Polytope of Type {8,12,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,12,6}*1152a
if this polytope has a name.
Group : SmallGroup(1152,97531)
Rank : 4
Schlafli Type : {8,12,6}
Number of vertices, edges, etc : 8, 48, 36, 6
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 : {4,12,6}*576b, {8,6,6}*576b
3-fold quotients : {8,12,2}*384a
4-fold quotients : {2,12,6}*288b, {4,6,6}*288b
6-fold quotients : {4,12,2}*192a, {8,6,2}*192
8-fold quotients : {2,6,6}*144c
9-fold quotients : {8,4,2}*128a
12-fold quotients : {2,12,2}*96, {4,6,2}*96a
16-fold quotients : {2,3,6}*72
18-fold quotients : {4,4,2}*64, {8,2,2}*64
24-fold quotients : {2,6,2}*48
36-fold quotients : {2,4,2}*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 := ( 1,289)( 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)( 73,361)( 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)( 91,379)( 92,380)( 93,381)( 94,382)( 95,383)( 96,384)( 97,385)( 98,386)( 99,387)(100,388)(101,389)(102,390)(103,391)(104,392)(105,393)(106,394)(107,395)(108,396)(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)(127,424)(128,425)(129,426)(130,427)(131,428)(132,429)(133,430)(134,431)(135,432)(136,415)(137,416)(138,417)(139,418)(140,419)(141,420)(142,421)(143,422)(144,423)(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)(217,505)(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)(235,523)(236,524)(237,525)(238,526)(239,527)(240,528)(241,529)(242,530)(243,531)(244,532)(245,533)(246,534)(247,535)(248,536)(249,537)(250,538)(251,539)(252,540)(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)(271,568)(272,569)(273,570)(274,571)(275,572)(276,573)(277,574)(278,575)(279,576)(280,559)(281,560)(282,561)(283,562)(284,563)(285,564)(286,565)(287,566)(288,567);;
s1 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 29, 30)( 31, 34)( 32, 36)( 33, 35)( 37, 46)( 38, 48)( 39, 47)( 40, 52)( 41, 54)( 42, 53)( 43, 49)( 44, 51)( 45, 50)( 55, 64)( 56, 66)( 57, 65)( 58, 70)( 59, 72)( 60, 71)( 61, 67)( 62, 69)( 63, 68)( 74, 75)( 76, 79)( 77, 81)( 78, 80)( 83, 84)( 85, 88)( 86, 90)( 87, 89)( 92, 93)( 94, 97)( 95, 99)( 96, 98)(101,102)(103,106)(104,108)(105,107)(109,118)(110,120)(111,119)(112,124)(113,126)(114,125)(115,121)(116,123)(117,122)(127,136)(128,138)(129,137)(130,142)(131,144)(132,143)(133,139)(134,141)(135,140)(145,163)(146,165)(147,164)(148,169)(149,171)(150,170)(151,166)(152,168)(153,167)(154,172)(155,174)(156,173)(157,178)(158,180)(159,179)(160,175)(161,177)(162,176)(181,208)(182,210)(183,209)(184,214)(185,216)(186,215)(187,211)(188,213)(189,212)(190,199)(191,201)(192,200)(193,205)(194,207)(195,206)(196,202)(197,204)(198,203)(217,235)(218,237)(219,236)(220,241)(221,243)(222,242)(223,238)(224,240)(225,239)(226,244)(227,246)(228,245)(229,250)(230,252)(231,251)(232,247)(233,249)(234,248)(253,280)(254,282)(255,281)(256,286)(257,288)(258,287)(259,283)(260,285)(261,284)(262,271)(263,273)(264,272)(265,277)(266,279)(267,278)(268,274)(269,276)(270,275)(289,325)(290,327)(291,326)(292,331)(293,333)(294,332)(295,328)(296,330)(297,329)(298,334)(299,336)(300,335)(301,340)(302,342)(303,341)(304,337)(305,339)(306,338)(307,343)(308,345)(309,344)(310,349)(311,351)(312,350)(313,346)(314,348)(315,347)(316,352)(317,354)(318,353)(319,358)(320,360)(321,359)(322,355)(323,357)(324,356)(361,397)(362,399)(363,398)(364,403)(365,405)(366,404)(367,400)(368,402)(369,401)(370,406)(371,408)(372,407)(373,412)(374,414)(375,413)(376,409)(377,411)(378,410)(379,415)(380,417)(381,416)(382,421)(383,423)(384,422)(385,418)(386,420)(387,419)(388,424)(389,426)(390,425)(391,430)(392,432)(393,431)(394,427)(395,429)(396,428)(433,487)(434,489)(435,488)(436,493)(437,495)(438,494)(439,490)(440,492)(441,491)(442,496)(443,498)(444,497)(445,502)(446,504)(447,503)(448,499)(449,501)(450,500)(451,469)(452,471)(453,470)(454,475)(455,477)(456,476)(457,472)(458,474)(459,473)(460,478)(461,480)(462,479)(463,484)(464,486)(465,485)(466,481)(467,483)(468,482)(505,559)(506,561)(507,560)(508,565)(509,567)(510,566)(511,562)(512,564)(513,563)(514,568)(515,570)(516,569)(517,574)(518,576)(519,575)(520,571)(521,573)(522,572)(523,541)(524,543)(525,542)(526,547)(527,549)(528,548)(529,544)(530,546)(531,545)(532,550)(533,552)(534,551)(535,556)(536,558)(537,557)(538,553)(539,555)(540,554);;
s2 := ( 1,146)( 2,145)( 3,147)( 4,152)( 5,151)( 6,153)( 7,149)( 8,148)( 9,150)( 10,155)( 11,154)( 12,156)( 13,161)( 14,160)( 15,162)( 16,158)( 17,157)( 18,159)( 19,164)( 20,163)( 21,165)( 22,170)( 23,169)( 24,171)( 25,167)( 26,166)( 27,168)( 28,173)( 29,172)( 30,174)( 31,179)( 32,178)( 33,180)( 34,176)( 35,175)( 36,177)( 37,182)( 38,181)( 39,183)( 40,188)( 41,187)( 42,189)( 43,185)( 44,184)( 45,186)( 46,191)( 47,190)( 48,192)( 49,197)( 50,196)( 51,198)( 52,194)( 53,193)( 54,195)( 55,200)( 56,199)( 57,201)( 58,206)( 59,205)( 60,207)( 61,203)( 62,202)( 63,204)( 64,209)( 65,208)( 66,210)( 67,215)( 68,214)( 69,216)( 70,212)( 71,211)( 72,213)( 73,218)( 74,217)( 75,219)( 76,224)( 77,223)( 78,225)( 79,221)( 80,220)( 81,222)( 82,227)( 83,226)( 84,228)( 85,233)( 86,232)( 87,234)( 88,230)( 89,229)( 90,231)( 91,236)( 92,235)( 93,237)( 94,242)( 95,241)( 96,243)( 97,239)( 98,238)( 99,240)(100,245)(101,244)(102,246)(103,251)(104,250)(105,252)(106,248)(107,247)(108,249)(109,254)(110,253)(111,255)(112,260)(113,259)(114,261)(115,257)(116,256)(117,258)(118,263)(119,262)(120,264)(121,269)(122,268)(123,270)(124,266)(125,265)(126,267)(127,272)(128,271)(129,273)(130,278)(131,277)(132,279)(133,275)(134,274)(135,276)(136,281)(137,280)(138,282)(139,287)(140,286)(141,288)(142,284)(143,283)(144,285)(289,434)(290,433)(291,435)(292,440)(293,439)(294,441)(295,437)(296,436)(297,438)(298,443)(299,442)(300,444)(301,449)(302,448)(303,450)(304,446)(305,445)(306,447)(307,452)(308,451)(309,453)(310,458)(311,457)(312,459)(313,455)(314,454)(315,456)(316,461)(317,460)(318,462)(319,467)(320,466)(321,468)(322,464)(323,463)(324,465)(325,470)(326,469)(327,471)(328,476)(329,475)(330,477)(331,473)(332,472)(333,474)(334,479)(335,478)(336,480)(337,485)(338,484)(339,486)(340,482)(341,481)(342,483)(343,488)(344,487)(345,489)(346,494)(347,493)(348,495)(349,491)(350,490)(351,492)(352,497)(353,496)(354,498)(355,503)(356,502)(357,504)(358,500)(359,499)(360,501)(361,506)(362,505)(363,507)(364,512)(365,511)(366,513)(367,509)(368,508)(369,510)(370,515)(371,514)(372,516)(373,521)(374,520)(375,522)(376,518)(377,517)(378,519)(379,524)(380,523)(381,525)(382,530)(383,529)(384,531)(385,527)(386,526)(387,528)(388,533)(389,532)(390,534)(391,539)(392,538)(393,540)(394,536)(395,535)(396,537)(397,542)(398,541)(399,543)(400,548)(401,547)(402,549)(403,545)(404,544)(405,546)(406,551)(407,550)(408,552)(409,557)(410,556)(411,558)(412,554)(413,553)(414,555)(415,560)(416,559)(417,561)(418,566)(419,565)(420,567)(421,563)(422,562)(423,564)(424,569)(425,568)(426,570)(427,575)(428,574)(429,576)(430,572)(431,571)(432,573);;
s3 := ( 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);;
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,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2,
s0*s1*s0*s1*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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)( 73,361)( 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)( 91,379)( 92,380)( 93,381)( 94,382)( 95,383)( 96,384)( 97,385)( 98,386)( 99,387)(100,388)(101,389)(102,390)(103,391)(104,392)(105,393)(106,394)(107,395)(108,396)(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)(127,424)(128,425)(129,426)(130,427)(131,428)(132,429)(133,430)(134,431)(135,432)(136,415)(137,416)(138,417)(139,418)(140,419)(141,420)(142,421)(143,422)(144,423)(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)(217,505)(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)(235,523)(236,524)(237,525)(238,526)(239,527)(240,528)(241,529)(242,530)(243,531)(244,532)(245,533)(246,534)(247,535)(248,536)(249,537)(250,538)(251,539)(252,540)(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)(271,568)(272,569)(273,570)(274,571)(275,572)(276,573)(277,574)(278,575)(279,576)(280,559)(281,560)(282,561)(283,562)(284,563)(285,564)(286,565)(287,566)(288,567);
s1 := Sym(576)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 29, 30)( 31, 34)( 32, 36)( 33, 35)( 37, 46)( 38, 48)( 39, 47)( 40, 52)( 41, 54)( 42, 53)( 43, 49)( 44, 51)( 45, 50)( 55, 64)( 56, 66)( 57, 65)( 58, 70)( 59, 72)( 60, 71)( 61, 67)( 62, 69)( 63, 68)( 74, 75)( 76, 79)( 77, 81)( 78, 80)( 83, 84)( 85, 88)( 86, 90)( 87, 89)( 92, 93)( 94, 97)( 95, 99)( 96, 98)(101,102)(103,106)(104,108)(105,107)(109,118)(110,120)(111,119)(112,124)(113,126)(114,125)(115,121)(116,123)(117,122)(127,136)(128,138)(129,137)(130,142)(131,144)(132,143)(133,139)(134,141)(135,140)(145,163)(146,165)(147,164)(148,169)(149,171)(150,170)(151,166)(152,168)(153,167)(154,172)(155,174)(156,173)(157,178)(158,180)(159,179)(160,175)(161,177)(162,176)(181,208)(182,210)(183,209)(184,214)(185,216)(186,215)(187,211)(188,213)(189,212)(190,199)(191,201)(192,200)(193,205)(194,207)(195,206)(196,202)(197,204)(198,203)(217,235)(218,237)(219,236)(220,241)(221,243)(222,242)(223,238)(224,240)(225,239)(226,244)(227,246)(228,245)(229,250)(230,252)(231,251)(232,247)(233,249)(234,248)(253,280)(254,282)(255,281)(256,286)(257,288)(258,287)(259,283)(260,285)(261,284)(262,271)(263,273)(264,272)(265,277)(266,279)(267,278)(268,274)(269,276)(270,275)(289,325)(290,327)(291,326)(292,331)(293,333)(294,332)(295,328)(296,330)(297,329)(298,334)(299,336)(300,335)(301,340)(302,342)(303,341)(304,337)(305,339)(306,338)(307,343)(308,345)(309,344)(310,349)(311,351)(312,350)(313,346)(314,348)(315,347)(316,352)(317,354)(318,353)(319,358)(320,360)(321,359)(322,355)(323,357)(324,356)(361,397)(362,399)(363,398)(364,403)(365,405)(366,404)(367,400)(368,402)(369,401)(370,406)(371,408)(372,407)(373,412)(374,414)(375,413)(376,409)(377,411)(378,410)(379,415)(380,417)(381,416)(382,421)(383,423)(384,422)(385,418)(386,420)(387,419)(388,424)(389,426)(390,425)(391,430)(392,432)(393,431)(394,427)(395,429)(396,428)(433,487)(434,489)(435,488)(436,493)(437,495)(438,494)(439,490)(440,492)(441,491)(442,496)(443,498)(444,497)(445,502)(446,504)(447,503)(448,499)(449,501)(450,500)(451,469)(452,471)(453,470)(454,475)(455,477)(456,476)(457,472)(458,474)(459,473)(460,478)(461,480)(462,479)(463,484)(464,486)(465,485)(466,481)(467,483)(468,482)(505,559)(506,561)(507,560)(508,565)(509,567)(510,566)(511,562)(512,564)(513,563)(514,568)(515,570)(516,569)(517,574)(518,576)(519,575)(520,571)(521,573)(522,572)(523,541)(524,543)(525,542)(526,547)(527,549)(528,548)(529,544)(530,546)(531,545)(532,550)(533,552)(534,551)(535,556)(536,558)(537,557)(538,553)(539,555)(540,554);
s2 := Sym(576)!( 1,146)( 2,145)( 3,147)( 4,152)( 5,151)( 6,153)( 7,149)( 8,148)( 9,150)( 10,155)( 11,154)( 12,156)( 13,161)( 14,160)( 15,162)( 16,158)( 17,157)( 18,159)( 19,164)( 20,163)( 21,165)( 22,170)( 23,169)( 24,171)( 25,167)( 26,166)( 27,168)( 28,173)( 29,172)( 30,174)( 31,179)( 32,178)( 33,180)( 34,176)( 35,175)( 36,177)( 37,182)( 38,181)( 39,183)( 40,188)( 41,187)( 42,189)( 43,185)( 44,184)( 45,186)( 46,191)( 47,190)( 48,192)( 49,197)( 50,196)( 51,198)( 52,194)( 53,193)( 54,195)( 55,200)( 56,199)( 57,201)( 58,206)( 59,205)( 60,207)( 61,203)( 62,202)( 63,204)( 64,209)( 65,208)( 66,210)( 67,215)( 68,214)( 69,216)( 70,212)( 71,211)( 72,213)( 73,218)( 74,217)( 75,219)( 76,224)( 77,223)( 78,225)( 79,221)( 80,220)( 81,222)( 82,227)( 83,226)( 84,228)( 85,233)( 86,232)( 87,234)( 88,230)( 89,229)( 90,231)( 91,236)( 92,235)( 93,237)( 94,242)( 95,241)( 96,243)( 97,239)( 98,238)( 99,240)(100,245)(101,244)(102,246)(103,251)(104,250)(105,252)(106,248)(107,247)(108,249)(109,254)(110,253)(111,255)(112,260)(113,259)(114,261)(115,257)(116,256)(117,258)(118,263)(119,262)(120,264)(121,269)(122,268)(123,270)(124,266)(125,265)(126,267)(127,272)(128,271)(129,273)(130,278)(131,277)(132,279)(133,275)(134,274)(135,276)(136,281)(137,280)(138,282)(139,287)(140,286)(141,288)(142,284)(143,283)(144,285)(289,434)(290,433)(291,435)(292,440)(293,439)(294,441)(295,437)(296,436)(297,438)(298,443)(299,442)(300,444)(301,449)(302,448)(303,450)(304,446)(305,445)(306,447)(307,452)(308,451)(309,453)(310,458)(311,457)(312,459)(313,455)(314,454)(315,456)(316,461)(317,460)(318,462)(319,467)(320,466)(321,468)(322,464)(323,463)(324,465)(325,470)(326,469)(327,471)(328,476)(329,475)(330,477)(331,473)(332,472)(333,474)(334,479)(335,478)(336,480)(337,485)(338,484)(339,486)(340,482)(341,481)(342,483)(343,488)(344,487)(345,489)(346,494)(347,493)(348,495)(349,491)(350,490)(351,492)(352,497)(353,496)(354,498)(355,503)(356,502)(357,504)(358,500)(359,499)(360,501)(361,506)(362,505)(363,507)(364,512)(365,511)(366,513)(367,509)(368,508)(369,510)(370,515)(371,514)(372,516)(373,521)(374,520)(375,522)(376,518)(377,517)(378,519)(379,524)(380,523)(381,525)(382,530)(383,529)(384,531)(385,527)(386,526)(387,528)(388,533)(389,532)(390,534)(391,539)(392,538)(393,540)(394,536)(395,535)(396,537)(397,542)(398,541)(399,543)(400,548)(401,547)(402,549)(403,545)(404,544)(405,546)(406,551)(407,550)(408,552)(409,557)(410,556)(411,558)(412,554)(413,553)(414,555)(415,560)(416,559)(417,561)(418,566)(419,565)(420,567)(421,563)(422,562)(423,564)(424,569)(425,568)(426,570)(427,575)(428,574)(429,576)(430,572)(431,571)(432,573);
s3 := 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);
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, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2,
s0*s1*s0*s1*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 >;
References : None.
to this polytope