Polytope of Type {6,24,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,24,4}*1152c
Also Known As : {{6,24|2},{24,4|2}}. if this polytope has another name.
Group : SmallGroup(1152,97537)
Rank : 4
Schlafli Type : {6,24,4}
Number of vertices, edges, etc : 6, 72, 48, 4
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}*576a, {6,24,2}*576a
3-fold quotients : {2,24,4}*384a, {6,8,4}*384a
4-fold quotients : {6,12,2}*288a, {6,6,4}*288a
6-fold quotients : {2,12,4}*192a, {6,4,4}*192, {2,24,2}*192, {6,8,2}*192
8-fold quotients : {6,6,2}*144a
9-fold quotients : {2,8,4}*128a
12-fold quotients : {2,12,2}*96, {2,6,4}*96a, {6,2,4}*96, {6,4,2}*96a
18-fold quotients : {2,4,4}*64, {2,8,2}*64
24-fold quotients : {3,2,4}*48, {2,6,2}*48, {6,2,2}*48
36-fold quotients : {2,2,4}*32, {2,4,2}*32
48-fold quotients : {2,3,2}*24, {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, 78)( 3, 80)( 4, 76)( 5, 81)( 6, 74)( 7, 79)( 8, 75)( 9, 77)( 10, 82)( 11, 87)( 12, 89)( 13, 85)( 14, 90)( 15, 83)( 16, 88)( 17, 84)( 18, 86)( 19, 91)( 20, 96)( 21, 98)( 22, 94)( 23, 99)( 24, 92)( 25, 97)( 26, 93)( 27, 95)( 28,100)( 29,105)( 30,107)( 31,103)( 32,108)( 33,101)( 34,106)( 35,102)( 36,104)( 37,109)( 38,114)( 39,116)( 40,112)( 41,117)( 42,110)( 43,115)( 44,111)( 45,113)( 46,118)( 47,123)( 48,125)( 49,121)( 50,126)( 51,119)( 52,124)( 53,120)( 54,122)( 55,127)( 56,132)( 57,134)( 58,130)( 59,135)( 60,128)( 61,133)( 62,129)( 63,131)( 64,136)( 65,141)( 66,143)( 67,139)( 68,144)( 69,137)( 70,142)( 71,138)( 72,140)(145,217)(146,222)(147,224)(148,220)(149,225)(150,218)(151,223)(152,219)(153,221)(154,226)(155,231)(156,233)(157,229)(158,234)(159,227)(160,232)(161,228)(162,230)(163,235)(164,240)(165,242)(166,238)(167,243)(168,236)(169,241)(170,237)(171,239)(172,244)(173,249)(174,251)(175,247)(176,252)(177,245)(178,250)(179,246)(180,248)(181,253)(182,258)(183,260)(184,256)(185,261)(186,254)(187,259)(188,255)(189,257)(190,262)(191,267)(192,269)(193,265)(194,270)(195,263)(196,268)(197,264)(198,266)(199,271)(200,276)(201,278)(202,274)(203,279)(204,272)(205,277)(206,273)(207,275)(208,280)(209,285)(210,287)(211,283)(212,288)(213,281)(214,286)(215,282)(216,284)(289,361)(290,366)(291,368)(292,364)(293,369)(294,362)(295,367)(296,363)(297,365)(298,370)(299,375)(300,377)(301,373)(302,378)(303,371)(304,376)(305,372)(306,374)(307,379)(308,384)(309,386)(310,382)(311,387)(312,380)(313,385)(314,381)(315,383)(316,388)(317,393)(318,395)(319,391)(320,396)(321,389)(322,394)(323,390)(324,392)(325,397)(326,402)(327,404)(328,400)(329,405)(330,398)(331,403)(332,399)(333,401)(334,406)(335,411)(336,413)(337,409)(338,414)(339,407)(340,412)(341,408)(342,410)(343,415)(344,420)(345,422)(346,418)(347,423)(348,416)(349,421)(350,417)(351,419)(352,424)(353,429)(354,431)(355,427)(356,432)(357,425)(358,430)(359,426)(360,428)(433,505)(434,510)(435,512)(436,508)(437,513)(438,506)(439,511)(440,507)(441,509)(442,514)(443,519)(444,521)(445,517)(446,522)(447,515)(448,520)(449,516)(450,518)(451,523)(452,528)(453,530)(454,526)(455,531)(456,524)(457,529)(458,525)(459,527)(460,532)(461,537)(462,539)(463,535)(464,540)(465,533)(466,538)(467,534)(468,536)(469,541)(470,546)(471,548)(472,544)(473,549)(474,542)(475,547)(476,543)(477,545)(478,550)(479,555)(480,557)(481,553)(482,558)(483,551)(484,556)(485,552)(486,554)(487,559)(488,564)(489,566)(490,562)(491,567)(492,560)(493,565)(494,561)(495,563)(496,568)(497,573)(498,575)(499,571)(500,576)(501,569)(502,574)(503,570)(504,572);;
s1 := ( 1,290)( 2,289)( 3,291)( 4,296)( 5,295)( 6,297)( 7,293)( 8,292)( 9,294)( 10,299)( 11,298)( 12,300)( 13,305)( 14,304)( 15,306)( 16,302)( 17,301)( 18,303)( 19,308)( 20,307)( 21,309)( 22,314)( 23,313)( 24,315)( 25,311)( 26,310)( 27,312)( 28,317)( 29,316)( 30,318)( 31,323)( 32,322)( 33,324)( 34,320)( 35,319)( 36,321)( 37,335)( 38,334)( 39,336)( 40,341)( 41,340)( 42,342)( 43,338)( 44,337)( 45,339)( 46,326)( 47,325)( 48,327)( 49,332)( 50,331)( 51,333)( 52,329)( 53,328)( 54,330)( 55,353)( 56,352)( 57,354)( 58,359)( 59,358)( 60,360)( 61,356)( 62,355)( 63,357)( 64,344)( 65,343)( 66,345)( 67,350)( 68,349)( 69,351)( 70,347)( 71,346)( 72,348)( 73,362)( 74,361)( 75,363)( 76,368)( 77,367)( 78,369)( 79,365)( 80,364)( 81,366)( 82,371)( 83,370)( 84,372)( 85,377)( 86,376)( 87,378)( 88,374)( 89,373)( 90,375)( 91,380)( 92,379)( 93,381)( 94,386)( 95,385)( 96,387)( 97,383)( 98,382)( 99,384)(100,389)(101,388)(102,390)(103,395)(104,394)(105,396)(106,392)(107,391)(108,393)(109,407)(110,406)(111,408)(112,413)(113,412)(114,414)(115,410)(116,409)(117,411)(118,398)(119,397)(120,399)(121,404)(122,403)(123,405)(124,401)(125,400)(126,402)(127,425)(128,424)(129,426)(130,431)(131,430)(132,432)(133,428)(134,427)(135,429)(136,416)(137,415)(138,417)(139,422)(140,421)(141,423)(142,419)(143,418)(144,420)(145,434)(146,433)(147,435)(148,440)(149,439)(150,441)(151,437)(152,436)(153,438)(154,443)(155,442)(156,444)(157,449)(158,448)(159,450)(160,446)(161,445)(162,447)(163,452)(164,451)(165,453)(166,458)(167,457)(168,459)(169,455)(170,454)(171,456)(172,461)(173,460)(174,462)(175,467)(176,466)(177,468)(178,464)(179,463)(180,465)(181,479)(182,478)(183,480)(184,485)(185,484)(186,486)(187,482)(188,481)(189,483)(190,470)(191,469)(192,471)(193,476)(194,475)(195,477)(196,473)(197,472)(198,474)(199,497)(200,496)(201,498)(202,503)(203,502)(204,504)(205,500)(206,499)(207,501)(208,488)(209,487)(210,489)(211,494)(212,493)(213,495)(214,491)(215,490)(216,492)(217,506)(218,505)(219,507)(220,512)(221,511)(222,513)(223,509)(224,508)(225,510)(226,515)(227,514)(228,516)(229,521)(230,520)(231,522)(232,518)(233,517)(234,519)(235,524)(236,523)(237,525)(238,530)(239,529)(240,531)(241,527)(242,526)(243,528)(244,533)(245,532)(246,534)(247,539)(248,538)(249,540)(250,536)(251,535)(252,537)(253,551)(254,550)(255,552)(256,557)(257,556)(258,558)(259,554)(260,553)(261,555)(262,542)(263,541)(264,543)(265,548)(266,547)(267,549)(268,545)(269,544)(270,546)(271,569)(272,568)(273,570)(274,575)(275,574)(276,576)(277,572)(278,571)(279,573)(280,560)(281,559)(282,561)(283,566)(284,565)(285,567)(286,563)(287,562)(288,564);;
s2 := ( 1, 73)( 2, 80)( 3, 78)( 4, 79)( 5, 77)( 6, 75)( 7, 76)( 8, 74)( 9, 81)( 10, 82)( 11, 89)( 12, 87)( 13, 88)( 14, 86)( 15, 84)( 16, 85)( 17, 83)( 18, 90)( 19, 91)( 20, 98)( 21, 96)( 22, 97)( 23, 95)( 24, 93)( 25, 94)( 26, 92)( 27, 99)( 28,100)( 29,107)( 30,105)( 31,106)( 32,104)( 33,102)( 34,103)( 35,101)( 36,108)( 37,118)( 38,125)( 39,123)( 40,124)( 41,122)( 42,120)( 43,121)( 44,119)( 45,126)( 46,109)( 47,116)( 48,114)( 49,115)( 50,113)( 51,111)( 52,112)( 53,110)( 54,117)( 55,136)( 56,143)( 57,141)( 58,142)( 59,140)( 60,138)( 61,139)( 62,137)( 63,144)( 64,127)( 65,134)( 66,132)( 67,133)( 68,131)( 69,129)( 70,130)( 71,128)( 72,135)(145,235)(146,242)(147,240)(148,241)(149,239)(150,237)(151,238)(152,236)(153,243)(154,244)(155,251)(156,249)(157,250)(158,248)(159,246)(160,247)(161,245)(162,252)(163,217)(164,224)(165,222)(166,223)(167,221)(168,219)(169,220)(170,218)(171,225)(172,226)(173,233)(174,231)(175,232)(176,230)(177,228)(178,229)(179,227)(180,234)(181,280)(182,287)(183,285)(184,286)(185,284)(186,282)(187,283)(188,281)(189,288)(190,271)(191,278)(192,276)(193,277)(194,275)(195,273)(196,274)(197,272)(198,279)(199,262)(200,269)(201,267)(202,268)(203,266)(204,264)(205,265)(206,263)(207,270)(208,253)(209,260)(210,258)(211,259)(212,257)(213,255)(214,256)(215,254)(216,261)(289,397)(290,404)(291,402)(292,403)(293,401)(294,399)(295,400)(296,398)(297,405)(298,406)(299,413)(300,411)(301,412)(302,410)(303,408)(304,409)(305,407)(306,414)(307,415)(308,422)(309,420)(310,421)(311,419)(312,417)(313,418)(314,416)(315,423)(316,424)(317,431)(318,429)(319,430)(320,428)(321,426)(322,427)(323,425)(324,432)(325,361)(326,368)(327,366)(328,367)(329,365)(330,363)(331,364)(332,362)(333,369)(334,370)(335,377)(336,375)(337,376)(338,374)(339,372)(340,373)(341,371)(342,378)(343,379)(344,386)(345,384)(346,385)(347,383)(348,381)(349,382)(350,380)(351,387)(352,388)(353,395)(354,393)(355,394)(356,392)(357,390)(358,391)(359,389)(360,396)(433,559)(434,566)(435,564)(436,565)(437,563)(438,561)(439,562)(440,560)(441,567)(442,568)(443,575)(444,573)(445,574)(446,572)(447,570)(448,571)(449,569)(450,576)(451,541)(452,548)(453,546)(454,547)(455,545)(456,543)(457,544)(458,542)(459,549)(460,550)(461,557)(462,555)(463,556)(464,554)(465,552)(466,553)(467,551)(468,558)(469,523)(470,530)(471,528)(472,529)(473,527)(474,525)(475,526)(476,524)(477,531)(478,532)(479,539)(480,537)(481,538)(482,536)(483,534)(484,535)(485,533)(486,540)(487,505)(488,512)(489,510)(490,511)(491,509)(492,507)(493,508)(494,506)(495,513)(496,514)(497,521)(498,519)(499,520)(500,518)(501,516)(502,517)(503,515)(504,522);;
s3 := ( 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]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(576)!( 1, 73)( 2, 78)( 3, 80)( 4, 76)( 5, 81)( 6, 74)( 7, 79)( 8, 75)( 9, 77)( 10, 82)( 11, 87)( 12, 89)( 13, 85)( 14, 90)( 15, 83)( 16, 88)( 17, 84)( 18, 86)( 19, 91)( 20, 96)( 21, 98)( 22, 94)( 23, 99)( 24, 92)( 25, 97)( 26, 93)( 27, 95)( 28,100)( 29,105)( 30,107)( 31,103)( 32,108)( 33,101)( 34,106)( 35,102)( 36,104)( 37,109)( 38,114)( 39,116)( 40,112)( 41,117)( 42,110)( 43,115)( 44,111)( 45,113)( 46,118)( 47,123)( 48,125)( 49,121)( 50,126)( 51,119)( 52,124)( 53,120)( 54,122)( 55,127)( 56,132)( 57,134)( 58,130)( 59,135)( 60,128)( 61,133)( 62,129)( 63,131)( 64,136)( 65,141)( 66,143)( 67,139)( 68,144)( 69,137)( 70,142)( 71,138)( 72,140)(145,217)(146,222)(147,224)(148,220)(149,225)(150,218)(151,223)(152,219)(153,221)(154,226)(155,231)(156,233)(157,229)(158,234)(159,227)(160,232)(161,228)(162,230)(163,235)(164,240)(165,242)(166,238)(167,243)(168,236)(169,241)(170,237)(171,239)(172,244)(173,249)(174,251)(175,247)(176,252)(177,245)(178,250)(179,246)(180,248)(181,253)(182,258)(183,260)(184,256)(185,261)(186,254)(187,259)(188,255)(189,257)(190,262)(191,267)(192,269)(193,265)(194,270)(195,263)(196,268)(197,264)(198,266)(199,271)(200,276)(201,278)(202,274)(203,279)(204,272)(205,277)(206,273)(207,275)(208,280)(209,285)(210,287)(211,283)(212,288)(213,281)(214,286)(215,282)(216,284)(289,361)(290,366)(291,368)(292,364)(293,369)(294,362)(295,367)(296,363)(297,365)(298,370)(299,375)(300,377)(301,373)(302,378)(303,371)(304,376)(305,372)(306,374)(307,379)(308,384)(309,386)(310,382)(311,387)(312,380)(313,385)(314,381)(315,383)(316,388)(317,393)(318,395)(319,391)(320,396)(321,389)(322,394)(323,390)(324,392)(325,397)(326,402)(327,404)(328,400)(329,405)(330,398)(331,403)(332,399)(333,401)(334,406)(335,411)(336,413)(337,409)(338,414)(339,407)(340,412)(341,408)(342,410)(343,415)(344,420)(345,422)(346,418)(347,423)(348,416)(349,421)(350,417)(351,419)(352,424)(353,429)(354,431)(355,427)(356,432)(357,425)(358,430)(359,426)(360,428)(433,505)(434,510)(435,512)(436,508)(437,513)(438,506)(439,511)(440,507)(441,509)(442,514)(443,519)(444,521)(445,517)(446,522)(447,515)(448,520)(449,516)(450,518)(451,523)(452,528)(453,530)(454,526)(455,531)(456,524)(457,529)(458,525)(459,527)(460,532)(461,537)(462,539)(463,535)(464,540)(465,533)(466,538)(467,534)(468,536)(469,541)(470,546)(471,548)(472,544)(473,549)(474,542)(475,547)(476,543)(477,545)(478,550)(479,555)(480,557)(481,553)(482,558)(483,551)(484,556)(485,552)(486,554)(487,559)(488,564)(489,566)(490,562)(491,567)(492,560)(493,565)(494,561)(495,563)(496,568)(497,573)(498,575)(499,571)(500,576)(501,569)(502,574)(503,570)(504,572);
s1 := Sym(576)!( 1,290)( 2,289)( 3,291)( 4,296)( 5,295)( 6,297)( 7,293)( 8,292)( 9,294)( 10,299)( 11,298)( 12,300)( 13,305)( 14,304)( 15,306)( 16,302)( 17,301)( 18,303)( 19,308)( 20,307)( 21,309)( 22,314)( 23,313)( 24,315)( 25,311)( 26,310)( 27,312)( 28,317)( 29,316)( 30,318)( 31,323)( 32,322)( 33,324)( 34,320)( 35,319)( 36,321)( 37,335)( 38,334)( 39,336)( 40,341)( 41,340)( 42,342)( 43,338)( 44,337)( 45,339)( 46,326)( 47,325)( 48,327)( 49,332)( 50,331)( 51,333)( 52,329)( 53,328)( 54,330)( 55,353)( 56,352)( 57,354)( 58,359)( 59,358)( 60,360)( 61,356)( 62,355)( 63,357)( 64,344)( 65,343)( 66,345)( 67,350)( 68,349)( 69,351)( 70,347)( 71,346)( 72,348)( 73,362)( 74,361)( 75,363)( 76,368)( 77,367)( 78,369)( 79,365)( 80,364)( 81,366)( 82,371)( 83,370)( 84,372)( 85,377)( 86,376)( 87,378)( 88,374)( 89,373)( 90,375)( 91,380)( 92,379)( 93,381)( 94,386)( 95,385)( 96,387)( 97,383)( 98,382)( 99,384)(100,389)(101,388)(102,390)(103,395)(104,394)(105,396)(106,392)(107,391)(108,393)(109,407)(110,406)(111,408)(112,413)(113,412)(114,414)(115,410)(116,409)(117,411)(118,398)(119,397)(120,399)(121,404)(122,403)(123,405)(124,401)(125,400)(126,402)(127,425)(128,424)(129,426)(130,431)(131,430)(132,432)(133,428)(134,427)(135,429)(136,416)(137,415)(138,417)(139,422)(140,421)(141,423)(142,419)(143,418)(144,420)(145,434)(146,433)(147,435)(148,440)(149,439)(150,441)(151,437)(152,436)(153,438)(154,443)(155,442)(156,444)(157,449)(158,448)(159,450)(160,446)(161,445)(162,447)(163,452)(164,451)(165,453)(166,458)(167,457)(168,459)(169,455)(170,454)(171,456)(172,461)(173,460)(174,462)(175,467)(176,466)(177,468)(178,464)(179,463)(180,465)(181,479)(182,478)(183,480)(184,485)(185,484)(186,486)(187,482)(188,481)(189,483)(190,470)(191,469)(192,471)(193,476)(194,475)(195,477)(196,473)(197,472)(198,474)(199,497)(200,496)(201,498)(202,503)(203,502)(204,504)(205,500)(206,499)(207,501)(208,488)(209,487)(210,489)(211,494)(212,493)(213,495)(214,491)(215,490)(216,492)(217,506)(218,505)(219,507)(220,512)(221,511)(222,513)(223,509)(224,508)(225,510)(226,515)(227,514)(228,516)(229,521)(230,520)(231,522)(232,518)(233,517)(234,519)(235,524)(236,523)(237,525)(238,530)(239,529)(240,531)(241,527)(242,526)(243,528)(244,533)(245,532)(246,534)(247,539)(248,538)(249,540)(250,536)(251,535)(252,537)(253,551)(254,550)(255,552)(256,557)(257,556)(258,558)(259,554)(260,553)(261,555)(262,542)(263,541)(264,543)(265,548)(266,547)(267,549)(268,545)(269,544)(270,546)(271,569)(272,568)(273,570)(274,575)(275,574)(276,576)(277,572)(278,571)(279,573)(280,560)(281,559)(282,561)(283,566)(284,565)(285,567)(286,563)(287,562)(288,564);
s2 := Sym(576)!( 1, 73)( 2, 80)( 3, 78)( 4, 79)( 5, 77)( 6, 75)( 7, 76)( 8, 74)( 9, 81)( 10, 82)( 11, 89)( 12, 87)( 13, 88)( 14, 86)( 15, 84)( 16, 85)( 17, 83)( 18, 90)( 19, 91)( 20, 98)( 21, 96)( 22, 97)( 23, 95)( 24, 93)( 25, 94)( 26, 92)( 27, 99)( 28,100)( 29,107)( 30,105)( 31,106)( 32,104)( 33,102)( 34,103)( 35,101)( 36,108)( 37,118)( 38,125)( 39,123)( 40,124)( 41,122)( 42,120)( 43,121)( 44,119)( 45,126)( 46,109)( 47,116)( 48,114)( 49,115)( 50,113)( 51,111)( 52,112)( 53,110)( 54,117)( 55,136)( 56,143)( 57,141)( 58,142)( 59,140)( 60,138)( 61,139)( 62,137)( 63,144)( 64,127)( 65,134)( 66,132)( 67,133)( 68,131)( 69,129)( 70,130)( 71,128)( 72,135)(145,235)(146,242)(147,240)(148,241)(149,239)(150,237)(151,238)(152,236)(153,243)(154,244)(155,251)(156,249)(157,250)(158,248)(159,246)(160,247)(161,245)(162,252)(163,217)(164,224)(165,222)(166,223)(167,221)(168,219)(169,220)(170,218)(171,225)(172,226)(173,233)(174,231)(175,232)(176,230)(177,228)(178,229)(179,227)(180,234)(181,280)(182,287)(183,285)(184,286)(185,284)(186,282)(187,283)(188,281)(189,288)(190,271)(191,278)(192,276)(193,277)(194,275)(195,273)(196,274)(197,272)(198,279)(199,262)(200,269)(201,267)(202,268)(203,266)(204,264)(205,265)(206,263)(207,270)(208,253)(209,260)(210,258)(211,259)(212,257)(213,255)(214,256)(215,254)(216,261)(289,397)(290,404)(291,402)(292,403)(293,401)(294,399)(295,400)(296,398)(297,405)(298,406)(299,413)(300,411)(301,412)(302,410)(303,408)(304,409)(305,407)(306,414)(307,415)(308,422)(309,420)(310,421)(311,419)(312,417)(313,418)(314,416)(315,423)(316,424)(317,431)(318,429)(319,430)(320,428)(321,426)(322,427)(323,425)(324,432)(325,361)(326,368)(327,366)(328,367)(329,365)(330,363)(331,364)(332,362)(333,369)(334,370)(335,377)(336,375)(337,376)(338,374)(339,372)(340,373)(341,371)(342,378)(343,379)(344,386)(345,384)(346,385)(347,383)(348,381)(349,382)(350,380)(351,387)(352,388)(353,395)(354,393)(355,394)(356,392)(357,390)(358,391)(359,389)(360,396)(433,559)(434,566)(435,564)(436,565)(437,563)(438,561)(439,562)(440,560)(441,567)(442,568)(443,575)(444,573)(445,574)(446,572)(447,570)(448,571)(449,569)(450,576)(451,541)(452,548)(453,546)(454,547)(455,545)(456,543)(457,544)(458,542)(459,549)(460,550)(461,557)(462,555)(463,556)(464,554)(465,552)(466,553)(467,551)(468,558)(469,523)(470,530)(471,528)(472,529)(473,527)(474,525)(475,526)(476,524)(477,531)(478,532)(479,539)(480,537)(481,538)(482,536)(483,534)(484,535)(485,533)(486,540)(487,505)(488,512)(489,510)(490,511)(491,509)(492,507)(493,508)(494,506)(495,513)(496,514)(497,521)(498,519)(499,520)(500,518)(501,516)(502,517)(503,515)(504,522);
s3 := 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>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope