Polytope of Type {8,4,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,4,8}*512d
if this polytope has a name.
Group : SmallGroup(512,158099)
Rank : 4
Schlafli Type : {8,4,8}
Number of vertices, edges, etc : 8, 16, 16, 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, {8,4,4}*256b
4-fold quotients : {4,4,4}*128, {2,4,8}*128a, {8,4,2}*128b, {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.
Permutation Representation (GAP) :
s0 := ( 1,161)( 2,162)( 3,163)( 4,164)( 5,166)( 6,165)( 7,168)( 8,167)
( 9,169)( 10,170)( 11,171)( 12,172)( 13,174)( 14,173)( 15,176)( 16,175)
( 17,177)( 18,178)( 19,179)( 20,180)( 21,182)( 22,181)( 23,184)( 24,183)
( 25,185)( 26,186)( 27,187)( 28,188)( 29,190)( 30,189)( 31,192)( 32,191)
( 33,129)( 34,130)( 35,131)( 36,132)( 37,134)( 38,133)( 39,136)( 40,135)
( 41,137)( 42,138)( 43,139)( 44,140)( 45,142)( 46,141)( 47,144)( 48,143)
( 49,145)( 50,146)( 51,147)( 52,148)( 53,150)( 54,149)( 55,152)( 56,151)
( 57,153)( 58,154)( 59,155)( 60,156)( 61,158)( 62,157)( 63,160)( 64,159)
( 65,229)( 66,230)( 67,231)( 68,232)( 69,225)( 70,226)( 71,227)( 72,228)
( 73,237)( 74,238)( 75,239)( 76,240)( 77,233)( 78,234)( 79,235)( 80,236)
( 81,245)( 82,246)( 83,247)( 84,248)( 85,241)( 86,242)( 87,243)( 88,244)
( 89,253)( 90,254)( 91,255)( 92,256)( 93,249)( 94,250)( 95,251)( 96,252)
( 97,197)( 98,198)( 99,199)(100,200)(101,193)(102,194)(103,195)(104,196)
(105,205)(106,206)(107,207)(108,208)(109,201)(110,202)(111,203)(112,204)
(113,213)(114,214)(115,215)(116,216)(117,209)(118,210)(119,211)(120,212)
(121,221)(122,222)(123,223)(124,224)(125,217)(126,218)(127,219)(128,220)
(257,417)(258,418)(259,419)(260,420)(261,422)(262,421)(263,424)(264,423)
(265,425)(266,426)(267,427)(268,428)(269,430)(270,429)(271,432)(272,431)
(273,433)(274,434)(275,435)(276,436)(277,438)(278,437)(279,440)(280,439)
(281,441)(282,442)(283,443)(284,444)(285,446)(286,445)(287,448)(288,447)
(289,385)(290,386)(291,387)(292,388)(293,390)(294,389)(295,392)(296,391)
(297,393)(298,394)(299,395)(300,396)(301,398)(302,397)(303,400)(304,399)
(305,401)(306,402)(307,403)(308,404)(309,406)(310,405)(311,408)(312,407)
(313,409)(314,410)(315,411)(316,412)(317,414)(318,413)(319,416)(320,415)
(321,485)(322,486)(323,487)(324,488)(325,481)(326,482)(327,483)(328,484)
(329,493)(330,494)(331,495)(332,496)(333,489)(334,490)(335,491)(336,492)
(337,501)(338,502)(339,503)(340,504)(341,497)(342,498)(343,499)(344,500)
(345,509)(346,510)(347,511)(348,512)(349,505)(350,506)(351,507)(352,508)
(353,453)(354,454)(355,455)(356,456)(357,449)(358,450)(359,451)(360,452)
(361,461)(362,462)(363,463)(364,464)(365,457)(366,458)(367,459)(368,460)
(369,469)(370,470)(371,471)(372,472)(373,465)(374,466)(375,467)(376,468)
(377,477)(378,478)(379,479)(380,480)(381,473)(382,474)(383,475)(384,476);;
s1 := ( 1, 65)( 2, 66)( 3, 67)( 4, 68)( 5, 70)( 6, 69)( 7, 72)( 8, 71)
( 9, 74)( 10, 73)( 11, 76)( 12, 75)( 13, 77)( 14, 78)( 15, 79)( 16, 80)
( 17, 81)( 18, 82)( 19, 83)( 20, 84)( 21, 86)( 22, 85)( 23, 88)( 24, 87)
( 25, 90)( 26, 89)( 27, 92)( 28, 91)( 29, 93)( 30, 94)( 31, 95)( 32, 96)
( 33, 97)( 34, 98)( 35, 99)( 36,100)( 37,102)( 38,101)( 39,104)( 40,103)
( 41,106)( 42,105)( 43,108)( 44,107)( 45,109)( 46,110)( 47,111)( 48,112)
( 49,113)( 50,114)( 51,115)( 52,116)( 53,118)( 54,117)( 55,120)( 56,119)
( 57,122)( 58,121)( 59,124)( 60,123)( 61,125)( 62,126)( 63,127)( 64,128)
(129,193)(130,194)(131,195)(132,196)(133,198)(134,197)(135,200)(136,199)
(137,202)(138,201)(139,204)(140,203)(141,205)(142,206)(143,207)(144,208)
(145,209)(146,210)(147,211)(148,212)(149,214)(150,213)(151,216)(152,215)
(153,218)(154,217)(155,220)(156,219)(157,221)(158,222)(159,223)(160,224)
(161,225)(162,226)(163,227)(164,228)(165,230)(166,229)(167,232)(168,231)
(169,234)(170,233)(171,236)(172,235)(173,237)(174,238)(175,239)(176,240)
(177,241)(178,242)(179,243)(180,244)(181,246)(182,245)(183,248)(184,247)
(185,250)(186,249)(187,252)(188,251)(189,253)(190,254)(191,255)(192,256)
(257,321)(258,322)(259,323)(260,324)(261,326)(262,325)(263,328)(264,327)
(265,330)(266,329)(267,332)(268,331)(269,333)(270,334)(271,335)(272,336)
(273,337)(274,338)(275,339)(276,340)(277,342)(278,341)(279,344)(280,343)
(281,346)(282,345)(283,348)(284,347)(285,349)(286,350)(287,351)(288,352)
(289,353)(290,354)(291,355)(292,356)(293,358)(294,357)(295,360)(296,359)
(297,362)(298,361)(299,364)(300,363)(301,365)(302,366)(303,367)(304,368)
(305,369)(306,370)(307,371)(308,372)(309,374)(310,373)(311,376)(312,375)
(313,378)(314,377)(315,380)(316,379)(317,381)(318,382)(319,383)(320,384)
(385,449)(386,450)(387,451)(388,452)(389,454)(390,453)(391,456)(392,455)
(393,458)(394,457)(395,460)(396,459)(397,461)(398,462)(399,463)(400,464)
(401,465)(402,466)(403,467)(404,468)(405,470)(406,469)(407,472)(408,471)
(409,474)(410,473)(411,476)(412,475)(413,477)(414,478)(415,479)(416,480)
(417,481)(418,482)(419,483)(420,484)(421,486)(422,485)(423,488)(424,487)
(425,490)(426,489)(427,492)(428,491)(429,493)(430,494)(431,495)(432,496)
(433,497)(434,498)(435,499)(436,500)(437,502)(438,501)(439,504)(440,503)
(441,506)(442,505)(443,508)(444,507)(445,509)(446,510)(447,511)(448,512);;
s2 := ( 1,417)( 2,418)( 3,419)( 4,420)( 5,422)( 6,421)( 7,424)( 8,423)
( 9,426)( 10,425)( 11,428)( 12,427)( 13,429)( 14,430)( 15,431)( 16,432)
( 17,435)( 18,436)( 19,433)( 20,434)( 21,440)( 22,439)( 23,438)( 24,437)
( 25,444)( 26,443)( 27,442)( 28,441)( 29,447)( 30,448)( 31,445)( 32,446)
( 33,401)( 34,402)( 35,403)( 36,404)( 37,406)( 38,405)( 39,408)( 40,407)
( 41,410)( 42,409)( 43,412)( 44,411)( 45,413)( 46,414)( 47,415)( 48,416)
( 49,385)( 50,386)( 51,387)( 52,388)( 53,390)( 54,389)( 55,392)( 56,391)
( 57,394)( 58,393)( 59,396)( 60,395)( 61,397)( 62,398)( 63,399)( 64,400)
( 65,493)( 66,494)( 67,495)( 68,496)( 69,489)( 70,490)( 71,491)( 72,492)
( 73,485)( 74,486)( 75,487)( 76,488)( 77,481)( 78,482)( 79,483)( 80,484)
( 81,511)( 82,512)( 83,509)( 84,510)( 85,507)( 86,508)( 87,505)( 88,506)
( 89,503)( 90,504)( 91,501)( 92,502)( 93,499)( 94,500)( 95,497)( 96,498)
( 97,477)( 98,478)( 99,479)(100,480)(101,473)(102,474)(103,475)(104,476)
(105,469)(106,470)(107,471)(108,472)(109,465)(110,466)(111,467)(112,468)
(113,461)(114,462)(115,463)(116,464)(117,457)(118,458)(119,459)(120,460)
(121,453)(122,454)(123,455)(124,456)(125,449)(126,450)(127,451)(128,452)
(129,305)(130,306)(131,307)(132,308)(133,310)(134,309)(135,312)(136,311)
(137,314)(138,313)(139,316)(140,315)(141,317)(142,318)(143,319)(144,320)
(145,289)(146,290)(147,291)(148,292)(149,294)(150,293)(151,296)(152,295)
(153,298)(154,297)(155,300)(156,299)(157,301)(158,302)(159,303)(160,304)
(161,257)(162,258)(163,259)(164,260)(165,262)(166,261)(167,264)(168,263)
(169,266)(170,265)(171,268)(172,267)(173,269)(174,270)(175,271)(176,272)
(177,275)(178,276)(179,273)(180,274)(181,280)(182,279)(183,278)(184,277)
(185,284)(186,283)(187,282)(188,281)(189,287)(190,288)(191,285)(192,286)
(193,381)(194,382)(195,383)(196,384)(197,377)(198,378)(199,379)(200,380)
(201,373)(202,374)(203,375)(204,376)(205,369)(206,370)(207,371)(208,372)
(209,365)(210,366)(211,367)(212,368)(213,361)(214,362)(215,363)(216,364)
(217,357)(218,358)(219,359)(220,360)(221,353)(222,354)(223,355)(224,356)
(225,333)(226,334)(227,335)(228,336)(229,329)(230,330)(231,331)(232,332)
(233,325)(234,326)(235,327)(236,328)(237,321)(238,322)(239,323)(240,324)
(241,351)(242,352)(243,349)(244,350)(245,347)(246,348)(247,345)(248,346)
(249,343)(250,344)(251,341)(252,342)(253,339)(254,340)(255,337)(256,338);;
s3 := ( 1, 33)( 2, 34)( 3, 35)( 4, 36)( 5, 37)( 6, 38)( 7, 39)( 8, 40)
( 9, 41)( 10, 42)( 11, 43)( 12, 44)( 13, 45)( 14, 46)( 15, 47)( 16, 48)
( 17, 51)( 18, 52)( 19, 49)( 20, 50)( 21, 55)( 22, 56)( 23, 53)( 24, 54)
( 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)
( 73,105)( 74,106)( 75,107)( 76,108)( 77,109)( 78,110)( 79,111)( 80,112)
( 81,115)( 82,116)( 83,113)( 84,114)( 85,119)( 86,120)( 87,117)( 88,118)
( 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)
(137,169)(138,170)(139,171)(140,172)(141,173)(142,174)(143,175)(144,176)
(145,179)(146,180)(147,177)(148,178)(149,183)(150,184)(151,181)(152,182)
(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)
(201,233)(202,234)(203,235)(204,236)(205,237)(206,238)(207,239)(208,240)
(209,243)(210,244)(211,241)(212,242)(213,247)(214,248)(215,245)(216,246)
(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)
(265,297)(266,298)(267,299)(268,300)(269,301)(270,302)(271,303)(272,304)
(273,307)(274,308)(275,305)(276,306)(277,311)(278,312)(279,309)(280,310)
(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)
(329,361)(330,362)(331,363)(332,364)(333,365)(334,366)(335,367)(336,368)
(337,371)(338,372)(339,369)(340,370)(341,375)(342,376)(343,373)(344,374)
(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)
(393,425)(394,426)(395,427)(396,428)(397,429)(398,430)(399,431)(400,432)
(401,435)(402,436)(403,433)(404,434)(405,439)(406,440)(407,437)(408,438)
(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)
(457,489)(458,490)(459,491)(460,492)(461,493)(462,494)(463,495)(464,496)
(465,499)(466,500)(467,497)(468,498)(469,503)(470,504)(471,501)(472,502)
(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, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1,
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)( 5,166)( 6,165)( 7,168)
( 8,167)( 9,169)( 10,170)( 11,171)( 12,172)( 13,174)( 14,173)( 15,176)
( 16,175)( 17,177)( 18,178)( 19,179)( 20,180)( 21,182)( 22,181)( 23,184)
( 24,183)( 25,185)( 26,186)( 27,187)( 28,188)( 29,190)( 30,189)( 31,192)
( 32,191)( 33,129)( 34,130)( 35,131)( 36,132)( 37,134)( 38,133)( 39,136)
( 40,135)( 41,137)( 42,138)( 43,139)( 44,140)( 45,142)( 46,141)( 47,144)
( 48,143)( 49,145)( 50,146)( 51,147)( 52,148)( 53,150)( 54,149)( 55,152)
( 56,151)( 57,153)( 58,154)( 59,155)( 60,156)( 61,158)( 62,157)( 63,160)
( 64,159)( 65,229)( 66,230)( 67,231)( 68,232)( 69,225)( 70,226)( 71,227)
( 72,228)( 73,237)( 74,238)( 75,239)( 76,240)( 77,233)( 78,234)( 79,235)
( 80,236)( 81,245)( 82,246)( 83,247)( 84,248)( 85,241)( 86,242)( 87,243)
( 88,244)( 89,253)( 90,254)( 91,255)( 92,256)( 93,249)( 94,250)( 95,251)
( 96,252)( 97,197)( 98,198)( 99,199)(100,200)(101,193)(102,194)(103,195)
(104,196)(105,205)(106,206)(107,207)(108,208)(109,201)(110,202)(111,203)
(112,204)(113,213)(114,214)(115,215)(116,216)(117,209)(118,210)(119,211)
(120,212)(121,221)(122,222)(123,223)(124,224)(125,217)(126,218)(127,219)
(128,220)(257,417)(258,418)(259,419)(260,420)(261,422)(262,421)(263,424)
(264,423)(265,425)(266,426)(267,427)(268,428)(269,430)(270,429)(271,432)
(272,431)(273,433)(274,434)(275,435)(276,436)(277,438)(278,437)(279,440)
(280,439)(281,441)(282,442)(283,443)(284,444)(285,446)(286,445)(287,448)
(288,447)(289,385)(290,386)(291,387)(292,388)(293,390)(294,389)(295,392)
(296,391)(297,393)(298,394)(299,395)(300,396)(301,398)(302,397)(303,400)
(304,399)(305,401)(306,402)(307,403)(308,404)(309,406)(310,405)(311,408)
(312,407)(313,409)(314,410)(315,411)(316,412)(317,414)(318,413)(319,416)
(320,415)(321,485)(322,486)(323,487)(324,488)(325,481)(326,482)(327,483)
(328,484)(329,493)(330,494)(331,495)(332,496)(333,489)(334,490)(335,491)
(336,492)(337,501)(338,502)(339,503)(340,504)(341,497)(342,498)(343,499)
(344,500)(345,509)(346,510)(347,511)(348,512)(349,505)(350,506)(351,507)
(352,508)(353,453)(354,454)(355,455)(356,456)(357,449)(358,450)(359,451)
(360,452)(361,461)(362,462)(363,463)(364,464)(365,457)(366,458)(367,459)
(368,460)(369,469)(370,470)(371,471)(372,472)(373,465)(374,466)(375,467)
(376,468)(377,477)(378,478)(379,479)(380,480)(381,473)(382,474)(383,475)
(384,476);
s1 := Sym(512)!( 1, 65)( 2, 66)( 3, 67)( 4, 68)( 5, 70)( 6, 69)( 7, 72)
( 8, 71)( 9, 74)( 10, 73)( 11, 76)( 12, 75)( 13, 77)( 14, 78)( 15, 79)
( 16, 80)( 17, 81)( 18, 82)( 19, 83)( 20, 84)( 21, 86)( 22, 85)( 23, 88)
( 24, 87)( 25, 90)( 26, 89)( 27, 92)( 28, 91)( 29, 93)( 30, 94)( 31, 95)
( 32, 96)( 33, 97)( 34, 98)( 35, 99)( 36,100)( 37,102)( 38,101)( 39,104)
( 40,103)( 41,106)( 42,105)( 43,108)( 44,107)( 45,109)( 46,110)( 47,111)
( 48,112)( 49,113)( 50,114)( 51,115)( 52,116)( 53,118)( 54,117)( 55,120)
( 56,119)( 57,122)( 58,121)( 59,124)( 60,123)( 61,125)( 62,126)( 63,127)
( 64,128)(129,193)(130,194)(131,195)(132,196)(133,198)(134,197)(135,200)
(136,199)(137,202)(138,201)(139,204)(140,203)(141,205)(142,206)(143,207)
(144,208)(145,209)(146,210)(147,211)(148,212)(149,214)(150,213)(151,216)
(152,215)(153,218)(154,217)(155,220)(156,219)(157,221)(158,222)(159,223)
(160,224)(161,225)(162,226)(163,227)(164,228)(165,230)(166,229)(167,232)
(168,231)(169,234)(170,233)(171,236)(172,235)(173,237)(174,238)(175,239)
(176,240)(177,241)(178,242)(179,243)(180,244)(181,246)(182,245)(183,248)
(184,247)(185,250)(186,249)(187,252)(188,251)(189,253)(190,254)(191,255)
(192,256)(257,321)(258,322)(259,323)(260,324)(261,326)(262,325)(263,328)
(264,327)(265,330)(266,329)(267,332)(268,331)(269,333)(270,334)(271,335)
(272,336)(273,337)(274,338)(275,339)(276,340)(277,342)(278,341)(279,344)
(280,343)(281,346)(282,345)(283,348)(284,347)(285,349)(286,350)(287,351)
(288,352)(289,353)(290,354)(291,355)(292,356)(293,358)(294,357)(295,360)
(296,359)(297,362)(298,361)(299,364)(300,363)(301,365)(302,366)(303,367)
(304,368)(305,369)(306,370)(307,371)(308,372)(309,374)(310,373)(311,376)
(312,375)(313,378)(314,377)(315,380)(316,379)(317,381)(318,382)(319,383)
(320,384)(385,449)(386,450)(387,451)(388,452)(389,454)(390,453)(391,456)
(392,455)(393,458)(394,457)(395,460)(396,459)(397,461)(398,462)(399,463)
(400,464)(401,465)(402,466)(403,467)(404,468)(405,470)(406,469)(407,472)
(408,471)(409,474)(410,473)(411,476)(412,475)(413,477)(414,478)(415,479)
(416,480)(417,481)(418,482)(419,483)(420,484)(421,486)(422,485)(423,488)
(424,487)(425,490)(426,489)(427,492)(428,491)(429,493)(430,494)(431,495)
(432,496)(433,497)(434,498)(435,499)(436,500)(437,502)(438,501)(439,504)
(440,503)(441,506)(442,505)(443,508)(444,507)(445,509)(446,510)(447,511)
(448,512);
s2 := Sym(512)!( 1,417)( 2,418)( 3,419)( 4,420)( 5,422)( 6,421)( 7,424)
( 8,423)( 9,426)( 10,425)( 11,428)( 12,427)( 13,429)( 14,430)( 15,431)
( 16,432)( 17,435)( 18,436)( 19,433)( 20,434)( 21,440)( 22,439)( 23,438)
( 24,437)( 25,444)( 26,443)( 27,442)( 28,441)( 29,447)( 30,448)( 31,445)
( 32,446)( 33,401)( 34,402)( 35,403)( 36,404)( 37,406)( 38,405)( 39,408)
( 40,407)( 41,410)( 42,409)( 43,412)( 44,411)( 45,413)( 46,414)( 47,415)
( 48,416)( 49,385)( 50,386)( 51,387)( 52,388)( 53,390)( 54,389)( 55,392)
( 56,391)( 57,394)( 58,393)( 59,396)( 60,395)( 61,397)( 62,398)( 63,399)
( 64,400)( 65,493)( 66,494)( 67,495)( 68,496)( 69,489)( 70,490)( 71,491)
( 72,492)( 73,485)( 74,486)( 75,487)( 76,488)( 77,481)( 78,482)( 79,483)
( 80,484)( 81,511)( 82,512)( 83,509)( 84,510)( 85,507)( 86,508)( 87,505)
( 88,506)( 89,503)( 90,504)( 91,501)( 92,502)( 93,499)( 94,500)( 95,497)
( 96,498)( 97,477)( 98,478)( 99,479)(100,480)(101,473)(102,474)(103,475)
(104,476)(105,469)(106,470)(107,471)(108,472)(109,465)(110,466)(111,467)
(112,468)(113,461)(114,462)(115,463)(116,464)(117,457)(118,458)(119,459)
(120,460)(121,453)(122,454)(123,455)(124,456)(125,449)(126,450)(127,451)
(128,452)(129,305)(130,306)(131,307)(132,308)(133,310)(134,309)(135,312)
(136,311)(137,314)(138,313)(139,316)(140,315)(141,317)(142,318)(143,319)
(144,320)(145,289)(146,290)(147,291)(148,292)(149,294)(150,293)(151,296)
(152,295)(153,298)(154,297)(155,300)(156,299)(157,301)(158,302)(159,303)
(160,304)(161,257)(162,258)(163,259)(164,260)(165,262)(166,261)(167,264)
(168,263)(169,266)(170,265)(171,268)(172,267)(173,269)(174,270)(175,271)
(176,272)(177,275)(178,276)(179,273)(180,274)(181,280)(182,279)(183,278)
(184,277)(185,284)(186,283)(187,282)(188,281)(189,287)(190,288)(191,285)
(192,286)(193,381)(194,382)(195,383)(196,384)(197,377)(198,378)(199,379)
(200,380)(201,373)(202,374)(203,375)(204,376)(205,369)(206,370)(207,371)
(208,372)(209,365)(210,366)(211,367)(212,368)(213,361)(214,362)(215,363)
(216,364)(217,357)(218,358)(219,359)(220,360)(221,353)(222,354)(223,355)
(224,356)(225,333)(226,334)(227,335)(228,336)(229,329)(230,330)(231,331)
(232,332)(233,325)(234,326)(235,327)(236,328)(237,321)(238,322)(239,323)
(240,324)(241,351)(242,352)(243,349)(244,350)(245,347)(246,348)(247,345)
(248,346)(249,343)(250,344)(251,341)(252,342)(253,339)(254,340)(255,337)
(256,338);
s3 := Sym(512)!( 1, 33)( 2, 34)( 3, 35)( 4, 36)( 5, 37)( 6, 38)( 7, 39)
( 8, 40)( 9, 41)( 10, 42)( 11, 43)( 12, 44)( 13, 45)( 14, 46)( 15, 47)
( 16, 48)( 17, 51)( 18, 52)( 19, 49)( 20, 50)( 21, 55)( 22, 56)( 23, 53)
( 24, 54)( 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)( 73,105)( 74,106)( 75,107)( 76,108)( 77,109)( 78,110)( 79,111)
( 80,112)( 81,115)( 82,116)( 83,113)( 84,114)( 85,119)( 86,120)( 87,117)
( 88,118)( 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)(137,169)(138,170)(139,171)(140,172)(141,173)(142,174)(143,175)
(144,176)(145,179)(146,180)(147,177)(148,178)(149,183)(150,184)(151,181)
(152,182)(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)(201,233)(202,234)(203,235)(204,236)(205,237)(206,238)(207,239)
(208,240)(209,243)(210,244)(211,241)(212,242)(213,247)(214,248)(215,245)
(216,246)(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)(265,297)(266,298)(267,299)(268,300)(269,301)(270,302)(271,303)
(272,304)(273,307)(274,308)(275,305)(276,306)(277,311)(278,312)(279,309)
(280,310)(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)(329,361)(330,362)(331,363)(332,364)(333,365)(334,366)(335,367)
(336,368)(337,371)(338,372)(339,369)(340,370)(341,375)(342,376)(343,373)
(344,374)(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)(393,425)(394,426)(395,427)(396,428)(397,429)(398,430)(399,431)
(400,432)(401,435)(402,436)(403,433)(404,434)(405,439)(406,440)(407,437)
(408,438)(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)(457,489)(458,490)(459,491)(460,492)(461,493)(462,494)(463,495)
(464,496)(465,499)(466,500)(467,497)(468,498)(469,503)(470,504)(471,501)
(472,502)(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,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope