Polytope of Type {4,8,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,8,8}*512b
if this polytope has a name.
Group : SmallGroup(512,153099)
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 :
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}*256b, {4,8,4}*256a
4-fold quotients : {4,4,4}*128, {2,4,8}*128b
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)
( 9,107)( 10,108)( 11,105)( 12,106)( 13,111)( 14,112)( 15,109)( 16,110)
( 17,116)( 18,115)( 19,114)( 20,113)( 21,120)( 22,119)( 23,118)( 24,117)
( 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, 75)( 42, 76)( 43, 73)( 44, 74)( 45, 79)( 46, 80)( 47, 77)( 48, 78)
( 49, 84)( 50, 83)( 51, 82)( 52, 81)( 53, 88)( 54, 87)( 55, 86)( 56, 85)
( 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)
(137,235)(138,236)(139,233)(140,234)(141,239)(142,240)(143,237)(144,238)
(145,244)(146,243)(147,242)(148,241)(149,248)(150,247)(151,246)(152,245)
(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)
(169,203)(170,204)(171,201)(172,202)(173,207)(174,208)(175,205)(176,206)
(177,212)(178,211)(179,210)(180,209)(181,216)(182,215)(183,214)(184,213)
(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)
(265,363)(266,364)(267,361)(268,362)(269,367)(270,368)(271,365)(272,366)
(273,372)(274,371)(275,370)(276,369)(277,376)(278,375)(279,374)(280,373)
(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)
(297,331)(298,332)(299,329)(300,330)(301,335)(302,336)(303,333)(304,334)
(305,340)(306,339)(307,338)(308,337)(309,344)(310,343)(311,342)(312,341)
(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)
(393,491)(394,492)(395,489)(396,490)(397,495)(398,496)(399,493)(400,494)
(401,500)(402,499)(403,498)(404,497)(405,504)(406,503)(407,502)(408,501)
(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)
(425,459)(426,460)(427,457)(428,458)(429,463)(430,464)(431,461)(432,462)
(433,468)(434,467)(435,466)(436,465)(437,472)(438,471)(439,470)(440,469)
(441,474)(442,473)(443,476)(444,475)(445,478)(446,477)(447,480)(448,479);;
s2 := ( 1,257)( 2,258)( 3,259)( 4,260)( 5,262)( 6,261)( 7,264)( 8,263)
( 9,268)( 10,267)( 11,266)( 12,265)( 13,271)( 14,272)( 15,269)( 16,270)
( 17,275)( 18,276)( 19,273)( 20,274)( 21,280)( 22,279)( 23,278)( 24,277)
( 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)
( 41,316)( 42,315)( 43,314)( 44,313)( 45,319)( 46,320)( 47,317)( 48,318)
( 49,289)( 50,290)( 51,291)( 52,292)( 53,294)( 54,293)( 55,296)( 56,295)
( 57,300)( 58,299)( 59,298)( 60,297)( 61,303)( 62,304)( 63,301)( 64,302)
( 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)
(137,412)(138,411)(139,410)(140,409)(141,415)(142,416)(143,413)(144,414)
(145,385)(146,386)(147,387)(148,388)(149,390)(150,389)(151,392)(152,391)
(153,396)(154,395)(155,394)(156,393)(157,399)(158,400)(159,397)(160,398)
(161,417)(162,418)(163,419)(164,420)(165,422)(166,421)(167,424)(168,423)
(169,428)(170,427)(171,426)(172,425)(173,431)(174,432)(175,429)(176,430)
(177,435)(178,436)(179,433)(180,434)(181,440)(182,439)(183,438)(184,437)
(185,442)(186,441)(187,444)(188,443)(189,445)(190,446)(191,447)(192,448)
(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, s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1,
s3*s0*s2*s3*s2*s1*s3*s2*s3*s1*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, 97)( 2, 98)( 3, 99)( 4,100)( 5,101)( 6,102)( 7,103)
( 8,104)( 9,107)( 10,108)( 11,105)( 12,106)( 13,111)( 14,112)( 15,109)
( 16,110)( 17,116)( 18,115)( 19,114)( 20,113)( 21,120)( 22,119)( 23,118)
( 24,117)( 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, 75)( 42, 76)( 43, 73)( 44, 74)( 45, 79)( 46, 80)( 47, 77)
( 48, 78)( 49, 84)( 50, 83)( 51, 82)( 52, 81)( 53, 88)( 54, 87)( 55, 86)
( 56, 85)( 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)(137,235)(138,236)(139,233)(140,234)(141,239)(142,240)(143,237)
(144,238)(145,244)(146,243)(147,242)(148,241)(149,248)(150,247)(151,246)
(152,245)(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)(169,203)(170,204)(171,201)(172,202)(173,207)(174,208)(175,205)
(176,206)(177,212)(178,211)(179,210)(180,209)(181,216)(182,215)(183,214)
(184,213)(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)(265,363)(266,364)(267,361)(268,362)(269,367)(270,368)(271,365)
(272,366)(273,372)(274,371)(275,370)(276,369)(277,376)(278,375)(279,374)
(280,373)(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)(297,331)(298,332)(299,329)(300,330)(301,335)(302,336)(303,333)
(304,334)(305,340)(306,339)(307,338)(308,337)(309,344)(310,343)(311,342)
(312,341)(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)(393,491)(394,492)(395,489)(396,490)(397,495)(398,496)(399,493)
(400,494)(401,500)(402,499)(403,498)(404,497)(405,504)(406,503)(407,502)
(408,501)(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)(425,459)(426,460)(427,457)(428,458)(429,463)(430,464)(431,461)
(432,462)(433,468)(434,467)(435,466)(436,465)(437,472)(438,471)(439,470)
(440,469)(441,474)(442,473)(443,476)(444,475)(445,478)(446,477)(447,480)
(448,479);
s2 := Sym(512)!( 1,257)( 2,258)( 3,259)( 4,260)( 5,262)( 6,261)( 7,264)
( 8,263)( 9,268)( 10,267)( 11,266)( 12,265)( 13,271)( 14,272)( 15,269)
( 16,270)( 17,275)( 18,276)( 19,273)( 20,274)( 21,280)( 22,279)( 23,278)
( 24,277)( 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)( 41,316)( 42,315)( 43,314)( 44,313)( 45,319)( 46,320)( 47,317)
( 48,318)( 49,289)( 50,290)( 51,291)( 52,292)( 53,294)( 54,293)( 55,296)
( 56,295)( 57,300)( 58,299)( 59,298)( 60,297)( 61,303)( 62,304)( 63,301)
( 64,302)( 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)(137,412)(138,411)(139,410)(140,409)(141,415)(142,416)(143,413)
(144,414)(145,385)(146,386)(147,387)(148,388)(149,390)(150,389)(151,392)
(152,391)(153,396)(154,395)(155,394)(156,393)(157,399)(158,400)(159,397)
(160,398)(161,417)(162,418)(163,419)(164,420)(165,422)(166,421)(167,424)
(168,423)(169,428)(170,427)(171,426)(172,425)(173,431)(174,432)(175,429)
(176,430)(177,435)(178,436)(179,433)(180,434)(181,440)(182,439)(183,438)
(184,437)(185,442)(186,441)(187,444)(188,443)(189,445)(190,446)(191,447)
(192,448)(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,
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1,
s3*s0*s2*s3*s2*s1*s3*s2*s3*s1*s0*s1*s2*s1 >;
References : None.
to this polytope