Polytope of Type {3,6,8,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,8,4}*1152a
if this polytope has a name.
Group : SmallGroup(1152,97534)
Rank : 5
Schlafli Type : {3,6,8,4}
Number of vertices, edges, etc : 3, 9, 24, 16, 4
Order of s0s1s2s3s4 : 24
Order of s0s1s2s3s4s3s2s1 : 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 : {3,6,8,2}*576, {3,6,4,4}*576
3-fold quotients : {3,2,8,4}*384a
4-fold quotients : {3,6,2,4}*288, {3,6,4,2}*288
6-fold quotients : {3,2,4,4}*192, {3,2,8,2}*192
8-fold quotients : {3,6,2,2}*144
12-fold quotients : {3,2,2,4}*96, {3,2,4,2}*96
24-fold quotients : {3,2,2,2}*48
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, 74)( 2, 73)( 3, 75)( 4, 80)( 5, 79)( 6, 81)( 7, 77)( 8, 76)( 9, 78)( 10, 83)( 11, 82)( 12, 84)( 13, 89)( 14, 88)( 15, 90)( 16, 86)( 17, 85)( 18, 87)( 19, 92)( 20, 91)( 21, 93)( 22, 98)( 23, 97)( 24, 99)( 25, 95)( 26, 94)( 27, 96)( 28,101)( 29,100)( 30,102)( 31,107)( 32,106)( 33,108)( 34,104)( 35,103)( 36,105)( 37,110)( 38,109)( 39,111)( 40,116)( 41,115)( 42,117)( 43,113)( 44,112)( 45,114)( 46,119)( 47,118)( 48,120)( 49,125)( 50,124)( 51,126)( 52,122)( 53,121)( 54,123)( 55,128)( 56,127)( 57,129)( 58,134)( 59,133)( 60,135)( 61,131)( 62,130)( 63,132)( 64,137)( 65,136)( 66,138)( 67,143)( 68,142)( 69,144)( 70,140)( 71,139)( 72,141)(145,218)(146,217)(147,219)(148,224)(149,223)(150,225)(151,221)(152,220)(153,222)(154,227)(155,226)(156,228)(157,233)(158,232)(159,234)(160,230)(161,229)(162,231)(163,236)(164,235)(165,237)(166,242)(167,241)(168,243)(169,239)(170,238)(171,240)(172,245)(173,244)(174,246)(175,251)(176,250)(177,252)(178,248)(179,247)(180,249)(181,254)(182,253)(183,255)(184,260)(185,259)(186,261)(187,257)(188,256)(189,258)(190,263)(191,262)(192,264)(193,269)(194,268)(195,270)(196,266)(197,265)(198,267)(199,272)(200,271)(201,273)(202,278)(203,277)(204,279)(205,275)(206,274)(207,276)(208,281)(209,280)(210,282)(211,287)(212,286)(213,288)(214,284)(215,283)(216,285)(289,362)(290,361)(291,363)(292,368)(293,367)(294,369)(295,365)(296,364)(297,366)(298,371)(299,370)(300,372)(301,377)(302,376)(303,378)(304,374)(305,373)(306,375)(307,380)(308,379)(309,381)(310,386)(311,385)(312,387)(313,383)(314,382)(315,384)(316,389)(317,388)(318,390)(319,395)(320,394)(321,396)(322,392)(323,391)(324,393)(325,398)(326,397)(327,399)(328,404)(329,403)(330,405)(331,401)(332,400)(333,402)(334,407)(335,406)(336,408)(337,413)(338,412)(339,414)(340,410)(341,409)(342,411)(343,416)(344,415)(345,417)(346,422)(347,421)(348,423)(349,419)(350,418)(351,420)(352,425)(353,424)(354,426)(355,431)(356,430)(357,432)(358,428)(359,427)(360,429)(433,506)(434,505)(435,507)(436,512)(437,511)(438,513)(439,509)(440,508)(441,510)(442,515)(443,514)(444,516)(445,521)(446,520)(447,522)(448,518)(449,517)(450,519)(451,524)(452,523)(453,525)(454,530)(455,529)(456,531)(457,527)(458,526)(459,528)(460,533)(461,532)(462,534)(463,539)(464,538)(465,540)(466,536)(467,535)(468,537)(469,542)(470,541)(471,543)(472,548)(473,547)(474,549)(475,545)(476,544)(477,546)(478,551)(479,550)(480,552)(481,557)(482,556)(483,558)(484,554)(485,553)(486,555)(487,560)(488,559)(489,561)(490,566)(491,565)(492,567)(493,563)(494,562)(495,564)(496,569)(497,568)(498,570)(499,575)(500,574)(501,576)(502,572)(503,571)(504,573);;
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)( 19,307)( 20,312)( 21,314)( 22,310)( 23,315)( 24,308)( 25,313)( 26,309)( 27,311)( 28,316)( 29,321)( 30,323)( 31,319)( 32,324)( 33,317)( 34,322)( 35,318)( 36,320)( 37,334)( 38,339)( 39,341)( 40,337)( 41,342)( 42,335)( 43,340)( 44,336)( 45,338)( 46,325)( 47,330)( 48,332)( 49,328)( 50,333)( 51,326)( 52,331)( 53,327)( 54,329)( 55,352)( 56,357)( 57,359)( 58,355)( 59,360)( 60,353)( 61,358)( 62,354)( 63,356)( 64,343)( 65,348)( 66,350)( 67,346)( 68,351)( 69,344)( 70,349)( 71,345)( 72,347)( 73,361)( 74,366)( 75,368)( 76,364)( 77,369)( 78,362)( 79,367)( 80,363)( 81,365)( 82,370)( 83,375)( 84,377)( 85,373)( 86,378)( 87,371)( 88,376)( 89,372)( 90,374)( 91,379)( 92,384)( 93,386)( 94,382)( 95,387)( 96,380)( 97,385)( 98,381)( 99,383)(100,388)(101,393)(102,395)(103,391)(104,396)(105,389)(106,394)(107,390)(108,392)(109,406)(110,411)(111,413)(112,409)(113,414)(114,407)(115,412)(116,408)(117,410)(118,397)(119,402)(120,404)(121,400)(122,405)(123,398)(124,403)(125,399)(126,401)(127,424)(128,429)(129,431)(130,427)(131,432)(132,425)(133,430)(134,426)(135,428)(136,415)(137,420)(138,422)(139,418)(140,423)(141,416)(142,421)(143,417)(144,419)(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)(163,451)(164,456)(165,458)(166,454)(167,459)(168,452)(169,457)(170,453)(171,455)(172,460)(173,465)(174,467)(175,463)(176,468)(177,461)(178,466)(179,462)(180,464)(181,478)(182,483)(183,485)(184,481)(185,486)(186,479)(187,484)(188,480)(189,482)(190,469)(191,474)(192,476)(193,472)(194,477)(195,470)(196,475)(197,471)(198,473)(199,496)(200,501)(201,503)(202,499)(203,504)(204,497)(205,502)(206,498)(207,500)(208,487)(209,492)(210,494)(211,490)(212,495)(213,488)(214,493)(215,489)(216,491)(217,505)(218,510)(219,512)(220,508)(221,513)(222,506)(223,511)(224,507)(225,509)(226,514)(227,519)(228,521)(229,517)(230,522)(231,515)(232,520)(233,516)(234,518)(235,523)(236,528)(237,530)(238,526)(239,531)(240,524)(241,529)(242,525)(243,527)(244,532)(245,537)(246,539)(247,535)(248,540)(249,533)(250,538)(251,534)(252,536)(253,550)(254,555)(255,557)(256,553)(257,558)(258,551)(259,556)(260,552)(261,554)(262,541)(263,546)(264,548)(265,544)(266,549)(267,542)(268,547)(269,543)(270,545)(271,568)(272,573)(273,575)(274,571)(275,576)(276,569)(277,574)(278,570)(279,572)(280,559)(281,564)(282,566)(283,562)(284,567)(285,560)(286,565)(287,561)(288,563);;
s3 := ( 37, 46)( 38, 47)( 39, 48)( 40, 49)( 41, 50)( 42, 51)( 43, 52)( 44, 53)( 45, 54)( 55, 64)( 56, 65)( 57, 66)( 58, 67)( 59, 68)( 60, 69)( 61, 70)( 62, 71)( 63, 72)(109,118)(110,119)(111,120)(112,121)(113,122)(114,123)(115,124)(116,125)(117,126)(127,136)(128,137)(129,138)(130,139)(131,140)(132,141)(133,142)(134,143)(135,144)(145,163)(146,164)(147,165)(148,166)(149,167)(150,168)(151,169)(152,170)(153,171)(154,172)(155,173)(156,174)(157,175)(158,176)(159,177)(160,178)(161,179)(162,180)(181,208)(182,209)(183,210)(184,211)(185,212)(186,213)(187,214)(188,215)(189,216)(190,199)(191,200)(192,201)(193,202)(194,203)(195,204)(196,205)(197,206)(198,207)(217,235)(218,236)(219,237)(220,238)(221,239)(222,240)(223,241)(224,242)(225,243)(226,244)(227,245)(228,246)(229,247)(230,248)(231,249)(232,250)(233,251)(234,252)(253,280)(254,281)(255,282)(256,283)(257,284)(258,285)(259,286)(260,287)(261,288)(262,271)(263,272)(264,273)(265,274)(266,275)(267,276)(268,277)(269,278)(270,279)(289,325)(290,326)(291,327)(292,328)(293,329)(294,330)(295,331)(296,332)(297,333)(298,334)(299,335)(300,336)(301,337)(302,338)(303,339)(304,340)(305,341)(306,342)(307,343)(308,344)(309,345)(310,346)(311,347)(312,348)(313,349)(314,350)(315,351)(316,352)(317,353)(318,354)(319,355)(320,356)(321,357)(322,358)(323,359)(324,360)(361,397)(362,398)(363,399)(364,400)(365,401)(366,402)(367,403)(368,404)(369,405)(370,406)(371,407)(372,408)(373,409)(374,410)(375,411)(376,412)(377,413)(378,414)(379,415)(380,416)(381,417)(382,418)(383,419)(384,420)(385,421)(386,422)(387,423)(388,424)(389,425)(390,426)(391,427)(392,428)(393,429)(394,430)(395,431)(396,432)(433,487)(434,488)(435,489)(436,490)(437,491)(438,492)(439,493)(440,494)(441,495)(442,496)(443,497)(444,498)(445,499)(446,500)(447,501)(448,502)(449,503)(450,504)(451,469)(452,470)(453,471)(454,472)(455,473)(456,474)(457,475)(458,476)(459,477)(460,478)(461,479)(462,480)(463,481)(464,482)(465,483)(466,484)(467,485)(468,486)(505,559)(506,560)(507,561)(508,562)(509,563)(510,564)(511,565)(512,566)(513,567)(514,568)(515,569)(516,570)(517,571)(518,572)(519,573)(520,574)(521,575)(522,576)(523,541)(524,542)(525,543)(526,544)(527,545)(528,546)(529,547)(530,548)(531,549)(532,550)(533,551)(534,552)(535,553)(536,554)(537,555)(538,556)(539,557)(540,558);;
s4 := ( 1,145)( 2,146)( 3,147)( 4,148)( 5,149)( 6,150)( 7,151)( 8,152)( 9,153)( 10,154)( 11,155)( 12,156)( 13,157)( 14,158)( 15,159)( 16,160)( 17,161)( 18,162)( 19,163)( 20,164)( 21,165)( 22,166)( 23,167)( 24,168)( 25,169)( 26,170)( 27,171)( 28,172)( 29,173)( 30,174)( 31,175)( 32,176)( 33,177)( 34,178)( 35,179)( 36,180)( 37,181)( 38,182)( 39,183)( 40,184)( 41,185)( 42,186)( 43,187)( 44,188)( 45,189)( 46,190)( 47,191)( 48,192)( 49,193)( 50,194)( 51,195)( 52,196)( 53,197)( 54,198)( 55,199)( 56,200)( 57,201)( 58,202)( 59,203)( 60,204)( 61,205)( 62,206)( 63,207)( 64,208)( 65,209)( 66,210)( 67,211)( 68,212)( 69,213)( 70,214)( 71,215)( 72,216)( 73,217)( 74,218)( 75,219)( 76,220)( 77,221)( 78,222)( 79,223)( 80,224)( 81,225)( 82,226)( 83,227)( 84,228)( 85,229)( 86,230)( 87,231)( 88,232)( 89,233)( 90,234)( 91,235)( 92,236)( 93,237)( 94,238)( 95,239)( 96,240)( 97,241)( 98,242)( 99,243)(100,244)(101,245)(102,246)(103,247)(104,248)(105,249)(106,250)(107,251)(108,252)(109,253)(110,254)(111,255)(112,256)(113,257)(114,258)(115,259)(116,260)(117,261)(118,262)(119,263)(120,264)(121,265)(122,266)(123,267)(124,268)(125,269)(126,270)(127,271)(128,272)(129,273)(130,274)(131,275)(132,276)(133,277)(134,278)(135,279)(136,280)(137,281)(138,282)(139,283)(140,284)(141,285)(142,286)(143,287)(144,288)(289,433)(290,434)(291,435)(292,436)(293,437)(294,438)(295,439)(296,440)(297,441)(298,442)(299,443)(300,444)(301,445)(302,446)(303,447)(304,448)(305,449)(306,450)(307,451)(308,452)(309,453)(310,454)(311,455)(312,456)(313,457)(314,458)(315,459)(316,460)(317,461)(318,462)(319,463)(320,464)(321,465)(322,466)(323,467)(324,468)(325,469)(326,470)(327,471)(328,472)(329,473)(330,474)(331,475)(332,476)(333,477)(334,478)(335,479)(336,480)(337,481)(338,482)(339,483)(340,484)(341,485)(342,486)(343,487)(344,488)(345,489)(346,490)(347,491)(348,492)(349,493)(350,494)(351,495)(352,496)(353,497)(354,498)(355,499)(356,500)(357,501)(358,502)(359,503)(360,504)(361,505)(362,506)(363,507)(364,508)(365,509)(366,510)(367,511)(368,512)(369,513)(370,514)(371,515)(372,516)(373,517)(374,518)(375,519)(376,520)(377,521)(378,522)(379,523)(380,524)(381,525)(382,526)(383,527)(384,528)(385,529)(386,530)(387,531)(388,532)(389,533)(390,534)(391,535)(392,536)(393,537)(394,538)(395,539)(396,540)(397,541)(398,542)(399,543)(400,544)(401,545)(402,546)(403,547)(404,548)(405,549)(406,550)(407,551)(408,552)(409,553)(410,554)(411,555)(412,556)(413,557)(414,558)(415,559)(416,560)(417,561)(418,562)(419,563)(420,564)(421,565)(422,566)(423,567)(424,568)(425,569)(426,570)(427,571)(428,572)(429,573)(430,574)(431,575)(432,576);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, 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 ];;
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, 74)( 2, 73)( 3, 75)( 4, 80)( 5, 79)( 6, 81)( 7, 77)( 8, 76)( 9, 78)( 10, 83)( 11, 82)( 12, 84)( 13, 89)( 14, 88)( 15, 90)( 16, 86)( 17, 85)( 18, 87)( 19, 92)( 20, 91)( 21, 93)( 22, 98)( 23, 97)( 24, 99)( 25, 95)( 26, 94)( 27, 96)( 28,101)( 29,100)( 30,102)( 31,107)( 32,106)( 33,108)( 34,104)( 35,103)( 36,105)( 37,110)( 38,109)( 39,111)( 40,116)( 41,115)( 42,117)( 43,113)( 44,112)( 45,114)( 46,119)( 47,118)( 48,120)( 49,125)( 50,124)( 51,126)( 52,122)( 53,121)( 54,123)( 55,128)( 56,127)( 57,129)( 58,134)( 59,133)( 60,135)( 61,131)( 62,130)( 63,132)( 64,137)( 65,136)( 66,138)( 67,143)( 68,142)( 69,144)( 70,140)( 71,139)( 72,141)(145,218)(146,217)(147,219)(148,224)(149,223)(150,225)(151,221)(152,220)(153,222)(154,227)(155,226)(156,228)(157,233)(158,232)(159,234)(160,230)(161,229)(162,231)(163,236)(164,235)(165,237)(166,242)(167,241)(168,243)(169,239)(170,238)(171,240)(172,245)(173,244)(174,246)(175,251)(176,250)(177,252)(178,248)(179,247)(180,249)(181,254)(182,253)(183,255)(184,260)(185,259)(186,261)(187,257)(188,256)(189,258)(190,263)(191,262)(192,264)(193,269)(194,268)(195,270)(196,266)(197,265)(198,267)(199,272)(200,271)(201,273)(202,278)(203,277)(204,279)(205,275)(206,274)(207,276)(208,281)(209,280)(210,282)(211,287)(212,286)(213,288)(214,284)(215,283)(216,285)(289,362)(290,361)(291,363)(292,368)(293,367)(294,369)(295,365)(296,364)(297,366)(298,371)(299,370)(300,372)(301,377)(302,376)(303,378)(304,374)(305,373)(306,375)(307,380)(308,379)(309,381)(310,386)(311,385)(312,387)(313,383)(314,382)(315,384)(316,389)(317,388)(318,390)(319,395)(320,394)(321,396)(322,392)(323,391)(324,393)(325,398)(326,397)(327,399)(328,404)(329,403)(330,405)(331,401)(332,400)(333,402)(334,407)(335,406)(336,408)(337,413)(338,412)(339,414)(340,410)(341,409)(342,411)(343,416)(344,415)(345,417)(346,422)(347,421)(348,423)(349,419)(350,418)(351,420)(352,425)(353,424)(354,426)(355,431)(356,430)(357,432)(358,428)(359,427)(360,429)(433,506)(434,505)(435,507)(436,512)(437,511)(438,513)(439,509)(440,508)(441,510)(442,515)(443,514)(444,516)(445,521)(446,520)(447,522)(448,518)(449,517)(450,519)(451,524)(452,523)(453,525)(454,530)(455,529)(456,531)(457,527)(458,526)(459,528)(460,533)(461,532)(462,534)(463,539)(464,538)(465,540)(466,536)(467,535)(468,537)(469,542)(470,541)(471,543)(472,548)(473,547)(474,549)(475,545)(476,544)(477,546)(478,551)(479,550)(480,552)(481,557)(482,556)(483,558)(484,554)(485,553)(486,555)(487,560)(488,559)(489,561)(490,566)(491,565)(492,567)(493,563)(494,562)(495,564)(496,569)(497,568)(498,570)(499,575)(500,574)(501,576)(502,572)(503,571)(504,573);
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)( 19,307)( 20,312)( 21,314)( 22,310)( 23,315)( 24,308)( 25,313)( 26,309)( 27,311)( 28,316)( 29,321)( 30,323)( 31,319)( 32,324)( 33,317)( 34,322)( 35,318)( 36,320)( 37,334)( 38,339)( 39,341)( 40,337)( 41,342)( 42,335)( 43,340)( 44,336)( 45,338)( 46,325)( 47,330)( 48,332)( 49,328)( 50,333)( 51,326)( 52,331)( 53,327)( 54,329)( 55,352)( 56,357)( 57,359)( 58,355)( 59,360)( 60,353)( 61,358)( 62,354)( 63,356)( 64,343)( 65,348)( 66,350)( 67,346)( 68,351)( 69,344)( 70,349)( 71,345)( 72,347)( 73,361)( 74,366)( 75,368)( 76,364)( 77,369)( 78,362)( 79,367)( 80,363)( 81,365)( 82,370)( 83,375)( 84,377)( 85,373)( 86,378)( 87,371)( 88,376)( 89,372)( 90,374)( 91,379)( 92,384)( 93,386)( 94,382)( 95,387)( 96,380)( 97,385)( 98,381)( 99,383)(100,388)(101,393)(102,395)(103,391)(104,396)(105,389)(106,394)(107,390)(108,392)(109,406)(110,411)(111,413)(112,409)(113,414)(114,407)(115,412)(116,408)(117,410)(118,397)(119,402)(120,404)(121,400)(122,405)(123,398)(124,403)(125,399)(126,401)(127,424)(128,429)(129,431)(130,427)(131,432)(132,425)(133,430)(134,426)(135,428)(136,415)(137,420)(138,422)(139,418)(140,423)(141,416)(142,421)(143,417)(144,419)(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)(163,451)(164,456)(165,458)(166,454)(167,459)(168,452)(169,457)(170,453)(171,455)(172,460)(173,465)(174,467)(175,463)(176,468)(177,461)(178,466)(179,462)(180,464)(181,478)(182,483)(183,485)(184,481)(185,486)(186,479)(187,484)(188,480)(189,482)(190,469)(191,474)(192,476)(193,472)(194,477)(195,470)(196,475)(197,471)(198,473)(199,496)(200,501)(201,503)(202,499)(203,504)(204,497)(205,502)(206,498)(207,500)(208,487)(209,492)(210,494)(211,490)(212,495)(213,488)(214,493)(215,489)(216,491)(217,505)(218,510)(219,512)(220,508)(221,513)(222,506)(223,511)(224,507)(225,509)(226,514)(227,519)(228,521)(229,517)(230,522)(231,515)(232,520)(233,516)(234,518)(235,523)(236,528)(237,530)(238,526)(239,531)(240,524)(241,529)(242,525)(243,527)(244,532)(245,537)(246,539)(247,535)(248,540)(249,533)(250,538)(251,534)(252,536)(253,550)(254,555)(255,557)(256,553)(257,558)(258,551)(259,556)(260,552)(261,554)(262,541)(263,546)(264,548)(265,544)(266,549)(267,542)(268,547)(269,543)(270,545)(271,568)(272,573)(273,575)(274,571)(275,576)(276,569)(277,574)(278,570)(279,572)(280,559)(281,564)(282,566)(283,562)(284,567)(285,560)(286,565)(287,561)(288,563);
s3 := Sym(576)!( 37, 46)( 38, 47)( 39, 48)( 40, 49)( 41, 50)( 42, 51)( 43, 52)( 44, 53)( 45, 54)( 55, 64)( 56, 65)( 57, 66)( 58, 67)( 59, 68)( 60, 69)( 61, 70)( 62, 71)( 63, 72)(109,118)(110,119)(111,120)(112,121)(113,122)(114,123)(115,124)(116,125)(117,126)(127,136)(128,137)(129,138)(130,139)(131,140)(132,141)(133,142)(134,143)(135,144)(145,163)(146,164)(147,165)(148,166)(149,167)(150,168)(151,169)(152,170)(153,171)(154,172)(155,173)(156,174)(157,175)(158,176)(159,177)(160,178)(161,179)(162,180)(181,208)(182,209)(183,210)(184,211)(185,212)(186,213)(187,214)(188,215)(189,216)(190,199)(191,200)(192,201)(193,202)(194,203)(195,204)(196,205)(197,206)(198,207)(217,235)(218,236)(219,237)(220,238)(221,239)(222,240)(223,241)(224,242)(225,243)(226,244)(227,245)(228,246)(229,247)(230,248)(231,249)(232,250)(233,251)(234,252)(253,280)(254,281)(255,282)(256,283)(257,284)(258,285)(259,286)(260,287)(261,288)(262,271)(263,272)(264,273)(265,274)(266,275)(267,276)(268,277)(269,278)(270,279)(289,325)(290,326)(291,327)(292,328)(293,329)(294,330)(295,331)(296,332)(297,333)(298,334)(299,335)(300,336)(301,337)(302,338)(303,339)(304,340)(305,341)(306,342)(307,343)(308,344)(309,345)(310,346)(311,347)(312,348)(313,349)(314,350)(315,351)(316,352)(317,353)(318,354)(319,355)(320,356)(321,357)(322,358)(323,359)(324,360)(361,397)(362,398)(363,399)(364,400)(365,401)(366,402)(367,403)(368,404)(369,405)(370,406)(371,407)(372,408)(373,409)(374,410)(375,411)(376,412)(377,413)(378,414)(379,415)(380,416)(381,417)(382,418)(383,419)(384,420)(385,421)(386,422)(387,423)(388,424)(389,425)(390,426)(391,427)(392,428)(393,429)(394,430)(395,431)(396,432)(433,487)(434,488)(435,489)(436,490)(437,491)(438,492)(439,493)(440,494)(441,495)(442,496)(443,497)(444,498)(445,499)(446,500)(447,501)(448,502)(449,503)(450,504)(451,469)(452,470)(453,471)(454,472)(455,473)(456,474)(457,475)(458,476)(459,477)(460,478)(461,479)(462,480)(463,481)(464,482)(465,483)(466,484)(467,485)(468,486)(505,559)(506,560)(507,561)(508,562)(509,563)(510,564)(511,565)(512,566)(513,567)(514,568)(515,569)(516,570)(517,571)(518,572)(519,573)(520,574)(521,575)(522,576)(523,541)(524,542)(525,543)(526,544)(527,545)(528,546)(529,547)(530,548)(531,549)(532,550)(533,551)(534,552)(535,553)(536,554)(537,555)(538,556)(539,557)(540,558);
s4 := Sym(576)!( 1,145)( 2,146)( 3,147)( 4,148)( 5,149)( 6,150)( 7,151)( 8,152)( 9,153)( 10,154)( 11,155)( 12,156)( 13,157)( 14,158)( 15,159)( 16,160)( 17,161)( 18,162)( 19,163)( 20,164)( 21,165)( 22,166)( 23,167)( 24,168)( 25,169)( 26,170)( 27,171)( 28,172)( 29,173)( 30,174)( 31,175)( 32,176)( 33,177)( 34,178)( 35,179)( 36,180)( 37,181)( 38,182)( 39,183)( 40,184)( 41,185)( 42,186)( 43,187)( 44,188)( 45,189)( 46,190)( 47,191)( 48,192)( 49,193)( 50,194)( 51,195)( 52,196)( 53,197)( 54,198)( 55,199)( 56,200)( 57,201)( 58,202)( 59,203)( 60,204)( 61,205)( 62,206)( 63,207)( 64,208)( 65,209)( 66,210)( 67,211)( 68,212)( 69,213)( 70,214)( 71,215)( 72,216)( 73,217)( 74,218)( 75,219)( 76,220)( 77,221)( 78,222)( 79,223)( 80,224)( 81,225)( 82,226)( 83,227)( 84,228)( 85,229)( 86,230)( 87,231)( 88,232)( 89,233)( 90,234)( 91,235)( 92,236)( 93,237)( 94,238)( 95,239)( 96,240)( 97,241)( 98,242)( 99,243)(100,244)(101,245)(102,246)(103,247)(104,248)(105,249)(106,250)(107,251)(108,252)(109,253)(110,254)(111,255)(112,256)(113,257)(114,258)(115,259)(116,260)(117,261)(118,262)(119,263)(120,264)(121,265)(122,266)(123,267)(124,268)(125,269)(126,270)(127,271)(128,272)(129,273)(130,274)(131,275)(132,276)(133,277)(134,278)(135,279)(136,280)(137,281)(138,282)(139,283)(140,284)(141,285)(142,286)(143,287)(144,288)(289,433)(290,434)(291,435)(292,436)(293,437)(294,438)(295,439)(296,440)(297,441)(298,442)(299,443)(300,444)(301,445)(302,446)(303,447)(304,448)(305,449)(306,450)(307,451)(308,452)(309,453)(310,454)(311,455)(312,456)(313,457)(314,458)(315,459)(316,460)(317,461)(318,462)(319,463)(320,464)(321,465)(322,466)(323,467)(324,468)(325,469)(326,470)(327,471)(328,472)(329,473)(330,474)(331,475)(332,476)(333,477)(334,478)(335,479)(336,480)(337,481)(338,482)(339,483)(340,484)(341,485)(342,486)(343,487)(344,488)(345,489)(346,490)(347,491)(348,492)(349,493)(350,494)(351,495)(352,496)(353,497)(354,498)(355,499)(356,500)(357,501)(358,502)(359,503)(360,504)(361,505)(362,506)(363,507)(364,508)(365,509)(366,510)(367,511)(368,512)(369,513)(370,514)(371,515)(372,516)(373,517)(374,518)(375,519)(376,520)(377,521)(378,522)(379,523)(380,524)(381,525)(382,526)(383,527)(384,528)(385,529)(386,530)(387,531)(388,532)(389,533)(390,534)(391,535)(392,536)(393,537)(394,538)(395,539)(396,540)(397,541)(398,542)(399,543)(400,544)(401,545)(402,546)(403,547)(404,548)(405,549)(406,550)(407,551)(408,552)(409,553)(410,554)(411,555)(412,556)(413,557)(414,558)(415,559)(416,560)(417,561)(418,562)(419,563)(420,564)(421,565)(422,566)(423,567)(424,568)(425,569)(426,570)(427,571)(428,572)(429,573)(430,574)(431,575)(432,576);
poly := sub<Sym(576)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
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 >;
References : None.
to this polytope