Polytope of Type {12,6,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6,8}*1152a
if this polytope has a name.
Group : SmallGroup(1152,119750)
Rank : 4
Schlafli Type : {12,6,8}
Number of vertices, edges, etc : 12, 36, 24, 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 : {6,6,8}*576b, {12,6,4}*576c
3-fold quotients : {4,6,8}*384a
4-fold quotients : {6,6,4}*288b, {12,6,2}*288c
6-fold quotients : {4,6,4}*192a, {2,6,8}*192
8-fold quotients : {6,6,2}*144b
9-fold quotients : {4,2,8}*128
12-fold quotients : {2,6,4}*96a, {4,6,2}*96a
16-fold quotients : {6,3,2}*72
18-fold quotients : {4,2,4}*64, {2,2,8}*64
24-fold quotients : {2,6,2}*48
36-fold quotients : {2,2,4}*32, {4,2,2}*32
48-fold quotients : {2,3,2}*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 := ( 1,145)( 2,150)( 3,152)( 4,148)( 5,153)( 6,146)( 7,151)( 8,147)( 9,149)( 10,154)( 11,159)( 12,161)( 13,157)( 14,162)( 15,155)( 16,160)( 17,156)( 18,158)( 19,163)( 20,168)( 21,170)( 22,166)( 23,171)( 24,164)( 25,169)( 26,165)( 27,167)( 28,172)( 29,177)( 30,179)( 31,175)( 32,180)( 33,173)( 34,178)( 35,174)( 36,176)( 37,181)( 38,186)( 39,188)( 40,184)( 41,189)( 42,182)( 43,187)( 44,183)( 45,185)( 46,190)( 47,195)( 48,197)( 49,193)( 50,198)( 51,191)( 52,196)( 53,192)( 54,194)( 55,199)( 56,204)( 57,206)( 58,202)( 59,207)( 60,200)( 61,205)( 62,201)( 63,203)( 64,208)( 65,213)( 66,215)( 67,211)( 68,216)( 69,209)( 70,214)( 71,210)( 72,212)( 73,217)( 74,222)( 75,224)( 76,220)( 77,225)( 78,218)( 79,223)( 80,219)( 81,221)( 82,226)( 83,231)( 84,233)( 85,229)( 86,234)( 87,227)( 88,232)( 89,228)( 90,230)( 91,235)( 92,240)( 93,242)( 94,238)( 95,243)( 96,236)( 97,241)( 98,237)( 99,239)(100,244)(101,249)(102,251)(103,247)(104,252)(105,245)(106,250)(107,246)(108,248)(109,253)(110,258)(111,260)(112,256)(113,261)(114,254)(115,259)(116,255)(117,257)(118,262)(119,267)(120,269)(121,265)(122,270)(123,263)(124,268)(125,264)(126,266)(127,271)(128,276)(129,278)(130,274)(131,279)(132,272)(133,277)(134,273)(135,275)(136,280)(137,285)(138,287)(139,283)(140,288)(141,281)(142,286)(143,282)(144,284)(289,433)(290,438)(291,440)(292,436)(293,441)(294,434)(295,439)(296,435)(297,437)(298,442)(299,447)(300,449)(301,445)(302,450)(303,443)(304,448)(305,444)(306,446)(307,451)(308,456)(309,458)(310,454)(311,459)(312,452)(313,457)(314,453)(315,455)(316,460)(317,465)(318,467)(319,463)(320,468)(321,461)(322,466)(323,462)(324,464)(325,469)(326,474)(327,476)(328,472)(329,477)(330,470)(331,475)(332,471)(333,473)(334,478)(335,483)(336,485)(337,481)(338,486)(339,479)(340,484)(341,480)(342,482)(343,487)(344,492)(345,494)(346,490)(347,495)(348,488)(349,493)(350,489)(351,491)(352,496)(353,501)(354,503)(355,499)(356,504)(357,497)(358,502)(359,498)(360,500)(361,505)(362,510)(363,512)(364,508)(365,513)(366,506)(367,511)(368,507)(369,509)(370,514)(371,519)(372,521)(373,517)(374,522)(375,515)(376,520)(377,516)(378,518)(379,523)(380,528)(381,530)(382,526)(383,531)(384,524)(385,529)(386,525)(387,527)(388,532)(389,537)(390,539)(391,535)(392,540)(393,533)(394,538)(395,534)(396,536)(397,541)(398,546)(399,548)(400,544)(401,549)(402,542)(403,547)(404,543)(405,545)(406,550)(407,555)(408,557)(409,553)(410,558)(411,551)(412,556)(413,552)(414,554)(415,559)(416,564)(417,566)(418,562)(419,567)(420,560)(421,565)(422,561)(423,563)(424,568)(425,573)(426,575)(427,571)(428,576)(429,569)(430,574)(431,570)(432,572);;
s1 := ( 1,110)( 2,109)( 3,111)( 4,116)( 5,115)( 6,117)( 7,113)( 8,112)( 9,114)( 10,119)( 11,118)( 12,120)( 13,125)( 14,124)( 15,126)( 16,122)( 17,121)( 18,123)( 19,128)( 20,127)( 21,129)( 22,134)( 23,133)( 24,135)( 25,131)( 26,130)( 27,132)( 28,137)( 29,136)( 30,138)( 31,143)( 32,142)( 33,144)( 34,140)( 35,139)( 36,141)( 37, 83)( 38, 82)( 39, 84)( 40, 89)( 41, 88)( 42, 90)( 43, 86)( 44, 85)( 45, 87)( 46, 74)( 47, 73)( 48, 75)( 49, 80)( 50, 79)( 51, 81)( 52, 77)( 53, 76)( 54, 78)( 55,101)( 56,100)( 57,102)( 58,107)( 59,106)( 60,108)( 61,104)( 62,103)( 63,105)( 64, 92)( 65, 91)( 66, 93)( 67, 98)( 68, 97)( 69, 99)( 70, 95)( 71, 94)( 72, 96)(145,272)(146,271)(147,273)(148,278)(149,277)(150,279)(151,275)(152,274)(153,276)(154,281)(155,280)(156,282)(157,287)(158,286)(159,288)(160,284)(161,283)(162,285)(163,254)(164,253)(165,255)(166,260)(167,259)(168,261)(169,257)(170,256)(171,258)(172,263)(173,262)(174,264)(175,269)(176,268)(177,270)(178,266)(179,265)(180,267)(181,245)(182,244)(183,246)(184,251)(185,250)(186,252)(187,248)(188,247)(189,249)(190,236)(191,235)(192,237)(193,242)(194,241)(195,243)(196,239)(197,238)(198,240)(199,227)(200,226)(201,228)(202,233)(203,232)(204,234)(205,230)(206,229)(207,231)(208,218)(209,217)(210,219)(211,224)(212,223)(213,225)(214,221)(215,220)(216,222)(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)(433,524)(434,523)(435,525)(436,530)(437,529)(438,531)(439,527)(440,526)(441,528)(442,533)(443,532)(444,534)(445,539)(446,538)(447,540)(448,536)(449,535)(450,537)(451,506)(452,505)(453,507)(454,512)(455,511)(456,513)(457,509)(458,508)(459,510)(460,515)(461,514)(462,516)(463,521)(464,520)(465,522)(466,518)(467,517)(468,519)(469,560)(470,559)(471,561)(472,566)(473,565)(474,567)(475,563)(476,562)(477,564)(478,569)(479,568)(480,570)(481,575)(482,574)(483,576)(484,572)(485,571)(486,573)(487,542)(488,541)(489,543)(490,548)(491,547)(492,549)(493,545)(494,544)(495,546)(496,551)(497,550)(498,552)(499,557)(500,556)(501,558)(502,554)(503,553)(504,555);;
s2 := ( 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)( 37,118)( 38,120)( 39,119)( 40,124)( 41,126)( 42,125)( 43,121)( 44,123)( 45,122)( 46,109)( 47,111)( 48,110)( 49,115)( 50,117)( 51,116)( 52,112)( 53,114)( 54,113)( 55,136)( 56,138)( 57,137)( 58,142)( 59,144)( 60,143)( 61,139)( 62,141)( 63,140)( 64,127)( 65,129)( 66,128)( 67,133)( 68,135)( 69,134)( 70,130)( 71,132)( 72,131)(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)(181,262)(182,264)(183,263)(184,268)(185,270)(186,269)(187,265)(188,267)(189,266)(190,253)(191,255)(192,254)(193,259)(194,261)(195,260)(196,256)(197,258)(198,257)(199,280)(200,282)(201,281)(202,286)(203,288)(204,287)(205,283)(206,285)(207,284)(208,271)(209,273)(210,272)(211,277)(212,279)(213,278)(214,274)(215,276)(216,275)(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)(325,406)(326,408)(327,407)(328,412)(329,414)(330,413)(331,409)(332,411)(333,410)(334,397)(335,399)(336,398)(337,403)(338,405)(339,404)(340,400)(341,402)(342,401)(343,424)(344,426)(345,425)(346,430)(347,432)(348,431)(349,427)(350,429)(351,428)(352,415)(353,417)(354,416)(355,421)(356,423)(357,422)(358,418)(359,420)(360,419)(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)(469,550)(470,552)(471,551)(472,556)(473,558)(474,557)(475,553)(476,555)(477,554)(478,541)(479,543)(480,542)(481,547)(482,549)(483,548)(484,544)(485,546)(486,545)(487,568)(488,570)(489,569)(490,574)(491,576)(492,575)(493,571)(494,573)(495,572)(496,559)(497,561)(498,560)(499,565)(500,567)(501,566)(502,562)(503,564)(504,563);;
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)( 19,307)( 20,308)( 21,309)( 22,310)( 23,311)( 24,312)( 25,313)( 26,314)( 27,315)( 28,316)( 29,317)( 30,318)( 31,319)( 32,320)( 33,321)( 34,322)( 35,323)( 36,324)( 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)( 55,352)( 56,353)( 57,354)( 58,355)( 59,356)( 60,357)( 61,358)( 62,359)( 63,360)( 64,343)( 65,344)( 66,345)( 67,346)( 68,347)( 69,348)( 70,349)( 71,350)( 72,351)( 73,397)( 74,398)( 75,399)( 76,400)( 77,401)( 78,402)( 79,403)( 80,404)( 81,405)( 82,406)( 83,407)( 84,408)( 85,409)( 86,410)( 87,411)( 88,412)( 89,413)( 90,414)( 91,415)( 92,416)( 93,417)( 94,418)( 95,419)( 96,420)( 97,421)( 98,422)( 99,423)(100,424)(101,425)(102,426)(103,427)(104,428)(105,429)(106,430)(107,431)(108,432)(109,361)(110,362)(111,363)(112,364)(113,365)(114,366)(115,367)(116,368)(117,369)(118,370)(119,371)(120,372)(121,373)(122,374)(123,375)(124,376)(125,377)(126,378)(127,379)(128,380)(129,381)(130,382)(131,383)(132,384)(133,385)(134,386)(135,387)(136,388)(137,389)(138,390)(139,391)(140,392)(141,393)(142,394)(143,395)(144,396)(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)(163,451)(164,452)(165,453)(166,454)(167,455)(168,456)(169,457)(170,458)(171,459)(172,460)(173,461)(174,462)(175,463)(176,464)(177,465)(178,466)(179,467)(180,468)(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)(199,496)(200,497)(201,498)(202,499)(203,500)(204,501)(205,502)(206,503)(207,504)(208,487)(209,488)(210,489)(211,490)(212,491)(213,492)(214,493)(215,494)(216,495)(217,541)(218,542)(219,543)(220,544)(221,545)(222,546)(223,547)(224,548)(225,549)(226,550)(227,551)(228,552)(229,553)(230,554)(231,555)(232,556)(233,557)(234,558)(235,559)(236,560)(237,561)(238,562)(239,563)(240,564)(241,565)(242,566)(243,567)(244,568)(245,569)(246,570)(247,571)(248,572)(249,573)(250,574)(251,575)(252,576)(253,505)(254,506)(255,507)(256,508)(257,509)(258,510)(259,511)(260,512)(261,513)(262,514)(263,515)(264,516)(265,517)(266,518)(267,519)(268,520)(269,521)(270,522)(271,523)(272,524)(273,525)(274,526)(275,527)(276,528)(277,529)(278,530)(279,531)(280,532)(281,533)(282,534)(283,535)(284,536)(285,537)(286,538)(287,539)(288,540);;
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,
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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)!( 1,145)( 2,150)( 3,152)( 4,148)( 5,153)( 6,146)( 7,151)( 8,147)( 9,149)( 10,154)( 11,159)( 12,161)( 13,157)( 14,162)( 15,155)( 16,160)( 17,156)( 18,158)( 19,163)( 20,168)( 21,170)( 22,166)( 23,171)( 24,164)( 25,169)( 26,165)( 27,167)( 28,172)( 29,177)( 30,179)( 31,175)( 32,180)( 33,173)( 34,178)( 35,174)( 36,176)( 37,181)( 38,186)( 39,188)( 40,184)( 41,189)( 42,182)( 43,187)( 44,183)( 45,185)( 46,190)( 47,195)( 48,197)( 49,193)( 50,198)( 51,191)( 52,196)( 53,192)( 54,194)( 55,199)( 56,204)( 57,206)( 58,202)( 59,207)( 60,200)( 61,205)( 62,201)( 63,203)( 64,208)( 65,213)( 66,215)( 67,211)( 68,216)( 69,209)( 70,214)( 71,210)( 72,212)( 73,217)( 74,222)( 75,224)( 76,220)( 77,225)( 78,218)( 79,223)( 80,219)( 81,221)( 82,226)( 83,231)( 84,233)( 85,229)( 86,234)( 87,227)( 88,232)( 89,228)( 90,230)( 91,235)( 92,240)( 93,242)( 94,238)( 95,243)( 96,236)( 97,241)( 98,237)( 99,239)(100,244)(101,249)(102,251)(103,247)(104,252)(105,245)(106,250)(107,246)(108,248)(109,253)(110,258)(111,260)(112,256)(113,261)(114,254)(115,259)(116,255)(117,257)(118,262)(119,267)(120,269)(121,265)(122,270)(123,263)(124,268)(125,264)(126,266)(127,271)(128,276)(129,278)(130,274)(131,279)(132,272)(133,277)(134,273)(135,275)(136,280)(137,285)(138,287)(139,283)(140,288)(141,281)(142,286)(143,282)(144,284)(289,433)(290,438)(291,440)(292,436)(293,441)(294,434)(295,439)(296,435)(297,437)(298,442)(299,447)(300,449)(301,445)(302,450)(303,443)(304,448)(305,444)(306,446)(307,451)(308,456)(309,458)(310,454)(311,459)(312,452)(313,457)(314,453)(315,455)(316,460)(317,465)(318,467)(319,463)(320,468)(321,461)(322,466)(323,462)(324,464)(325,469)(326,474)(327,476)(328,472)(329,477)(330,470)(331,475)(332,471)(333,473)(334,478)(335,483)(336,485)(337,481)(338,486)(339,479)(340,484)(341,480)(342,482)(343,487)(344,492)(345,494)(346,490)(347,495)(348,488)(349,493)(350,489)(351,491)(352,496)(353,501)(354,503)(355,499)(356,504)(357,497)(358,502)(359,498)(360,500)(361,505)(362,510)(363,512)(364,508)(365,513)(366,506)(367,511)(368,507)(369,509)(370,514)(371,519)(372,521)(373,517)(374,522)(375,515)(376,520)(377,516)(378,518)(379,523)(380,528)(381,530)(382,526)(383,531)(384,524)(385,529)(386,525)(387,527)(388,532)(389,537)(390,539)(391,535)(392,540)(393,533)(394,538)(395,534)(396,536)(397,541)(398,546)(399,548)(400,544)(401,549)(402,542)(403,547)(404,543)(405,545)(406,550)(407,555)(408,557)(409,553)(410,558)(411,551)(412,556)(413,552)(414,554)(415,559)(416,564)(417,566)(418,562)(419,567)(420,560)(421,565)(422,561)(423,563)(424,568)(425,573)(426,575)(427,571)(428,576)(429,569)(430,574)(431,570)(432,572);
s1 := Sym(576)!( 1,110)( 2,109)( 3,111)( 4,116)( 5,115)( 6,117)( 7,113)( 8,112)( 9,114)( 10,119)( 11,118)( 12,120)( 13,125)( 14,124)( 15,126)( 16,122)( 17,121)( 18,123)( 19,128)( 20,127)( 21,129)( 22,134)( 23,133)( 24,135)( 25,131)( 26,130)( 27,132)( 28,137)( 29,136)( 30,138)( 31,143)( 32,142)( 33,144)( 34,140)( 35,139)( 36,141)( 37, 83)( 38, 82)( 39, 84)( 40, 89)( 41, 88)( 42, 90)( 43, 86)( 44, 85)( 45, 87)( 46, 74)( 47, 73)( 48, 75)( 49, 80)( 50, 79)( 51, 81)( 52, 77)( 53, 76)( 54, 78)( 55,101)( 56,100)( 57,102)( 58,107)( 59,106)( 60,108)( 61,104)( 62,103)( 63,105)( 64, 92)( 65, 91)( 66, 93)( 67, 98)( 68, 97)( 69, 99)( 70, 95)( 71, 94)( 72, 96)(145,272)(146,271)(147,273)(148,278)(149,277)(150,279)(151,275)(152,274)(153,276)(154,281)(155,280)(156,282)(157,287)(158,286)(159,288)(160,284)(161,283)(162,285)(163,254)(164,253)(165,255)(166,260)(167,259)(168,261)(169,257)(170,256)(171,258)(172,263)(173,262)(174,264)(175,269)(176,268)(177,270)(178,266)(179,265)(180,267)(181,245)(182,244)(183,246)(184,251)(185,250)(186,252)(187,248)(188,247)(189,249)(190,236)(191,235)(192,237)(193,242)(194,241)(195,243)(196,239)(197,238)(198,240)(199,227)(200,226)(201,228)(202,233)(203,232)(204,234)(205,230)(206,229)(207,231)(208,218)(209,217)(210,219)(211,224)(212,223)(213,225)(214,221)(215,220)(216,222)(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)(433,524)(434,523)(435,525)(436,530)(437,529)(438,531)(439,527)(440,526)(441,528)(442,533)(443,532)(444,534)(445,539)(446,538)(447,540)(448,536)(449,535)(450,537)(451,506)(452,505)(453,507)(454,512)(455,511)(456,513)(457,509)(458,508)(459,510)(460,515)(461,514)(462,516)(463,521)(464,520)(465,522)(466,518)(467,517)(468,519)(469,560)(470,559)(471,561)(472,566)(473,565)(474,567)(475,563)(476,562)(477,564)(478,569)(479,568)(480,570)(481,575)(482,574)(483,576)(484,572)(485,571)(486,573)(487,542)(488,541)(489,543)(490,548)(491,547)(492,549)(493,545)(494,544)(495,546)(496,551)(497,550)(498,552)(499,557)(500,556)(501,558)(502,554)(503,553)(504,555);
s2 := 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)( 37,118)( 38,120)( 39,119)( 40,124)( 41,126)( 42,125)( 43,121)( 44,123)( 45,122)( 46,109)( 47,111)( 48,110)( 49,115)( 50,117)( 51,116)( 52,112)( 53,114)( 54,113)( 55,136)( 56,138)( 57,137)( 58,142)( 59,144)( 60,143)( 61,139)( 62,141)( 63,140)( 64,127)( 65,129)( 66,128)( 67,133)( 68,135)( 69,134)( 70,130)( 71,132)( 72,131)(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)(181,262)(182,264)(183,263)(184,268)(185,270)(186,269)(187,265)(188,267)(189,266)(190,253)(191,255)(192,254)(193,259)(194,261)(195,260)(196,256)(197,258)(198,257)(199,280)(200,282)(201,281)(202,286)(203,288)(204,287)(205,283)(206,285)(207,284)(208,271)(209,273)(210,272)(211,277)(212,279)(213,278)(214,274)(215,276)(216,275)(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)(325,406)(326,408)(327,407)(328,412)(329,414)(330,413)(331,409)(332,411)(333,410)(334,397)(335,399)(336,398)(337,403)(338,405)(339,404)(340,400)(341,402)(342,401)(343,424)(344,426)(345,425)(346,430)(347,432)(348,431)(349,427)(350,429)(351,428)(352,415)(353,417)(354,416)(355,421)(356,423)(357,422)(358,418)(359,420)(360,419)(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)(469,550)(470,552)(471,551)(472,556)(473,558)(474,557)(475,553)(476,555)(477,554)(478,541)(479,543)(480,542)(481,547)(482,549)(483,548)(484,544)(485,546)(486,545)(487,568)(488,570)(489,569)(490,574)(491,576)(492,575)(493,571)(494,573)(495,572)(496,559)(497,561)(498,560)(499,565)(500,567)(501,566)(502,562)(503,564)(504,563);
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)( 19,307)( 20,308)( 21,309)( 22,310)( 23,311)( 24,312)( 25,313)( 26,314)( 27,315)( 28,316)( 29,317)( 30,318)( 31,319)( 32,320)( 33,321)( 34,322)( 35,323)( 36,324)( 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)( 55,352)( 56,353)( 57,354)( 58,355)( 59,356)( 60,357)( 61,358)( 62,359)( 63,360)( 64,343)( 65,344)( 66,345)( 67,346)( 68,347)( 69,348)( 70,349)( 71,350)( 72,351)( 73,397)( 74,398)( 75,399)( 76,400)( 77,401)( 78,402)( 79,403)( 80,404)( 81,405)( 82,406)( 83,407)( 84,408)( 85,409)( 86,410)( 87,411)( 88,412)( 89,413)( 90,414)( 91,415)( 92,416)( 93,417)( 94,418)( 95,419)( 96,420)( 97,421)( 98,422)( 99,423)(100,424)(101,425)(102,426)(103,427)(104,428)(105,429)(106,430)(107,431)(108,432)(109,361)(110,362)(111,363)(112,364)(113,365)(114,366)(115,367)(116,368)(117,369)(118,370)(119,371)(120,372)(121,373)(122,374)(123,375)(124,376)(125,377)(126,378)(127,379)(128,380)(129,381)(130,382)(131,383)(132,384)(133,385)(134,386)(135,387)(136,388)(137,389)(138,390)(139,391)(140,392)(141,393)(142,394)(143,395)(144,396)(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)(163,451)(164,452)(165,453)(166,454)(167,455)(168,456)(169,457)(170,458)(171,459)(172,460)(173,461)(174,462)(175,463)(176,464)(177,465)(178,466)(179,467)(180,468)(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)(199,496)(200,497)(201,498)(202,499)(203,500)(204,501)(205,502)(206,503)(207,504)(208,487)(209,488)(210,489)(211,490)(212,491)(213,492)(214,493)(215,494)(216,495)(217,541)(218,542)(219,543)(220,544)(221,545)(222,546)(223,547)(224,548)(225,549)(226,550)(227,551)(228,552)(229,553)(230,554)(231,555)(232,556)(233,557)(234,558)(235,559)(236,560)(237,561)(238,562)(239,563)(240,564)(241,565)(242,566)(243,567)(244,568)(245,569)(246,570)(247,571)(248,572)(249,573)(250,574)(251,575)(252,576)(253,505)(254,506)(255,507)(256,508)(257,509)(258,510)(259,511)(260,512)(261,513)(262,514)(263,515)(264,516)(265,517)(266,518)(267,519)(268,520)(269,521)(270,522)(271,523)(272,524)(273,525)(274,526)(275,527)(276,528)(277,529)(278,530)(279,531)(280,532)(281,533)(282,534)(283,535)(284,536)(285,537)(286,538)(287,539)(288,540);
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, s0*s1*s2*s0*s1*s0*s1*s2*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope