Polytope of Type {4,8,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,8,4}*512g
if this polytope has a name.
Group : SmallGroup(512,406983)
Rank : 4
Schlafli Type : {4,8,4}
Number of vertices, edges, etc : 4, 32, 32, 8
Order of s0s1s2s3 : 4
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 : {4,4,4}*256a
4-fold quotients : {4,4,4}*128, {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, 97)( 2, 98)( 3, 99)( 4,100)( 5,101)( 6,102)( 7,103)( 8,104)
( 9,108)( 10,107)( 11,106)( 12,105)( 13,112)( 14,111)( 15,110)( 16,109)
( 17,115)( 18,116)( 19,113)( 20,114)( 21,119)( 22,120)( 23,117)( 24,118)
( 25,122)( 26,121)( 27,124)( 28,123)( 29,126)( 30,125)( 31,128)( 32,127)
( 33, 65)( 34, 66)( 35, 67)( 36, 68)( 37, 69)( 38, 70)( 39, 71)( 40, 72)
( 41, 76)( 42, 75)( 43, 74)( 44, 73)( 45, 80)( 46, 79)( 47, 78)( 48, 77)
( 49, 83)( 50, 84)( 51, 81)( 52, 82)( 53, 87)( 54, 88)( 55, 85)( 56, 86)
( 57, 90)( 58, 89)( 59, 92)( 60, 91)( 61, 94)( 62, 93)( 63, 96)( 64, 95)
(129,225)(130,226)(131,227)(132,228)(133,229)(134,230)(135,231)(136,232)
(137,236)(138,235)(139,234)(140,233)(141,240)(142,239)(143,238)(144,237)
(145,243)(146,244)(147,241)(148,242)(149,247)(150,248)(151,245)(152,246)
(153,250)(154,249)(155,252)(156,251)(157,254)(158,253)(159,256)(160,255)
(161,193)(162,194)(163,195)(164,196)(165,197)(166,198)(167,199)(168,200)
(169,204)(170,203)(171,202)(172,201)(173,208)(174,207)(175,206)(176,205)
(177,211)(178,212)(179,209)(180,210)(181,215)(182,216)(183,213)(184,214)
(185,218)(186,217)(187,220)(188,219)(189,222)(190,221)(191,224)(192,223)
(257,353)(258,354)(259,355)(260,356)(261,357)(262,358)(263,359)(264,360)
(265,364)(266,363)(267,362)(268,361)(269,368)(270,367)(271,366)(272,365)
(273,371)(274,372)(275,369)(276,370)(277,375)(278,376)(279,373)(280,374)
(281,378)(282,377)(283,380)(284,379)(285,382)(286,381)(287,384)(288,383)
(289,321)(290,322)(291,323)(292,324)(293,325)(294,326)(295,327)(296,328)
(297,332)(298,331)(299,330)(300,329)(301,336)(302,335)(303,334)(304,333)
(305,339)(306,340)(307,337)(308,338)(309,343)(310,344)(311,341)(312,342)
(313,346)(314,345)(315,348)(316,347)(317,350)(318,349)(319,352)(320,351)
(385,481)(386,482)(387,483)(388,484)(389,485)(390,486)(391,487)(392,488)
(393,492)(394,491)(395,490)(396,489)(397,496)(398,495)(399,494)(400,493)
(401,499)(402,500)(403,497)(404,498)(405,503)(406,504)(407,501)(408,502)
(409,506)(410,505)(411,508)(412,507)(413,510)(414,509)(415,512)(416,511)
(417,449)(418,450)(419,451)(420,452)(421,453)(422,454)(423,455)(424,456)
(425,460)(426,459)(427,458)(428,457)(429,464)(430,463)(431,462)(432,461)
(433,467)(434,468)(435,465)(436,466)(437,471)(438,472)(439,469)(440,470)
(441,474)(442,473)(443,476)(444,475)(445,478)(446,477)(447,480)(448,479);;
s2 := ( 1,257)( 2,258)( 3,260)( 4,259)( 5,262)( 6,261)( 7,263)( 8,264)
( 9,265)( 10,266)( 11,268)( 12,267)( 13,270)( 14,269)( 15,271)( 16,272)
( 17,273)( 18,274)( 19,276)( 20,275)( 21,278)( 22,277)( 23,279)( 24,280)
( 25,281)( 26,282)( 27,284)( 28,283)( 29,286)( 30,285)( 31,287)( 32,288)
( 33,305)( 34,306)( 35,308)( 36,307)( 37,310)( 38,309)( 39,311)( 40,312)
( 41,313)( 42,314)( 43,316)( 44,315)( 45,318)( 46,317)( 47,319)( 48,320)
( 49,289)( 50,290)( 51,292)( 52,291)( 53,294)( 54,293)( 55,295)( 56,296)
( 57,297)( 58,298)( 59,300)( 60,299)( 61,302)( 62,301)( 63,303)( 64,304)
( 65,329)( 66,330)( 67,332)( 68,331)( 69,334)( 70,333)( 71,335)( 72,336)
( 73,321)( 74,322)( 75,324)( 76,323)( 77,326)( 78,325)( 79,327)( 80,328)
( 81,346)( 82,345)( 83,347)( 84,348)( 85,349)( 86,350)( 87,352)( 88,351)
( 89,338)( 90,337)( 91,339)( 92,340)( 93,341)( 94,342)( 95,344)( 96,343)
( 97,379)( 98,380)( 99,378)(100,377)(101,384)(102,383)(103,381)(104,382)
(105,371)(106,372)(107,370)(108,369)(109,376)(110,375)(111,373)(112,374)
(113,364)(114,363)(115,361)(116,362)(117,367)(118,368)(119,366)(120,365)
(121,356)(122,355)(123,353)(124,354)(125,359)(126,360)(127,358)(128,357)
(129,401)(130,402)(131,404)(132,403)(133,406)(134,405)(135,407)(136,408)
(137,409)(138,410)(139,412)(140,411)(141,414)(142,413)(143,415)(144,416)
(145,385)(146,386)(147,388)(148,387)(149,390)(150,389)(151,391)(152,392)
(153,393)(154,394)(155,396)(156,395)(157,398)(158,397)(159,399)(160,400)
(161,417)(162,418)(163,420)(164,419)(165,422)(166,421)(167,423)(168,424)
(169,425)(170,426)(171,428)(172,427)(173,430)(174,429)(175,431)(176,432)
(177,433)(178,434)(179,436)(180,435)(181,438)(182,437)(183,439)(184,440)
(185,441)(186,442)(187,444)(188,443)(189,446)(190,445)(191,447)(192,448)
(193,475)(194,476)(195,474)(196,473)(197,480)(198,479)(199,477)(200,478)
(201,467)(202,468)(203,466)(204,465)(205,472)(206,471)(207,469)(208,470)
(209,460)(210,459)(211,457)(212,458)(213,463)(214,464)(215,462)(216,461)
(217,452)(218,451)(219,449)(220,450)(221,455)(222,456)(223,454)(224,453)
(225,489)(226,490)(227,492)(228,491)(229,494)(230,493)(231,495)(232,496)
(233,481)(234,482)(235,484)(236,483)(237,486)(238,485)(239,487)(240,488)
(241,506)(242,505)(243,507)(244,508)(245,509)(246,510)(247,512)(248,511)
(249,498)(250,497)(251,499)(252,500)(253,501)(254,502)(255,504)(256,503);;
s3 := ( 1, 33)( 2, 34)( 3, 35)( 4, 36)( 5, 37)( 6, 38)( 7, 39)( 8, 40)
( 9, 44)( 10, 43)( 11, 42)( 12, 41)( 13, 48)( 14, 47)( 15, 46)( 16, 45)
( 17, 49)( 18, 50)( 19, 51)( 20, 52)( 21, 53)( 22, 54)( 23, 55)( 24, 56)
( 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)
( 73,108)( 74,107)( 75,106)( 76,105)( 77,112)( 78,111)( 79,110)( 80,109)
( 81,113)( 82,114)( 83,115)( 84,116)( 85,117)( 86,118)( 87,119)( 88,120)
( 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)
(137,172)(138,171)(139,170)(140,169)(141,176)(142,175)(143,174)(144,173)
(145,177)(146,178)(147,179)(148,180)(149,181)(150,182)(151,183)(152,184)
(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)
(201,236)(202,235)(203,234)(204,233)(205,240)(206,239)(207,238)(208,237)
(209,241)(210,242)(211,243)(212,244)(213,245)(214,246)(215,247)(216,248)
(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)
(265,300)(266,299)(267,298)(268,297)(269,304)(270,303)(271,302)(272,301)
(273,305)(274,306)(275,307)(276,308)(277,309)(278,310)(279,311)(280,312)
(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)
(329,364)(330,363)(331,362)(332,361)(333,368)(334,367)(335,366)(336,365)
(337,369)(338,370)(339,371)(340,372)(341,373)(342,374)(343,375)(344,376)
(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)
(393,428)(394,427)(395,426)(396,425)(397,432)(398,431)(399,430)(400,429)
(401,433)(402,434)(403,435)(404,436)(405,437)(406,438)(407,439)(408,440)
(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)
(457,492)(458,491)(459,490)(460,489)(461,496)(462,495)(463,494)(464,493)
(465,497)(466,498)(467,499)(468,500)(469,501)(470,502)(471,503)(472,504)
(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*s3*s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*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, 97)( 2, 98)( 3, 99)( 4,100)( 5,101)( 6,102)( 7,103)
( 8,104)( 9,108)( 10,107)( 11,106)( 12,105)( 13,112)( 14,111)( 15,110)
( 16,109)( 17,115)( 18,116)( 19,113)( 20,114)( 21,119)( 22,120)( 23,117)
( 24,118)( 25,122)( 26,121)( 27,124)( 28,123)( 29,126)( 30,125)( 31,128)
( 32,127)( 33, 65)( 34, 66)( 35, 67)( 36, 68)( 37, 69)( 38, 70)( 39, 71)
( 40, 72)( 41, 76)( 42, 75)( 43, 74)( 44, 73)( 45, 80)( 46, 79)( 47, 78)
( 48, 77)( 49, 83)( 50, 84)( 51, 81)( 52, 82)( 53, 87)( 54, 88)( 55, 85)
( 56, 86)( 57, 90)( 58, 89)( 59, 92)( 60, 91)( 61, 94)( 62, 93)( 63, 96)
( 64, 95)(129,225)(130,226)(131,227)(132,228)(133,229)(134,230)(135,231)
(136,232)(137,236)(138,235)(139,234)(140,233)(141,240)(142,239)(143,238)
(144,237)(145,243)(146,244)(147,241)(148,242)(149,247)(150,248)(151,245)
(152,246)(153,250)(154,249)(155,252)(156,251)(157,254)(158,253)(159,256)
(160,255)(161,193)(162,194)(163,195)(164,196)(165,197)(166,198)(167,199)
(168,200)(169,204)(170,203)(171,202)(172,201)(173,208)(174,207)(175,206)
(176,205)(177,211)(178,212)(179,209)(180,210)(181,215)(182,216)(183,213)
(184,214)(185,218)(186,217)(187,220)(188,219)(189,222)(190,221)(191,224)
(192,223)(257,353)(258,354)(259,355)(260,356)(261,357)(262,358)(263,359)
(264,360)(265,364)(266,363)(267,362)(268,361)(269,368)(270,367)(271,366)
(272,365)(273,371)(274,372)(275,369)(276,370)(277,375)(278,376)(279,373)
(280,374)(281,378)(282,377)(283,380)(284,379)(285,382)(286,381)(287,384)
(288,383)(289,321)(290,322)(291,323)(292,324)(293,325)(294,326)(295,327)
(296,328)(297,332)(298,331)(299,330)(300,329)(301,336)(302,335)(303,334)
(304,333)(305,339)(306,340)(307,337)(308,338)(309,343)(310,344)(311,341)
(312,342)(313,346)(314,345)(315,348)(316,347)(317,350)(318,349)(319,352)
(320,351)(385,481)(386,482)(387,483)(388,484)(389,485)(390,486)(391,487)
(392,488)(393,492)(394,491)(395,490)(396,489)(397,496)(398,495)(399,494)
(400,493)(401,499)(402,500)(403,497)(404,498)(405,503)(406,504)(407,501)
(408,502)(409,506)(410,505)(411,508)(412,507)(413,510)(414,509)(415,512)
(416,511)(417,449)(418,450)(419,451)(420,452)(421,453)(422,454)(423,455)
(424,456)(425,460)(426,459)(427,458)(428,457)(429,464)(430,463)(431,462)
(432,461)(433,467)(434,468)(435,465)(436,466)(437,471)(438,472)(439,469)
(440,470)(441,474)(442,473)(443,476)(444,475)(445,478)(446,477)(447,480)
(448,479);
s2 := Sym(512)!( 1,257)( 2,258)( 3,260)( 4,259)( 5,262)( 6,261)( 7,263)
( 8,264)( 9,265)( 10,266)( 11,268)( 12,267)( 13,270)( 14,269)( 15,271)
( 16,272)( 17,273)( 18,274)( 19,276)( 20,275)( 21,278)( 22,277)( 23,279)
( 24,280)( 25,281)( 26,282)( 27,284)( 28,283)( 29,286)( 30,285)( 31,287)
( 32,288)( 33,305)( 34,306)( 35,308)( 36,307)( 37,310)( 38,309)( 39,311)
( 40,312)( 41,313)( 42,314)( 43,316)( 44,315)( 45,318)( 46,317)( 47,319)
( 48,320)( 49,289)( 50,290)( 51,292)( 52,291)( 53,294)( 54,293)( 55,295)
( 56,296)( 57,297)( 58,298)( 59,300)( 60,299)( 61,302)( 62,301)( 63,303)
( 64,304)( 65,329)( 66,330)( 67,332)( 68,331)( 69,334)( 70,333)( 71,335)
( 72,336)( 73,321)( 74,322)( 75,324)( 76,323)( 77,326)( 78,325)( 79,327)
( 80,328)( 81,346)( 82,345)( 83,347)( 84,348)( 85,349)( 86,350)( 87,352)
( 88,351)( 89,338)( 90,337)( 91,339)( 92,340)( 93,341)( 94,342)( 95,344)
( 96,343)( 97,379)( 98,380)( 99,378)(100,377)(101,384)(102,383)(103,381)
(104,382)(105,371)(106,372)(107,370)(108,369)(109,376)(110,375)(111,373)
(112,374)(113,364)(114,363)(115,361)(116,362)(117,367)(118,368)(119,366)
(120,365)(121,356)(122,355)(123,353)(124,354)(125,359)(126,360)(127,358)
(128,357)(129,401)(130,402)(131,404)(132,403)(133,406)(134,405)(135,407)
(136,408)(137,409)(138,410)(139,412)(140,411)(141,414)(142,413)(143,415)
(144,416)(145,385)(146,386)(147,388)(148,387)(149,390)(150,389)(151,391)
(152,392)(153,393)(154,394)(155,396)(156,395)(157,398)(158,397)(159,399)
(160,400)(161,417)(162,418)(163,420)(164,419)(165,422)(166,421)(167,423)
(168,424)(169,425)(170,426)(171,428)(172,427)(173,430)(174,429)(175,431)
(176,432)(177,433)(178,434)(179,436)(180,435)(181,438)(182,437)(183,439)
(184,440)(185,441)(186,442)(187,444)(188,443)(189,446)(190,445)(191,447)
(192,448)(193,475)(194,476)(195,474)(196,473)(197,480)(198,479)(199,477)
(200,478)(201,467)(202,468)(203,466)(204,465)(205,472)(206,471)(207,469)
(208,470)(209,460)(210,459)(211,457)(212,458)(213,463)(214,464)(215,462)
(216,461)(217,452)(218,451)(219,449)(220,450)(221,455)(222,456)(223,454)
(224,453)(225,489)(226,490)(227,492)(228,491)(229,494)(230,493)(231,495)
(232,496)(233,481)(234,482)(235,484)(236,483)(237,486)(238,485)(239,487)
(240,488)(241,506)(242,505)(243,507)(244,508)(245,509)(246,510)(247,512)
(248,511)(249,498)(250,497)(251,499)(252,500)(253,501)(254,502)(255,504)
(256,503);
s3 := Sym(512)!( 1, 33)( 2, 34)( 3, 35)( 4, 36)( 5, 37)( 6, 38)( 7, 39)
( 8, 40)( 9, 44)( 10, 43)( 11, 42)( 12, 41)( 13, 48)( 14, 47)( 15, 46)
( 16, 45)( 17, 49)( 18, 50)( 19, 51)( 20, 52)( 21, 53)( 22, 54)( 23, 55)
( 24, 56)( 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)( 73,108)( 74,107)( 75,106)( 76,105)( 77,112)( 78,111)( 79,110)
( 80,109)( 81,113)( 82,114)( 83,115)( 84,116)( 85,117)( 86,118)( 87,119)
( 88,120)( 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)(137,172)(138,171)(139,170)(140,169)(141,176)(142,175)(143,174)
(144,173)(145,177)(146,178)(147,179)(148,180)(149,181)(150,182)(151,183)
(152,184)(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)(201,236)(202,235)(203,234)(204,233)(205,240)(206,239)(207,238)
(208,237)(209,241)(210,242)(211,243)(212,244)(213,245)(214,246)(215,247)
(216,248)(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)(265,300)(266,299)(267,298)(268,297)(269,304)(270,303)(271,302)
(272,301)(273,305)(274,306)(275,307)(276,308)(277,309)(278,310)(279,311)
(280,312)(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)(329,364)(330,363)(331,362)(332,361)(333,368)(334,367)(335,366)
(336,365)(337,369)(338,370)(339,371)(340,372)(341,373)(342,374)(343,375)
(344,376)(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)(393,428)(394,427)(395,426)(396,425)(397,432)(398,431)(399,430)
(400,429)(401,433)(402,434)(403,435)(404,436)(405,437)(406,438)(407,439)
(408,440)(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)(457,492)(458,491)(459,490)(460,489)(461,496)(462,495)(463,494)
(464,493)(465,497)(466,498)(467,499)(468,500)(469,501)(470,502)(471,503)
(472,504)(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*s3*s2*s3*s2*s3*s2*s3,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1 >;
References : None.
to this polytope