Polytope of Type {8,4,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,4,8}*512b
Also Known As : {{8,4|2},{4,8|2}}. if this polytope has another name.
Group : SmallGroup(512,151987)
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
Self-Dual
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 : {8,2,8}*256, {4,4,8}*256a, {8,4,4}*256a
4-fold quotients : {4,4,4}*128, {2,4,8}*128a, {8,4,2}*128a, {4,2,8}*128, {8,2,4}*128
8-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64, {2,2,8}*64, {8,2,2}*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, 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);;
s1 := ( 1,417)( 2,418)( 3,419)( 4,420)( 5,421)( 6,422)( 7,423)( 8,424)
( 9,425)( 10,426)( 11,427)( 12,428)( 13,429)( 14,430)( 15,431)( 16,432)
( 17,435)( 18,436)( 19,433)( 20,434)( 21,439)( 22,440)( 23,437)( 24,438)
( 25,443)( 26,444)( 27,441)( 28,442)( 29,447)( 30,448)( 31,445)( 32,446)
( 33,401)( 34,402)( 35,403)( 36,404)( 37,405)( 38,406)( 39,407)( 40,408)
( 41,409)( 42,410)( 43,411)( 44,412)( 45,413)( 46,414)( 47,415)( 48,416)
( 49,385)( 50,386)( 51,387)( 52,388)( 53,389)( 54,390)( 55,391)( 56,392)
( 57,393)( 58,394)( 59,395)( 60,396)( 61,397)( 62,398)( 63,399)( 64,400)
( 65,494)( 66,493)( 67,496)( 68,495)( 69,489)( 70,490)( 71,491)( 72,492)
( 73,485)( 74,486)( 75,487)( 76,488)( 77,482)( 78,481)( 79,484)( 80,483)
( 81,512)( 82,511)( 83,510)( 84,509)( 85,507)( 86,508)( 87,505)( 88,506)
( 89,503)( 90,504)( 91,501)( 92,502)( 93,500)( 94,499)( 95,498)( 96,497)
( 97,478)( 98,477)( 99,480)(100,479)(101,473)(102,474)(103,475)(104,476)
(105,469)(106,470)(107,471)(108,472)(109,466)(110,465)(111,468)(112,467)
(113,462)(114,461)(115,464)(116,463)(117,457)(118,458)(119,459)(120,460)
(121,453)(122,454)(123,455)(124,456)(125,450)(126,449)(127,452)(128,451)
(129,305)(130,306)(131,307)(132,308)(133,309)(134,310)(135,311)(136,312)
(137,313)(138,314)(139,315)(140,316)(141,317)(142,318)(143,319)(144,320)
(145,289)(146,290)(147,291)(148,292)(149,293)(150,294)(151,295)(152,296)
(153,297)(154,298)(155,299)(156,300)(157,301)(158,302)(159,303)(160,304)
(161,257)(162,258)(163,259)(164,260)(165,261)(166,262)(167,263)(168,264)
(169,265)(170,266)(171,267)(172,268)(173,269)(174,270)(175,271)(176,272)
(177,275)(178,276)(179,273)(180,274)(181,279)(182,280)(183,277)(184,278)
(185,283)(186,284)(187,281)(188,282)(189,287)(190,288)(191,285)(192,286)
(193,382)(194,381)(195,384)(196,383)(197,377)(198,378)(199,379)(200,380)
(201,373)(202,374)(203,375)(204,376)(205,370)(206,369)(207,372)(208,371)
(209,366)(210,365)(211,368)(212,367)(213,361)(214,362)(215,363)(216,364)
(217,357)(218,358)(219,359)(220,360)(221,354)(222,353)(223,356)(224,355)
(225,334)(226,333)(227,336)(228,335)(229,329)(230,330)(231,331)(232,332)
(233,325)(234,326)(235,327)(236,328)(237,322)(238,321)(239,324)(240,323)
(241,352)(242,351)(243,350)(244,349)(245,347)(246,348)(247,345)(248,346)
(249,343)(250,344)(251,341)(252,342)(253,340)(254,339)(255,338)(256,337);;
s2 := ( 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);;
s3 := ( 1,161)( 2,162)( 3,163)( 4,164)( 5,166)( 6,165)( 7,168)( 8,167)
( 9,170)( 10,169)( 11,172)( 12,171)( 13,173)( 14,174)( 15,175)( 16,176)
( 17,177)( 18,178)( 19,179)( 20,180)( 21,182)( 22,181)( 23,184)( 24,183)
( 25,186)( 26,185)( 27,188)( 28,187)( 29,189)( 30,190)( 31,191)( 32,192)
( 33,129)( 34,130)( 35,131)( 36,132)( 37,134)( 38,133)( 39,136)( 40,135)
( 41,138)( 42,137)( 43,140)( 44,139)( 45,141)( 46,142)( 47,143)( 48,144)
( 49,145)( 50,146)( 51,147)( 52,148)( 53,150)( 54,149)( 55,152)( 56,151)
( 57,154)( 58,153)( 59,156)( 60,155)( 61,157)( 62,158)( 63,159)( 64,160)
( 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)(261,422)(262,421)(263,424)(264,423)
(265,426)(266,425)(267,428)(268,427)(269,429)(270,430)(271,431)(272,432)
(273,433)(274,434)(275,435)(276,436)(277,438)(278,437)(279,440)(280,439)
(281,442)(282,441)(283,444)(284,443)(285,445)(286,446)(287,447)(288,448)
(289,385)(290,386)(291,387)(292,388)(293,390)(294,389)(295,392)(296,391)
(297,394)(298,393)(299,396)(300,395)(301,397)(302,398)(303,399)(304,400)
(305,401)(306,402)(307,403)(308,404)(309,406)(310,405)(311,408)(312,407)
(313,410)(314,409)(315,412)(316,411)(317,413)(318,414)(319,415)(320,416)
(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);;
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*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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, 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);
s1 := Sym(512)!( 1,417)( 2,418)( 3,419)( 4,420)( 5,421)( 6,422)( 7,423)
( 8,424)( 9,425)( 10,426)( 11,427)( 12,428)( 13,429)( 14,430)( 15,431)
( 16,432)( 17,435)( 18,436)( 19,433)( 20,434)( 21,439)( 22,440)( 23,437)
( 24,438)( 25,443)( 26,444)( 27,441)( 28,442)( 29,447)( 30,448)( 31,445)
( 32,446)( 33,401)( 34,402)( 35,403)( 36,404)( 37,405)( 38,406)( 39,407)
( 40,408)( 41,409)( 42,410)( 43,411)( 44,412)( 45,413)( 46,414)( 47,415)
( 48,416)( 49,385)( 50,386)( 51,387)( 52,388)( 53,389)( 54,390)( 55,391)
( 56,392)( 57,393)( 58,394)( 59,395)( 60,396)( 61,397)( 62,398)( 63,399)
( 64,400)( 65,494)( 66,493)( 67,496)( 68,495)( 69,489)( 70,490)( 71,491)
( 72,492)( 73,485)( 74,486)( 75,487)( 76,488)( 77,482)( 78,481)( 79,484)
( 80,483)( 81,512)( 82,511)( 83,510)( 84,509)( 85,507)( 86,508)( 87,505)
( 88,506)( 89,503)( 90,504)( 91,501)( 92,502)( 93,500)( 94,499)( 95,498)
( 96,497)( 97,478)( 98,477)( 99,480)(100,479)(101,473)(102,474)(103,475)
(104,476)(105,469)(106,470)(107,471)(108,472)(109,466)(110,465)(111,468)
(112,467)(113,462)(114,461)(115,464)(116,463)(117,457)(118,458)(119,459)
(120,460)(121,453)(122,454)(123,455)(124,456)(125,450)(126,449)(127,452)
(128,451)(129,305)(130,306)(131,307)(132,308)(133,309)(134,310)(135,311)
(136,312)(137,313)(138,314)(139,315)(140,316)(141,317)(142,318)(143,319)
(144,320)(145,289)(146,290)(147,291)(148,292)(149,293)(150,294)(151,295)
(152,296)(153,297)(154,298)(155,299)(156,300)(157,301)(158,302)(159,303)
(160,304)(161,257)(162,258)(163,259)(164,260)(165,261)(166,262)(167,263)
(168,264)(169,265)(170,266)(171,267)(172,268)(173,269)(174,270)(175,271)
(176,272)(177,275)(178,276)(179,273)(180,274)(181,279)(182,280)(183,277)
(184,278)(185,283)(186,284)(187,281)(188,282)(189,287)(190,288)(191,285)
(192,286)(193,382)(194,381)(195,384)(196,383)(197,377)(198,378)(199,379)
(200,380)(201,373)(202,374)(203,375)(204,376)(205,370)(206,369)(207,372)
(208,371)(209,366)(210,365)(211,368)(212,367)(213,361)(214,362)(215,363)
(216,364)(217,357)(218,358)(219,359)(220,360)(221,354)(222,353)(223,356)
(224,355)(225,334)(226,333)(227,336)(228,335)(229,329)(230,330)(231,331)
(232,332)(233,325)(234,326)(235,327)(236,328)(237,322)(238,321)(239,324)
(240,323)(241,352)(242,351)(243,350)(244,349)(245,347)(246,348)(247,345)
(248,346)(249,343)(250,344)(251,341)(252,342)(253,340)(254,339)(255,338)
(256,337);
s2 := 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);
s3 := Sym(512)!( 1,161)( 2,162)( 3,163)( 4,164)( 5,166)( 6,165)( 7,168)
( 8,167)( 9,170)( 10,169)( 11,172)( 12,171)( 13,173)( 14,174)( 15,175)
( 16,176)( 17,177)( 18,178)( 19,179)( 20,180)( 21,182)( 22,181)( 23,184)
( 24,183)( 25,186)( 26,185)( 27,188)( 28,187)( 29,189)( 30,190)( 31,191)
( 32,192)( 33,129)( 34,130)( 35,131)( 36,132)( 37,134)( 38,133)( 39,136)
( 40,135)( 41,138)( 42,137)( 43,140)( 44,139)( 45,141)( 46,142)( 47,143)
( 48,144)( 49,145)( 50,146)( 51,147)( 52,148)( 53,150)( 54,149)( 55,152)
( 56,151)( 57,154)( 58,153)( 59,156)( 60,155)( 61,157)( 62,158)( 63,159)
( 64,160)( 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)(261,422)(262,421)(263,424)
(264,423)(265,426)(266,425)(267,428)(268,427)(269,429)(270,430)(271,431)
(272,432)(273,433)(274,434)(275,435)(276,436)(277,438)(278,437)(279,440)
(280,439)(281,442)(282,441)(283,444)(284,443)(285,445)(286,446)(287,447)
(288,448)(289,385)(290,386)(291,387)(292,388)(293,390)(294,389)(295,392)
(296,391)(297,394)(298,393)(299,396)(300,395)(301,397)(302,398)(303,399)
(304,400)(305,401)(306,402)(307,403)(308,404)(309,406)(310,405)(311,408)
(312,407)(313,410)(314,409)(315,412)(316,411)(317,413)(318,414)(319,415)
(320,416)(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);
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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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