Polytope of Type {4,8,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,8,4}*512d
if this polytope has a name.
Group : SmallGroup(512,156515)
Rank : 4
Schlafli Type : {4,8,4}
Number of vertices, edges, etc : 4, 32, 32, 8
Order of s0s1s2s3 : 8
Order of s0s1s2s3s2s1 : 2
Special Properties :
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 : {4,8,4}*256a, {4,4,4}*256a, {4,8,4}*256c
4-fold quotients : {4,4,4}*128, {4,8,2}*128b, {2,4,4}*128
8-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*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.
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, 83)( 18, 84)( 19, 81)( 20, 82)( 21, 87)( 22, 88)( 23, 85)( 24, 86)
( 25, 92)( 26, 91)( 27, 90)( 28, 89)( 29, 96)( 30, 95)( 31, 94)( 32, 93)
( 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)
( 49,115)( 50,116)( 51,113)( 52,114)( 53,119)( 54,120)( 55,117)( 56,118)
( 57,124)( 58,123)( 59,122)( 60,121)( 61,128)( 62,127)( 63,126)( 64,125)
(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)
(145,211)(146,212)(147,209)(148,210)(149,215)(150,216)(151,213)(152,214)
(153,220)(154,219)(155,218)(156,217)(157,224)(158,223)(159,222)(160,221)
(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)
(177,243)(178,244)(179,241)(180,242)(181,247)(182,248)(183,245)(184,246)
(185,252)(186,251)(187,250)(188,249)(189,256)(190,255)(191,254)(192,253)
(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)
(273,339)(274,340)(275,337)(276,338)(277,343)(278,344)(279,341)(280,342)
(281,348)(282,347)(283,346)(284,345)(285,352)(286,351)(287,350)(288,349)
(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)
(305,371)(306,372)(307,369)(308,370)(309,375)(310,376)(311,373)(312,374)
(313,380)(314,379)(315,378)(316,377)(317,384)(318,383)(319,382)(320,381)
(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)
(401,467)(402,468)(403,465)(404,466)(405,471)(406,472)(407,469)(408,470)
(409,476)(410,475)(411,474)(412,473)(413,480)(414,479)(415,478)(416,477)
(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)
(433,499)(434,500)(435,497)(436,498)(437,503)(438,504)(439,501)(440,502)
(441,508)(442,507)(443,506)(444,505)(445,512)(446,511)(447,510)(448,509);;
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)
( 17,273)( 18,274)( 19,275)( 20,276)( 21,278)( 22,277)( 23,280)( 24,279)
( 25,282)( 26,281)( 27,284)( 28,283)( 29,285)( 30,286)( 31,287)( 32,288)
( 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)
( 81,345)( 82,346)( 83,347)( 84,348)( 85,350)( 86,349)( 87,352)( 88,351)
( 89,337)( 90,338)( 91,339)( 92,340)( 93,342)( 94,341)( 95,344)( 96,343)
( 97,379)( 98,380)( 99,377)(100,378)(101,384)(102,383)(103,382)(104,381)
(105,371)(106,372)(107,369)(108,370)(109,376)(110,375)(111,374)(112,373)
(113,363)(114,364)(115,361)(116,362)(117,368)(118,367)(119,366)(120,365)
(121,355)(122,356)(123,353)(124,354)(125,360)(126,359)(127,358)(128,357)
(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)
(177,433)(178,434)(179,435)(180,436)(181,438)(182,437)(183,440)(184,439)
(185,442)(186,441)(187,444)(188,443)(189,445)(190,446)(191,447)(192,448)
(193,475)(194,476)(195,473)(196,474)(197,480)(198,479)(199,478)(200,477)
(201,467)(202,468)(203,465)(204,466)(205,472)(206,471)(207,470)(208,469)
(209,459)(210,460)(211,457)(212,458)(213,464)(214,463)(215,462)(216,461)
(217,451)(218,452)(219,449)(220,450)(221,456)(222,455)(223,454)(224,453)
(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)
(241,505)(242,506)(243,507)(244,508)(245,510)(246,509)(247,512)(248,511)
(249,497)(250,498)(251,499)(252,500)(253,502)(254,501)(255,504)(256,503);;
s3 := ( 1, 33)( 2, 34)( 3, 35)( 4, 36)( 5, 37)( 6, 38)( 7, 39)( 8, 40)
( 9, 43)( 10, 44)( 11, 41)( 12, 42)( 13, 47)( 14, 48)( 15, 45)( 16, 46)
( 17, 49)( 18, 50)( 19, 51)( 20, 52)( 21, 53)( 22, 54)( 23, 55)( 24, 56)
( 25, 59)( 26, 60)( 27, 57)( 28, 58)( 29, 63)( 30, 64)( 31, 61)( 32, 62)
( 65, 97)( 66, 98)( 67, 99)( 68,100)( 69,101)( 70,102)( 71,103)( 72,104)
( 73,107)( 74,108)( 75,105)( 76,106)( 77,111)( 78,112)( 79,109)( 80,110)
( 81,113)( 82,114)( 83,115)( 84,116)( 85,117)( 86,118)( 87,119)( 88,120)
( 89,123)( 90,124)( 91,121)( 92,122)( 93,127)( 94,128)( 95,125)( 96,126)
(129,161)(130,162)(131,163)(132,164)(133,165)(134,166)(135,167)(136,168)
(137,171)(138,172)(139,169)(140,170)(141,175)(142,176)(143,173)(144,174)
(145,177)(146,178)(147,179)(148,180)(149,181)(150,182)(151,183)(152,184)
(153,187)(154,188)(155,185)(156,186)(157,191)(158,192)(159,189)(160,190)
(193,225)(194,226)(195,227)(196,228)(197,229)(198,230)(199,231)(200,232)
(201,235)(202,236)(203,233)(204,234)(205,239)(206,240)(207,237)(208,238)
(209,241)(210,242)(211,243)(212,244)(213,245)(214,246)(215,247)(216,248)
(217,251)(218,252)(219,249)(220,250)(221,255)(222,256)(223,253)(224,254)
(257,289)(258,290)(259,291)(260,292)(261,293)(262,294)(263,295)(264,296)
(265,299)(266,300)(267,297)(268,298)(269,303)(270,304)(271,301)(272,302)
(273,305)(274,306)(275,307)(276,308)(277,309)(278,310)(279,311)(280,312)
(281,315)(282,316)(283,313)(284,314)(285,319)(286,320)(287,317)(288,318)
(321,353)(322,354)(323,355)(324,356)(325,357)(326,358)(327,359)(328,360)
(329,363)(330,364)(331,361)(332,362)(333,367)(334,368)(335,365)(336,366)
(337,369)(338,370)(339,371)(340,372)(341,373)(342,374)(343,375)(344,376)
(345,379)(346,380)(347,377)(348,378)(349,383)(350,384)(351,381)(352,382)
(385,417)(386,418)(387,419)(388,420)(389,421)(390,422)(391,423)(392,424)
(393,427)(394,428)(395,425)(396,426)(397,431)(398,432)(399,429)(400,430)
(401,433)(402,434)(403,435)(404,436)(405,437)(406,438)(407,439)(408,440)
(409,443)(410,444)(411,441)(412,442)(413,447)(414,448)(415,445)(416,446)
(449,481)(450,482)(451,483)(452,484)(453,485)(454,486)(455,487)(456,488)
(457,491)(458,492)(459,489)(460,490)(461,495)(462,496)(463,493)(464,494)
(465,497)(466,498)(467,499)(468,500)(469,501)(470,502)(471,503)(472,504)
(473,507)(474,508)(475,505)(476,506)(477,511)(478,512)(479,509)(480,510);;
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*s3*s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1,
s3*s0*s2*s1*s3*s2*s3*s1*s2*s3*s0*s1*s2*s1 ];;
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, 83)( 18, 84)( 19, 81)( 20, 82)( 21, 87)( 22, 88)( 23, 85)
( 24, 86)( 25, 92)( 26, 91)( 27, 90)( 28, 89)( 29, 96)( 30, 95)( 31, 94)
( 32, 93)( 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)( 49,115)( 50,116)( 51,113)( 52,114)( 53,119)( 54,120)( 55,117)
( 56,118)( 57,124)( 58,123)( 59,122)( 60,121)( 61,128)( 62,127)( 63,126)
( 64,125)(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)(145,211)(146,212)(147,209)(148,210)(149,215)(150,216)(151,213)
(152,214)(153,220)(154,219)(155,218)(156,217)(157,224)(158,223)(159,222)
(160,221)(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)(177,243)(178,244)(179,241)(180,242)(181,247)(182,248)(183,245)
(184,246)(185,252)(186,251)(187,250)(188,249)(189,256)(190,255)(191,254)
(192,253)(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)(273,339)(274,340)(275,337)(276,338)(277,343)(278,344)(279,341)
(280,342)(281,348)(282,347)(283,346)(284,345)(285,352)(286,351)(287,350)
(288,349)(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)(305,371)(306,372)(307,369)(308,370)(309,375)(310,376)(311,373)
(312,374)(313,380)(314,379)(315,378)(316,377)(317,384)(318,383)(319,382)
(320,381)(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)(401,467)(402,468)(403,465)(404,466)(405,471)(406,472)(407,469)
(408,470)(409,476)(410,475)(411,474)(412,473)(413,480)(414,479)(415,478)
(416,477)(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)(433,499)(434,500)(435,497)(436,498)(437,503)(438,504)(439,501)
(440,502)(441,508)(442,507)(443,506)(444,505)(445,512)(446,511)(447,510)
(448,509);
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)( 17,273)( 18,274)( 19,275)( 20,276)( 21,278)( 22,277)( 23,280)
( 24,279)( 25,282)( 26,281)( 27,284)( 28,283)( 29,285)( 30,286)( 31,287)
( 32,288)( 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)( 81,345)( 82,346)( 83,347)( 84,348)( 85,350)( 86,349)( 87,352)
( 88,351)( 89,337)( 90,338)( 91,339)( 92,340)( 93,342)( 94,341)( 95,344)
( 96,343)( 97,379)( 98,380)( 99,377)(100,378)(101,384)(102,383)(103,382)
(104,381)(105,371)(106,372)(107,369)(108,370)(109,376)(110,375)(111,374)
(112,373)(113,363)(114,364)(115,361)(116,362)(117,368)(118,367)(119,366)
(120,365)(121,355)(122,356)(123,353)(124,354)(125,360)(126,359)(127,358)
(128,357)(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)(177,433)(178,434)(179,435)(180,436)(181,438)(182,437)(183,440)
(184,439)(185,442)(186,441)(187,444)(188,443)(189,445)(190,446)(191,447)
(192,448)(193,475)(194,476)(195,473)(196,474)(197,480)(198,479)(199,478)
(200,477)(201,467)(202,468)(203,465)(204,466)(205,472)(206,471)(207,470)
(208,469)(209,459)(210,460)(211,457)(212,458)(213,464)(214,463)(215,462)
(216,461)(217,451)(218,452)(219,449)(220,450)(221,456)(222,455)(223,454)
(224,453)(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)(241,505)(242,506)(243,507)(244,508)(245,510)(246,509)(247,512)
(248,511)(249,497)(250,498)(251,499)(252,500)(253,502)(254,501)(255,504)
(256,503);
s3 := Sym(512)!( 1, 33)( 2, 34)( 3, 35)( 4, 36)( 5, 37)( 6, 38)( 7, 39)
( 8, 40)( 9, 43)( 10, 44)( 11, 41)( 12, 42)( 13, 47)( 14, 48)( 15, 45)
( 16, 46)( 17, 49)( 18, 50)( 19, 51)( 20, 52)( 21, 53)( 22, 54)( 23, 55)
( 24, 56)( 25, 59)( 26, 60)( 27, 57)( 28, 58)( 29, 63)( 30, 64)( 31, 61)
( 32, 62)( 65, 97)( 66, 98)( 67, 99)( 68,100)( 69,101)( 70,102)( 71,103)
( 72,104)( 73,107)( 74,108)( 75,105)( 76,106)( 77,111)( 78,112)( 79,109)
( 80,110)( 81,113)( 82,114)( 83,115)( 84,116)( 85,117)( 86,118)( 87,119)
( 88,120)( 89,123)( 90,124)( 91,121)( 92,122)( 93,127)( 94,128)( 95,125)
( 96,126)(129,161)(130,162)(131,163)(132,164)(133,165)(134,166)(135,167)
(136,168)(137,171)(138,172)(139,169)(140,170)(141,175)(142,176)(143,173)
(144,174)(145,177)(146,178)(147,179)(148,180)(149,181)(150,182)(151,183)
(152,184)(153,187)(154,188)(155,185)(156,186)(157,191)(158,192)(159,189)
(160,190)(193,225)(194,226)(195,227)(196,228)(197,229)(198,230)(199,231)
(200,232)(201,235)(202,236)(203,233)(204,234)(205,239)(206,240)(207,237)
(208,238)(209,241)(210,242)(211,243)(212,244)(213,245)(214,246)(215,247)
(216,248)(217,251)(218,252)(219,249)(220,250)(221,255)(222,256)(223,253)
(224,254)(257,289)(258,290)(259,291)(260,292)(261,293)(262,294)(263,295)
(264,296)(265,299)(266,300)(267,297)(268,298)(269,303)(270,304)(271,301)
(272,302)(273,305)(274,306)(275,307)(276,308)(277,309)(278,310)(279,311)
(280,312)(281,315)(282,316)(283,313)(284,314)(285,319)(286,320)(287,317)
(288,318)(321,353)(322,354)(323,355)(324,356)(325,357)(326,358)(327,359)
(328,360)(329,363)(330,364)(331,361)(332,362)(333,367)(334,368)(335,365)
(336,366)(337,369)(338,370)(339,371)(340,372)(341,373)(342,374)(343,375)
(344,376)(345,379)(346,380)(347,377)(348,378)(349,383)(350,384)(351,381)
(352,382)(385,417)(386,418)(387,419)(388,420)(389,421)(390,422)(391,423)
(392,424)(393,427)(394,428)(395,425)(396,426)(397,431)(398,432)(399,429)
(400,430)(401,433)(402,434)(403,435)(404,436)(405,437)(406,438)(407,439)
(408,440)(409,443)(410,444)(411,441)(412,442)(413,447)(414,448)(415,445)
(416,446)(449,481)(450,482)(451,483)(452,484)(453,485)(454,486)(455,487)
(456,488)(457,491)(458,492)(459,489)(460,490)(461,495)(462,496)(463,493)
(464,494)(465,497)(466,498)(467,499)(468,500)(469,501)(470,502)(471,503)
(472,504)(473,507)(474,508)(475,505)(476,506)(477,511)(478,512)(479,509)
(480,510);
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*s3*s2*s3*s2*s3*s2*s3,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1,
s3*s0*s2*s1*s3*s2*s3*s1*s2*s3*s0*s1*s2*s1 >;
References : None.
to this polytope