)( 8,296)( 9,297)( 10,298)( 11,299)( 12,300)( 13,301)( 14,302)( 15,303)( 16,304)( 17,305)( 18,306)( 19,316)( 20,317)( 21,318)( 22,319)( 23,320)( 24,321)( 25,322)( 26,323)( 27,324)( 28,307)( 29,308)( 30,309)( 31,310)( 32,311)( 33,312)( 34,313)( 35,314)( 36,315)( 37,334)( 38,335)( 39,336)( 40,337)( 41,338)( 42,339)( 43,340)( 44,341)( 45,342)( 46,325)( 47,326)( 48,327)( 49,328)( 50,329)( 51,330)( 52,331)( 53,332)( 54,333)( 55,343)( 56,344)( 57,345)( 58,346)( 59,347)( 60,348)( 61,349)( 62,350)( 63,351)( 64,352)( 65,353)( 66,354)( 67,355)( 68,356)( 69,357)( 70,358)( 71,359)( 72,360)( 73,361)( 74,362)( 75,363)( 76,364)( 77,365)( 78,366)( 79,367)( 80,368)( 81,369)( 82,370)( 83,371)( 84,372)( 85,373)( 86,374)( 87,375)( 88,376)( 89,377)( 90,378)( 91,388)( 92,389)( 93,390)( 94,391)( 95,392)( 96,393)( 97,394)( 98,395)( 99,396)(100,379)(101,380)(102,381)(103,382)(104,383)(105,384)(106,385)(107,386)(108,387)(109,406)(110,407)(111,408)(112,409)(113,410)(114,411)(115,412)(116,413)(117,414)(118,397)(119,398)(120,399)(121,400)(122,401)(123,402)(124,403)(125,404)(126,405)(127,415)(128,416)(129,417)(130,418)(131,419)(132,420)(133,421)(134,422)(135,423)(136,424)(137,425)(138,426)(139,427)(140,428)(141,429)(142,430)(143,431)(144,432)(145,433)(146,434)(147,435)(148,436)(149,437)(150,438)(151,439)(152,440)(153,441)(154,442)(155,443)(156,444)(157,445)(158,446)(159,447)(160,448)(161,449)(162,450)(163,460)(164,461)(165,462)(166,463)(167,464)(168,465)(169,466)(170,467)(171,468)(172,451)(173,452)(174,453)(175,454)(176,455)(177,456)(178,457)(179,458)(180,459)(181,478)(182,479)(183,480)(184,481)(185,482)(186,483)(187,484)(188,485)(189,486)(190,469)(191,470)(192,471)(193,472)(194,473)(195,474)(196,475)(197,476)(198,477)(199,487)(200,488)(201,489)(202,490)(203,491)(204,492)(205,493)(206,494)(207,495)(208,496)(209,497)(210,498)(211,499)(212,500)(213,501)(214,502)(215,503)(216,504)(217,505)(218,506)(219,507)(220,508)(221,509)(222,510)(223,511)(224,512)(225,513)(226,514)(227,515)(228,516)(229,517)(230,518)(231,519)(232,520)(233,521)(234,522)(235,532)(236,533)(237,534)(238,535)(239,536)(240,537)(241,538)(242,539)(243,540)(244,523)(245,524)(246,525)(247,526)(248,527)(249,528)(250,529)(251,530)(252,531)(253,550)(254,551)(255,552)(256,553)(257,554)(258,555)(259,556)(260,557)(261,558)(262,541)(263,542)(264,543)(265,544)(266,545)(267,546)(268,547)(269,548)(270,549)(271,559)(272,560)(273,561)(274,562)(275,563)(276,564)(277,565)(278,566)(279,567)(280,568)(281,569)(282,570)(283,571)(284,572)(285,573)(286,574)(287,575)(288,576);
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,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope