Polytope of Type {4,8,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,8,8}*512a
if this polytope has a name.
Group : SmallGroup(512,152907)
Rank : 4
Schlafli Type : {4,8,8}
Number of vertices, edges, etc : 4, 16, 32, 8
Order of s0s1s2s3 : 8
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 : {4,4,8}*256a, {4,8,4}*256a
4-fold quotients : {4,4,4}*128, {2,4,8}*128a, {4,2,8}*128
8-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64, {2,2,8}*64
16-fold quotients : {2,2,4}*32, {2,4,2}*32, {4,2,2}*32
32-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 := ( 1,161)( 2,162)( 3,163)( 4,164)( 5,165)( 6,166)( 7,167)( 8,168)( 9,170)( 10,169)( 11,172)( 12,171)( 13,174)( 14,173)( 15,176)( 16,175)( 17,177)( 18,178)( 19,179)( 20,180)( 21,181)( 22,182)( 23,183)( 24,184)( 25,186)( 26,185)( 27,188)( 28,187)( 29,190)( 30,189)( 31,192)( 32,191)( 33,129)( 34,130)( 35,131)( 36,132)( 37,133)( 38,134)( 39,135)( 40,136)( 41,138)( 42,137)( 43,140)( 44,139)( 45,142)( 46,141)( 47,144)( 48,143)( 49,145)( 50,146)( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)( 56,152)( 57,154)( 58,153)( 59,156)( 60,155)( 61,158)( 62,157)( 63,160)( 64,159)( 65,229)( 66,230)( 67,231)( 68,232)( 69,225)( 70,226)( 71,227)( 72,228)( 73,238)( 74,237)( 75,240)( 76,239)( 77,234)( 78,233)( 79,236)( 80,235)( 81,245)( 82,246)( 83,247)( 84,248)( 85,241)( 86,242)( 87,243)( 88,244)( 89,254)( 90,253)( 91,256)( 92,255)( 93,250)( 94,249)( 95,252)( 96,251)( 97,197)( 98,198)( 99,199)(100,200)(101,193)(102,194)(103,195)(104,196)(105,206)(106,205)(107,208)(108,207)(109,202)(110,201)(111,204)(112,203)(113,213)(114,214)(115,215)(116,216)(117,209)(118,210)(119,211)(120,212)(121,222)(122,221)(123,224)(124,223)(125,218)(126,217)(127,220)(128,219)(257,417)(258,418)(259,419)(260,420)(261,421)(262,422)(263,423)(264,424)(265,426)(266,425)(267,428)(268,427)(269,430)(270,429)(271,432)(272,431)(273,433)(274,434)(275,435)(276,436)(277,437)(278,438)(279,439)(280,440)(281,442)(282,441)(283,444)(284,443)(285,446)(286,445)(287,448)(288,447)(289,385)(290,386)(291,387)(292,388)(293,389)(294,390)(295,391)(296,392)(297,394)(298,393)(299,396)(300,395)(301,398)(302,397)(303,400)(304,399)(305,401)(306,402)(307,403)(308,404)(309,405)(310,406)(311,407)(312,408)(313,410)(314,409)(315,412)(316,411)(317,414)(318,413)(319,416)(320,415)(321,485)(322,486)(323,487)(324,488)(325,481)(326,482)(327,483)(328,484)(329,494)(330,493)(331,496)(332,495)(333,490)(334,489)(335,492)(336,491)(337,501)(338,502)(339,503)(340,504)(341,497)(342,498)(343,499)(344,500)(345,510)(346,509)(347,512)(348,511)(349,506)(350,505)(351,508)(352,507)(353,453)(354,454)(355,455)(356,456)(357,449)(358,450)(359,451)(360,452)(361,462)(362,461)(363,464)(364,463)(365,458)(366,457)(367,460)(368,459)(369,469)(370,470)(371,471)(372,472)(373,465)(374,466)(375,467)(376,468)(377,478)(378,477)(379,480)(380,479)(381,474)(382,473)(383,476)(384,475);;
s1 := ( 1, 65)( 2, 66)( 3, 67)( 4, 68)( 5, 69)( 6, 70)( 7, 71)( 8, 72)( 9, 74)( 10, 73)( 11, 76)( 12, 75)( 13, 78)( 14, 77)( 15, 80)( 16, 79)( 17, 82)( 18, 81)( 19, 84)( 20, 83)( 21, 86)( 22, 85)( 23, 88)( 24, 87)( 25, 89)( 26, 90)( 27, 91)( 28, 92)( 29, 93)( 30, 94)( 31, 95)( 32, 96)( 33, 97)( 34, 98)( 35, 99)( 36,100)( 37,101)( 38,102)( 39,103)( 40,104)( 41,106)( 42,105)( 43,108)( 44,107)( 45,110)( 46,109)( 47,112)( 48,111)( 49,114)( 50,113)( 51,116)( 52,115)( 53,118)( 54,117)( 55,120)( 56,119)( 57,121)( 58,122)( 59,123)( 60,124)( 61,125)( 62,126)( 63,127)( 64,128)(129,193)(130,194)(131,195)(132,196)(133,197)(134,198)(135,199)(136,200)(137,202)(138,201)(139,204)(140,203)(141,206)(142,205)(143,208)(144,207)(145,210)(146,209)(147,212)(148,211)(149,214)(150,213)(151,216)(152,215)(153,217)(154,218)(155,219)(156,220)(157,221)(158,222)(159,223)(160,224)(161,225)(162,226)(163,227)(164,228)(165,229)(166,230)(167,231)(168,232)(169,234)(170,233)(171,236)(172,235)(173,238)(174,237)(175,240)(176,239)(177,242)(178,241)(179,244)(180,243)(181,246)(182,245)(183,248)(184,247)(185,249)(186,250)(187,251)(188,252)(189,253)(190,254)(191,255)(192,256)(257,321)(258,322)(259,323)(260,324)(261,325)(262,326)(263,327)(264,328)(265,330)(266,329)(267,332)(268,331)(269,334)(270,333)(271,336)(272,335)(273,338)(274,337)(275,340)(276,339)(277,342)(278,341)(279,344)(280,343)(281,345)(282,346)(283,347)(284,348)(285,349)(286,350)(287,351)(288,352)(289,353)(290,354)(291,355)(292,356)(293,357)(294,358)(295,359)(296,360)(297,362)(298,361)(299,364)(300,363)(301,366)(302,365)(303,368)(304,367)(305,370)(306,369)(307,372)(308,371)(309,374)(310,373)(311,376)(312,375)(313,377)(314,378)(315,379)(316,380)(317,381)(318,382)(319,383)(320,384)(385,449)(386,450)(387,451)(388,452)(389,453)(390,454)(391,455)(392,456)(393,458)(394,457)(395,460)(396,459)(397,462)(398,461)(399,464)(400,463)(401,466)(402,465)(403,468)(404,467)(405,470)(406,469)(407,472)(408,471)(409,473)(410,474)(411,475)(412,476)(413,477)(414,478)(415,479)(416,480)(417,481)(418,482)(419,483)(420,484)(421,485)(422,486)(423,487)(424,488)(425,490)(426,489)(427,492)(428,491)(429,494)(430,493)(431,496)(432,495)(433,498)(434,497)(435,500)(436,499)(437,502)(438,501)(439,504)(440,503)(441,505)(442,506)(443,507)(444,508)(445,509)(446,510)(447,511)(448,512);;
s2 := ( 1,257)( 2,258)( 3,259)( 4,260)( 5,262)( 6,261)( 7,264)( 8,263)( 9,266)( 10,265)( 11,268)( 12,267)( 13,269)( 14,270)( 15,271)( 16,272)( 17,275)( 18,276)( 19,273)( 20,274)( 21,280)( 22,279)( 23,278)( 24,277)( 25,284)( 26,283)( 27,282)( 28,281)( 29,287)( 30,288)( 31,285)( 32,286)( 33,305)( 34,306)( 35,307)( 36,308)( 37,310)( 38,309)( 39,312)( 40,311)( 41,314)( 42,313)( 43,316)( 44,315)( 45,317)( 46,318)( 47,319)( 48,320)( 49,289)( 50,290)( 51,291)( 52,292)( 53,294)( 54,293)( 55,296)( 56,295)( 57,298)( 58,297)( 59,300)( 60,299)( 61,301)( 62,302)( 63,303)( 64,304)( 65,329)( 66,330)( 67,331)( 68,332)( 69,334)( 70,333)( 71,336)( 72,335)( 73,321)( 74,322)( 75,323)( 76,324)( 77,326)( 78,325)( 79,328)( 80,327)( 81,347)( 82,348)( 83,345)( 84,346)( 85,352)( 86,351)( 87,350)( 88,349)( 89,339)( 90,340)( 91,337)( 92,338)( 93,344)( 94,343)( 95,342)( 96,341)( 97,378)( 98,377)( 99,380)(100,379)(101,381)(102,382)(103,383)(104,384)(105,370)(106,369)(107,372)(108,371)(109,373)(110,374)(111,375)(112,376)(113,362)(114,361)(115,364)(116,363)(117,365)(118,366)(119,367)(120,368)(121,354)(122,353)(123,356)(124,355)(125,357)(126,358)(127,359)(128,360)(129,401)(130,402)(131,403)(132,404)(133,406)(134,405)(135,408)(136,407)(137,410)(138,409)(139,412)(140,411)(141,413)(142,414)(143,415)(144,416)(145,385)(146,386)(147,387)(148,388)(149,390)(150,389)(151,392)(152,391)(153,394)(154,393)(155,396)(156,395)(157,397)(158,398)(159,399)(160,400)(161,417)(162,418)(163,419)(164,420)(165,422)(166,421)(167,424)(168,423)(169,426)(170,425)(171,428)(172,427)(173,429)(174,430)(175,431)(176,432)(177,435)(178,436)(179,433)(180,434)(181,440)(182,439)(183,438)(184,437)(185,444)(186,443)(187,442)(188,441)(189,447)(190,448)(191,445)(192,446)(193,474)(194,473)(195,476)(196,475)(197,477)(198,478)(199,479)(200,480)(201,466)(202,465)(203,468)(204,467)(205,469)(206,470)(207,471)(208,472)(209,458)(210,457)(211,460)(212,459)(213,461)(214,462)(215,463)(216,464)(217,450)(218,449)(219,452)(220,451)(221,453)(222,454)(223,455)(224,456)(225,489)(226,490)(227,491)(228,492)(229,494)(230,493)(231,496)(232,495)(233,481)(234,482)(235,483)(236,484)(237,486)(238,485)(239,488)(240,487)(241,507)(242,508)(243,505)(244,506)(245,512)(246,511)(247,510)(248,509)(249,499)(250,500)(251,497)(252,498)(253,504)(254,503)(255,502)(256,501);;
s3 := ( 1, 33)( 2, 34)( 3, 35)( 4, 36)( 5, 37)( 6, 38)( 7, 39)( 8, 40)( 9, 42)( 10, 41)( 11, 44)( 12, 43)( 13, 46)( 14, 45)( 15, 48)( 16, 47)( 17, 51)( 18, 52)( 19, 49)( 20, 50)( 21, 55)( 22, 56)( 23, 53)( 24, 54)( 25, 60)( 26, 59)( 27, 58)( 28, 57)( 29, 64)( 30, 63)( 31, 62)( 32, 61)( 65, 97)( 66, 98)( 67, 99)( 68,100)( 69,101)( 70,102)( 71,103)( 72,104)( 73,106)( 74,105)( 75,108)( 76,107)( 77,110)( 78,109)( 79,112)( 80,111)( 81,115)( 82,116)( 83,113)( 84,114)( 85,119)( 86,120)( 87,117)( 88,118)( 89,124)( 90,123)( 91,122)( 92,121)( 93,128)( 94,127)( 95,126)( 96,125)(129,161)(130,162)(131,163)(132,164)(133,165)(134,166)(135,167)(136,168)(137,170)(138,169)(139,172)(140,171)(141,174)(142,173)(143,176)(144,175)(145,179)(146,180)(147,177)(148,178)(149,183)(150,184)(151,181)(152,182)(153,188)(154,187)(155,186)(156,185)(157,192)(158,191)(159,190)(160,189)(193,225)(194,226)(195,227)(196,228)(197,229)(198,230)(199,231)(200,232)(201,234)(202,233)(203,236)(204,235)(205,238)(206,237)(207,240)(208,239)(209,243)(210,244)(211,241)(212,242)(213,247)(214,248)(215,245)(216,246)(217,252)(218,251)(219,250)(220,249)(221,256)(222,255)(223,254)(224,253)(257,289)(258,290)(259,291)(260,292)(261,293)(262,294)(263,295)(264,296)(265,298)(266,297)(267,300)(268,299)(269,302)(270,301)(271,304)(272,303)(273,307)(274,308)(275,305)(276,306)(277,311)(278,312)(279,309)(280,310)(281,316)(282,315)(283,314)(284,313)(285,320)(286,319)(287,318)(288,317)(321,353)(322,354)(323,355)(324,356)(325,357)(326,358)(327,359)(328,360)(329,362)(330,361)(331,364)(332,363)(333,366)(334,365)(335,368)(336,367)(337,371)(338,372)(339,369)(340,370)(341,375)(342,376)(343,373)(344,374)(345,380)(346,379)(347,378)(348,377)(349,384)(350,383)(351,382)(352,381)(385,417)(386,418)(387,419)(388,420)(389,421)(390,422)(391,423)(392,424)(393,426)(394,425)(395,428)(396,427)(397,430)(398,429)(399,432)(400,431)(401,435)(402,436)(403,433)(404,434)(405,439)(406,440)(407,437)(408,438)(409,444)(410,443)(411,442)(412,441)(413,448)(414,447)(415,446)(416,445)(449,481)(450,482)(451,483)(452,484)(453,485)(454,486)(455,487)(456,488)(457,490)(458,489)(459,492)(460,491)(461,494)(462,493)(463,496)(464,495)(465,499)(466,500)(467,497)(468,498)(469,503)(470,504)(471,501)(472,502)(473,508)(474,507)(475,506)(476,505)(477,512)(478,511)(479,510)(480,509);;
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,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s1*s2*s3*s1*s2*s1*s2*s3*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(512)!( 1,161)( 2,162)( 3,163)( 4,164)( 5,165)( 6,166)( 7,167)( 8,168)( 9,170)( 10,169)( 11,172)( 12,171)( 13,174)( 14,173)( 15,176)( 16,175)( 17,177)( 18,178)( 19,179)( 20,180)( 21,181)( 22,182)( 23,183)( 24,184)( 25,186)( 26,185)( 27,188)( 28,187)( 29,190)( 30,189)( 31,192)( 32,191)( 33,129)( 34,130)( 35,131)( 36,132)( 37,133)( 38,134)( 39,135)( 40,136)( 41,138)( 42,137)( 43,140)( 44,139)( 45,142)( 46,141)( 47,144)( 48,143)( 49,145)( 50,146)( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)( 56,152)( 57,154)( 58,153)( 59,156)( 60,155)( 61,158)( 62,157)( 63,160)( 64,159)( 65,229)( 66,230)( 67,231)( 68,232)( 69,225)( 70,226)( 71,227)( 72,228)( 73,238)( 74,237)( 75,240)( 76,239)( 77,234)( 78,233)( 79,236)( 80,235)( 81,245)( 82,246)( 83,247)( 84,248)( 85,241)( 86,242)( 87,243)( 88,244)( 89,254)( 90,253)( 91,256)( 92,255)( 93,250)( 94,249)( 95,252)( 96,251)( 97,197)( 98,198)( 99,199)(100,200)(101,193)(102,194)(103,195)(104,196)(105,206)(106,205)(107,208)(108,207)(109,202)(110,201)(111,204)(112,203)(113,213)(114,214)(115,215)(116,216)(117,209)(118,210)(119,211)(120,212)(121,222)(122,221)(123,224)(124,223)(125,218)(126,217)(127,220)(128,219)(257,417)(258,418)(259,419)(260,420)(261,421)(262,422)(263,423)(264,424)(265,426)(266,425)(267,428)(268,427)(269,430)(270,429)(271,432)(272,431)(273,433)(274,434)(275,435)(276,436)(277,437)(278,438)(279,439)(280,440)(281,442)(282,441)(283,444)(284,443)(285,446)(286,445)(287,448)(288,447)(289,385)(290,386)(291,387)(292,388)(293,389)(294,390)(295,391)(296,392)(297,394)(298,393)(299,396)(300,395)(301,398)(302,397)(303,400)(304,399)(305,401)(306,402)(307,403)(308,404)(309,405)(310,406)(311,407)(312,408)(313,410)(314,409)(315,412)(316,411)(317,414)(318,413)(319,416)(320,415)(321,485)(322,486)(323,487)(324,488)(325,481)(326,482)(327,483)(328,484)(329,494)(330,493)(331,496)(332,495)(333,490)(334,489)(335,492)(336,491)(337,501)(338,502)(339,503)(340,504)(341,497)(342,498)(343,499)(344,500)(345,510)(346,509)(347,512)(348,511)(349,506)(350,505)(351,508)(352,507)(353,453)(354,454)(355,455)(356,456)(357,449)(358,450)(359,451)(360,452)(361,462)(362,461)(363,464)(364,463)(365,458)(366,457)(367,460)(368,459)(369,469)(370,470)(371,471)(372,472)(373,465)(374,466)(375,467)(376,468)(377,478)(378,477)(379,480)(380,479)(381,474)(382,473)(383,476)(384,475);
s1 := Sym(512)!( 1, 65)( 2, 66)( 3, 67)( 4, 68)( 5, 69)( 6, 70)( 7, 71)( 8, 72)( 9, 74)( 10, 73)( 11, 76)( 12, 75)( 13, 78)( 14, 77)( 15, 80)( 16, 79)( 17, 82)( 18, 81)( 19, 84)( 20, 83)( 21, 86)( 22, 85)( 23, 88)( 24, 87)( 25, 89)( 26, 90)( 27, 91)( 28, 92)( 29, 93)( 30, 94)( 31, 95)( 32, 96)( 33, 97)( 34, 98)( 35, 99)( 36,100)( 37,101)( 38,102)( 39,103)( 40,104)( 41,106)( 42,105)( 43,108)( 44,107)( 45,110)( 46,109)( 47,112)( 48,111)( 49,114)( 50,113)( 51,116)( 52,115)( 53,118)( 54,117)( 55,120)( 56,119)( 57,121)( 58,122)( 59,123)( 60,124)( 61,125)( 62,126)( 63,127)( 64,128)(129,193)(130,194)(131,195)(132,196)(133,197)(134,198)(135,199)(136,200)(137,202)(138,201)(139,204)(140,203)(141,206)(142,205)(143,208)(144,207)(145,210)(146,209)(147,212)(148,211)(149,214)(150,213)(151,216)(152,215)(153,217)(154,218)(155,219)(156,220)(157,221)(158,222)(159,223)(160,224)(161,225)(162,226)(163,227)(164,228)(165,229)(166,230)(167,231)(168,232)(169,234)(170,233)(171,236)(172,235)(173,238)(174,237)(175,240)(176,239)(177,242)(178,241)(179,244)(180,243)(181,246)(182,245)(183,248)(184,247)(185,249)(186,250)(187,251)(188,252)(189,253)(190,254)(191,255)(192,256)(257,321)(258,322)(259,323)(260,324)(261,325)(262,326)(263,327)(264,328)(265,330)(266,329)(267,332)(268,331)(269,334)(270,333)(271,336)(272,335)(273,338)(274,337)(275,340)(276,339)(277,342)(278,341)(279,344)(280,343)(281,345)(282,346)(283,347)(284,348)(285,349)(286,350)(287,351)(288,352)(289,353)(290,354)(291,355)(292,356)(293,357)(294,358)(295,359)(296,360)(297,362)(298,361)(299,364)(300,363)(301,366)(302,365)(303,368)(304,367)(305,370)(306,369)(307,372)(308,371)(309,374)(310,373)(311,376)(312,375)(313,377)(314,378)(315,379)(316,380)(317,381)(318,382)(319,383)(320,384)(385,449)(386,450)(387,451)(388,452)(389,453)(390,454)(391,455)(392,456)(393,458)(394,457)(395,460)(396,459)(397,462)(398,461)(399,464)(400,463)(401,466)(402,465)(403,468)(404,467)(405,470)(406,469)(407,472)(408,471)(409,473)(410,474)(411,475)(412,476)(413,477)(414,478)(415,479)(416,480)(417,481)(418,482)(419,483)(420,484)(421,485)(422,486)(423,487)(424,488)(425,490)(426,489)(427,492)(428,491)(429,494)(430,493)(431,496)(432,495)(433,498)(434,497)(435,500)(436,499)(437,502)(438,501)(439,504)(440,503)(441,505)(442,506)(443,507)(444,508)(445,509)(446,510)(447,511)(448,512);
s2 := Sym(512)!( 1,257)( 2,258)( 3,259)( 4,260)( 5,262)( 6,261)( 7,264)( 8,263)( 9,266)( 10,265)( 11,268)( 12,267)( 13,269)( 14,270)( 15,271)( 16,272)( 17,275)( 18,276)( 19,273)( 20,274)( 21,280)( 22,279)( 23,278)( 24,277)( 25,284)( 26,283)( 27,282)( 28,281)( 29,287)( 30,288)( 31,285)( 32,286)( 33,305)( 34,306)( 35,307)( 36,308)( 37,310)( 38,309)( 39,312)( 40,311)( 41,314)( 42,313)( 43,316)( 44,315)( 45,317)( 46,318)( 47,319)( 48,320)( 49,289)( 50,290)( 51,291)( 52,292)( 53,294)( 54,293)( 55,296)( 56,295)( 57,298)( 58,297)( 59,300)( 60,299)( 61,301)( 62,302)( 63,303)( 64,304)( 65,329)( 66,330)( 67,331)( 68,332)( 69,334)( 70,333)( 71,336)( 72,335)( 73,321)( 74,322)( 75,323)( 76,324)( 77,326)( 78,325)( 79,328)( 80,327)( 81,347)( 82,348)( 83,345)( 84,346)( 85,352)( 86,351)( 87,350)( 88,349)( 89,339)( 90,340)( 91,337)( 92,338)( 93,344)( 94,343)( 95,342)( 96,341)( 97,378)( 98,377)( 99,380)(100,379)(101,381)(102,382)(103,383)(104,384)(105,370)(106,369)(107,372)(108,371)(109,373)(110,374)(111,375)(112,376)(113,362)(114,361)(115,364)(116,363)(117,365)(118,366)(119,367)(120,368)(121,354)(122,353)(123,356)(124,355)(125,357)(126,358)(127,359)(128,360)(129,401)(130,402)(131,403)(132,404)(133,406)(134,405)(135,408)(136,407)(137,410)(138,409)(139,412)(140,411)(141,413)(142,414)(143,415)(144,416)(145,385)(146,386)(147,387)(148,388)(149,390)(150,389)(151,392)(152,391)(153,394)(154,393)(155,396)(156,395)(157,397)(158,398)(159,399)(160,400)(161,417)(162,418)(163,419)(164,420)(165,422)(166,421)(167,424)(168,423)(169,426)(170,425)(171,428)(172,427)(173,429)(174,430)(175,431)(176,432)(177,435)(178,436)(179,433)(180,434)(181,440)(182,439)(183,438)(184,437)(185,444)(186,443)(187,442)(188,441)(189,447)(190,448)(191,445)(192,446)(193,474)(194,473)(195,476)(196,475)(197,477)(198,478)(199,479)(200,480)(201,466)(202,465)(203,468)(204,467)(205,469)(206,470)(207,471)(208,472)(209,458)(210,457)(211,460)(212,459)(213,461)(214,462)(215,463)(216,464)(217,450)(218,449)(219,452)(220,451)(221,453)(222,454)(223,455)(224,456)(225,489)(226,490)(227,491)(228,492)(229,494)(230,493)(231,496)(232,495)(233,481)(234,482)(235,483)(236,484)(237,486)(238,485)(239,488)(240,487)(241,507)(242,508)(243,505)(244,506)(245,512)(246,511)(247,510)(248,509)(249,499)(250,500)(251,497)(252,498)(253,504)(254,503)(255,502)(256,501);
s3 := Sym(512)!( 1, 33)( 2, 34)( 3, 35)( 4, 36)( 5, 37)( 6, 38)( 7, 39)( 8, 40)( 9, 42)( 10, 41)( 11, 44)( 12, 43)( 13, 46)( 14, 45)( 15, 48)( 16, 47)( 17, 51)( 18, 52)( 19, 49)( 20, 50)( 21, 55)( 22, 56)( 23, 53)( 24, 54)( 25, 60)( 26, 59)( 27, 58)( 28, 57)( 29, 64)( 30, 63)( 31, 62)( 32, 61)( 65, 97)( 66, 98)( 67, 99)( 68,100)( 69,101)( 70,102)( 71,103)( 72,104)( 73,106)( 74,105)( 75,108)( 76,107)( 77,110)( 78,109)( 79,112)( 80,111)( 81,115)( 82,116)( 83,113)( 84,114)( 85,119)( 86,120)( 87,117)( 88,118)( 89,124)( 90,123)( 91,122)( 92,121)( 93,128)( 94,127)( 95,126)( 96,125)(129,161)(130,162)(131,163)(132,164)(133,165)(134,166)(135,167)(136,168)(137,170)(138,169)(139,172)(140,171)(141,174)(142,173)(143,176)(144,175)(145,179)(146,180)(147,177)(148,178)(149,183)(150,184)(151,181)(152,182)(153,188)(154,187)(155,186)(156,185)(157,192)(158,191)(159,190)(160,189)(193,225)(194,226)(195,227)(196,228)(197,229)(198,230)(199,231)(200,232)(201,234)(202,233)(203,236)(204,235)(205,238)(206,237)(207,240)(208,239)(209,243)(210,244)(211,241)(212,242)(213,247)(214,248)(215,245)(216,246)(217,252)(218,251)(219,250)(220,249)(221,256)(222,255)(223,254)(224,253)(257,289)(258,290)(259,291)(260,292)(261,293)(262,294)(263,295)(264,296)(265,298)(266,297)(267,300)(268,299)(269,302)(270,301)(271,304)(272,303)(273,307)(274,308)(275,305)(276,306)(277,311)(278,312)(279,309)(280,310)(281,316)(282,315)(283,314)(284,313)(285,320)(286,319)(287,318)(288,317)(321,353)(322,354)(323,355)(324,356)(325,357)(326,358)(327,359)(328,360)(329,362)(330,361)(331,364)(332,363)(333,366)(334,365)(335,368)(336,367)(337,371)(338,372)(339,369)(340,370)(341,375)(342,376)(343,373)(344,374)(345,380)(346,379)(347,378)(348,377)(349,384)(350,383)(351,382)(352,381)(385,417)(386,418)(387,419)(388,420)(389,421)(390,422)(391,423)(392,424)(393,426)(394,425)(395,428)(396,427)(397,430)(398,429)(399,432)(400,431)(401,435)(402,436)(403,433)(404,434)(405,439)(406,440)(407,437)(408,438)(409,444)(410,443)(411,442)(412,441)(413,448)(414,447)(415,446)(416,445)(449,481)(450,482)(451,483)(452,484)(453,485)(454,486)(455,487)(456,488)(457,490)(458,489)(459,492)(460,491)(461,494)(462,493)(463,496)(464,495)(465,499)(466,500)(467,497)(468,498)(469,503)(470,504)(471,501)(472,502)(473,508)(474,507)(475,506)(476,505)(477,512)(478,511)(479,510)(480,509);
poly := sub<Sym(512)|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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope