Polytope of Type {4,8,6} with group SmallGroup(1152,97555)

Overview

Group: SmallGroup(1152,97555)
Rank: 4
Schläfli Type: {4,8,6}
Vertices, edges, …: 4, 48, 72, 18
Order of s₀s₁s₂s₃: 8
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Universal
Orientable
Flat

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

{2,4,6}*144

9-fold

{4,8,2}*128a

18-fold

36-fold

72-fold

{2,2,2}*16

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s2*s3)^2> of order 3

6 facets

6 of {4,8}*64a

4 vertex figures

4 of 3-fold non-regular quotient of {8,6}*288

P/N, where N=<(s2*s1*s2*s3)^2> of order 3

6 facets

6 of {4,8}*64a

4 vertex figures

4 of 3-fold non-regular quotient of {8,6}*288

Representations

Permutation Representation (GAP)

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

References

None.

to this polytope.