Polytope of Type {8,4,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,4,4}*512d
if this polytope has a name.
Group : SmallGroup(512,407039)
Rank : 4
Schlafli Type : {8,4,4}
Number of vertices, edges, etc : 16, 32, 16, 4
Order of s0s1s2s3 : 4
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 : {4,4,4}*256b, {8,4,2}*256b
4-fold quotients : {4,4,4}*128, {4,4,2}*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, 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, 50)( 18, 49)( 19, 52)( 20, 51)( 21, 54)( 22, 53)( 23, 56)( 24, 55)
( 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)
( 73,108)( 74,107)( 75,106)( 76,105)( 77,112)( 78,111)( 79,110)( 80,109)
( 81,114)( 82,113)( 83,116)( 84,115)( 85,118)( 86,117)( 87,120)( 88,119)
( 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)
(137,172)(138,171)(139,170)(140,169)(141,176)(142,175)(143,174)(144,173)
(145,178)(146,177)(147,180)(148,179)(149,182)(150,181)(151,184)(152,183)
(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)
(201,236)(202,235)(203,234)(204,233)(205,240)(206,239)(207,238)(208,237)
(209,242)(210,241)(211,244)(212,243)(213,246)(214,245)(215,248)(216,247)
(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)
(265,300)(266,299)(267,298)(268,297)(269,304)(270,303)(271,302)(272,301)
(273,306)(274,305)(275,308)(276,307)(277,310)(278,309)(279,312)(280,311)
(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)
(329,364)(330,363)(331,362)(332,361)(333,368)(334,367)(335,366)(336,365)
(337,370)(338,369)(339,372)(340,371)(341,374)(342,373)(343,376)(344,375)
(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)
(393,428)(394,427)(395,426)(396,425)(397,432)(398,431)(399,430)(400,429)
(401,434)(402,433)(403,436)(404,435)(405,438)(406,437)(407,440)(408,439)
(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)
(457,492)(458,491)(459,490)(460,489)(461,496)(462,495)(463,494)(464,493)
(465,498)(466,497)(467,500)(468,499)(469,502)(470,501)(471,504)(472,503)
(473,507)(474,508)(475,505)(476,506)(477,511)(478,512)(479,509)(480,510);;
s1 := ( 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)
( 17,274)( 18,273)( 19,275)( 20,276)( 21,277)( 22,278)( 23,280)( 24,279)
( 25,282)( 26,281)( 27,283)( 28,284)( 29,285)( 30,286)( 31,288)( 32,287)
( 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)
( 81,345)( 82,346)( 83,348)( 84,347)( 85,350)( 86,349)( 87,351)( 88,352)
( 89,337)( 90,338)( 91,340)( 92,339)( 93,342)( 94,341)( 95,343)( 96,344)
( 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)
(177,434)(178,433)(179,435)(180,436)(181,437)(182,438)(183,440)(184,439)
(185,442)(186,441)(187,443)(188,444)(189,445)(190,446)(191,448)(192,447)
(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)
(241,505)(242,506)(243,508)(244,507)(245,510)(246,509)(247,511)(248,512)
(249,497)(250,498)(251,500)(252,499)(253,502)(254,501)(255,503)(256,504);;
s2 := ( 1, 65)( 2, 66)( 3, 67)( 4, 68)( 5, 69)( 6, 70)( 7, 71)( 8, 72)
( 9, 73)( 10, 74)( 11, 75)( 12, 76)( 13, 77)( 14, 78)( 15, 79)( 16, 80)
( 17, 83)( 18, 84)( 19, 81)( 20, 82)( 21, 87)( 22, 88)( 23, 85)( 24, 86)
( 25, 91)( 26, 92)( 27, 89)( 28, 90)( 29, 95)( 30, 96)( 31, 93)( 32, 94)
( 33, 97)( 34, 98)( 35, 99)( 36,100)( 37,101)( 38,102)( 39,103)( 40,104)
( 41,105)( 42,106)( 43,107)( 44,108)( 45,109)( 46,110)( 47,111)( 48,112)
( 49,115)( 50,116)( 51,113)( 52,114)( 53,119)( 54,120)( 55,117)( 56,118)
( 57,123)( 58,124)( 59,121)( 60,122)( 61,127)( 62,128)( 63,125)( 64,126)
(129,193)(130,194)(131,195)(132,196)(133,197)(134,198)(135,199)(136,200)
(137,201)(138,202)(139,203)(140,204)(141,205)(142,206)(143,207)(144,208)
(145,211)(146,212)(147,209)(148,210)(149,215)(150,216)(151,213)(152,214)
(153,219)(154,220)(155,217)(156,218)(157,223)(158,224)(159,221)(160,222)
(161,225)(162,226)(163,227)(164,228)(165,229)(166,230)(167,231)(168,232)
(169,233)(170,234)(171,235)(172,236)(173,237)(174,238)(175,239)(176,240)
(177,243)(178,244)(179,241)(180,242)(181,247)(182,248)(183,245)(184,246)
(185,251)(186,252)(187,249)(188,250)(189,255)(190,256)(191,253)(192,254)
(257,321)(258,322)(259,323)(260,324)(261,325)(262,326)(263,327)(264,328)
(265,329)(266,330)(267,331)(268,332)(269,333)(270,334)(271,335)(272,336)
(273,339)(274,340)(275,337)(276,338)(277,343)(278,344)(279,341)(280,342)
(281,347)(282,348)(283,345)(284,346)(285,351)(286,352)(287,349)(288,350)
(289,353)(290,354)(291,355)(292,356)(293,357)(294,358)(295,359)(296,360)
(297,361)(298,362)(299,363)(300,364)(301,365)(302,366)(303,367)(304,368)
(305,371)(306,372)(307,369)(308,370)(309,375)(310,376)(311,373)(312,374)
(313,379)(314,380)(315,377)(316,378)(317,383)(318,384)(319,381)(320,382)
(385,449)(386,450)(387,451)(388,452)(389,453)(390,454)(391,455)(392,456)
(393,457)(394,458)(395,459)(396,460)(397,461)(398,462)(399,463)(400,464)
(401,467)(402,468)(403,465)(404,466)(405,471)(406,472)(407,469)(408,470)
(409,475)(410,476)(411,473)(412,474)(413,479)(414,480)(415,477)(416,478)
(417,481)(418,482)(419,483)(420,484)(421,485)(422,486)(423,487)(424,488)
(425,489)(426,490)(427,491)(428,492)(429,493)(430,494)(431,495)(432,496)
(433,499)(434,500)(435,497)(436,498)(437,503)(438,504)(439,501)(440,502)
(441,507)(442,508)(443,505)(444,506)(445,511)(446,512)(447,509)(448,510);;
s3 := ( 1,180)( 2,179)( 3,178)( 4,177)( 5,184)( 6,183)( 7,182)( 8,181)
( 9,188)( 10,187)( 11,186)( 12,185)( 13,192)( 14,191)( 15,190)( 16,189)
( 17,163)( 18,164)( 19,161)( 20,162)( 21,167)( 22,168)( 23,165)( 24,166)
( 25,171)( 26,172)( 27,169)( 28,170)( 29,175)( 30,176)( 31,173)( 32,174)
( 33,147)( 34,148)( 35,145)( 36,146)( 37,151)( 38,152)( 39,149)( 40,150)
( 41,155)( 42,156)( 43,153)( 44,154)( 45,159)( 46,160)( 47,157)( 48,158)
( 49,132)( 50,131)( 51,130)( 52,129)( 53,136)( 54,135)( 55,134)( 56,133)
( 57,140)( 58,139)( 59,138)( 60,137)( 61,144)( 62,143)( 63,142)( 64,141)
( 65,248)( 66,247)( 67,246)( 68,245)( 69,244)( 70,243)( 71,242)( 72,241)
( 73,256)( 74,255)( 75,254)( 76,253)( 77,252)( 78,251)( 79,250)( 80,249)
( 81,231)( 82,232)( 83,229)( 84,230)( 85,227)( 86,228)( 87,225)( 88,226)
( 89,239)( 90,240)( 91,237)( 92,238)( 93,235)( 94,236)( 95,233)( 96,234)
( 97,215)( 98,216)( 99,213)(100,214)(101,211)(102,212)(103,209)(104,210)
(105,223)(106,224)(107,221)(108,222)(109,219)(110,220)(111,217)(112,218)
(113,200)(114,199)(115,198)(116,197)(117,196)(118,195)(119,194)(120,193)
(121,208)(122,207)(123,206)(124,205)(125,204)(126,203)(127,202)(128,201)
(257,436)(258,435)(259,434)(260,433)(261,440)(262,439)(263,438)(264,437)
(265,444)(266,443)(267,442)(268,441)(269,448)(270,447)(271,446)(272,445)
(273,419)(274,420)(275,417)(276,418)(277,423)(278,424)(279,421)(280,422)
(281,427)(282,428)(283,425)(284,426)(285,431)(286,432)(287,429)(288,430)
(289,403)(290,404)(291,401)(292,402)(293,407)(294,408)(295,405)(296,406)
(297,411)(298,412)(299,409)(300,410)(301,415)(302,416)(303,413)(304,414)
(305,388)(306,387)(307,386)(308,385)(309,392)(310,391)(311,390)(312,389)
(313,396)(314,395)(315,394)(316,393)(317,400)(318,399)(319,398)(320,397)
(321,504)(322,503)(323,502)(324,501)(325,500)(326,499)(327,498)(328,497)
(329,512)(330,511)(331,510)(332,509)(333,508)(334,507)(335,506)(336,505)
(337,487)(338,488)(339,485)(340,486)(341,483)(342,484)(343,481)(344,482)
(345,495)(346,496)(347,493)(348,494)(349,491)(350,492)(351,489)(352,490)
(353,471)(354,472)(355,469)(356,470)(357,467)(358,468)(359,465)(360,466)
(361,479)(362,480)(363,477)(364,478)(365,475)(366,476)(367,473)(368,474)
(369,456)(370,455)(371,454)(372,453)(373,452)(374,451)(375,450)(376,449)
(377,464)(378,463)(379,462)(380,461)(381,460)(382,459)(383,458)(384,457);;
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*s3*s2*s3*s2*s3*s2*s3,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1 ];;
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, 44)( 10, 43)( 11, 42)( 12, 41)( 13, 48)( 14, 47)( 15, 46)
( 16, 45)( 17, 50)( 18, 49)( 19, 52)( 20, 51)( 21, 54)( 22, 53)( 23, 56)
( 24, 55)( 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)( 73,108)( 74,107)( 75,106)( 76,105)( 77,112)( 78,111)( 79,110)
( 80,109)( 81,114)( 82,113)( 83,116)( 84,115)( 85,118)( 86,117)( 87,120)
( 88,119)( 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)(137,172)(138,171)(139,170)(140,169)(141,176)(142,175)(143,174)
(144,173)(145,178)(146,177)(147,180)(148,179)(149,182)(150,181)(151,184)
(152,183)(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)(201,236)(202,235)(203,234)(204,233)(205,240)(206,239)(207,238)
(208,237)(209,242)(210,241)(211,244)(212,243)(213,246)(214,245)(215,248)
(216,247)(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)(265,300)(266,299)(267,298)(268,297)(269,304)(270,303)(271,302)
(272,301)(273,306)(274,305)(275,308)(276,307)(277,310)(278,309)(279,312)
(280,311)(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)(329,364)(330,363)(331,362)(332,361)(333,368)(334,367)(335,366)
(336,365)(337,370)(338,369)(339,372)(340,371)(341,374)(342,373)(343,376)
(344,375)(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)(393,428)(394,427)(395,426)(396,425)(397,432)(398,431)(399,430)
(400,429)(401,434)(402,433)(403,436)(404,435)(405,438)(406,437)(407,440)
(408,439)(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)(457,492)(458,491)(459,490)(460,489)(461,496)(462,495)(463,494)
(464,493)(465,498)(466,497)(467,500)(468,499)(469,502)(470,501)(471,504)
(472,503)(473,507)(474,508)(475,505)(476,506)(477,511)(478,512)(479,509)
(480,510);
s1 := 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)( 17,274)( 18,273)( 19,275)( 20,276)( 21,277)( 22,278)( 23,280)
( 24,279)( 25,282)( 26,281)( 27,283)( 28,284)( 29,285)( 30,286)( 31,288)
( 32,287)( 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)( 81,345)( 82,346)( 83,348)( 84,347)( 85,350)( 86,349)( 87,351)
( 88,352)( 89,337)( 90,338)( 91,340)( 92,339)( 93,342)( 94,341)( 95,343)
( 96,344)( 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)(177,434)(178,433)(179,435)(180,436)(181,437)(182,438)(183,440)
(184,439)(185,442)(186,441)(187,443)(188,444)(189,445)(190,446)(191,448)
(192,447)(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)(241,505)(242,506)(243,508)(244,507)(245,510)(246,509)(247,511)
(248,512)(249,497)(250,498)(251,500)(252,499)(253,502)(254,501)(255,503)
(256,504);
s2 := Sym(512)!( 1, 65)( 2, 66)( 3, 67)( 4, 68)( 5, 69)( 6, 70)( 7, 71)
( 8, 72)( 9, 73)( 10, 74)( 11, 75)( 12, 76)( 13, 77)( 14, 78)( 15, 79)
( 16, 80)( 17, 83)( 18, 84)( 19, 81)( 20, 82)( 21, 87)( 22, 88)( 23, 85)
( 24, 86)( 25, 91)( 26, 92)( 27, 89)( 28, 90)( 29, 95)( 30, 96)( 31, 93)
( 32, 94)( 33, 97)( 34, 98)( 35, 99)( 36,100)( 37,101)( 38,102)( 39,103)
( 40,104)( 41,105)( 42,106)( 43,107)( 44,108)( 45,109)( 46,110)( 47,111)
( 48,112)( 49,115)( 50,116)( 51,113)( 52,114)( 53,119)( 54,120)( 55,117)
( 56,118)( 57,123)( 58,124)( 59,121)( 60,122)( 61,127)( 62,128)( 63,125)
( 64,126)(129,193)(130,194)(131,195)(132,196)(133,197)(134,198)(135,199)
(136,200)(137,201)(138,202)(139,203)(140,204)(141,205)(142,206)(143,207)
(144,208)(145,211)(146,212)(147,209)(148,210)(149,215)(150,216)(151,213)
(152,214)(153,219)(154,220)(155,217)(156,218)(157,223)(158,224)(159,221)
(160,222)(161,225)(162,226)(163,227)(164,228)(165,229)(166,230)(167,231)
(168,232)(169,233)(170,234)(171,235)(172,236)(173,237)(174,238)(175,239)
(176,240)(177,243)(178,244)(179,241)(180,242)(181,247)(182,248)(183,245)
(184,246)(185,251)(186,252)(187,249)(188,250)(189,255)(190,256)(191,253)
(192,254)(257,321)(258,322)(259,323)(260,324)(261,325)(262,326)(263,327)
(264,328)(265,329)(266,330)(267,331)(268,332)(269,333)(270,334)(271,335)
(272,336)(273,339)(274,340)(275,337)(276,338)(277,343)(278,344)(279,341)
(280,342)(281,347)(282,348)(283,345)(284,346)(285,351)(286,352)(287,349)
(288,350)(289,353)(290,354)(291,355)(292,356)(293,357)(294,358)(295,359)
(296,360)(297,361)(298,362)(299,363)(300,364)(301,365)(302,366)(303,367)
(304,368)(305,371)(306,372)(307,369)(308,370)(309,375)(310,376)(311,373)
(312,374)(313,379)(314,380)(315,377)(316,378)(317,383)(318,384)(319,381)
(320,382)(385,449)(386,450)(387,451)(388,452)(389,453)(390,454)(391,455)
(392,456)(393,457)(394,458)(395,459)(396,460)(397,461)(398,462)(399,463)
(400,464)(401,467)(402,468)(403,465)(404,466)(405,471)(406,472)(407,469)
(408,470)(409,475)(410,476)(411,473)(412,474)(413,479)(414,480)(415,477)
(416,478)(417,481)(418,482)(419,483)(420,484)(421,485)(422,486)(423,487)
(424,488)(425,489)(426,490)(427,491)(428,492)(429,493)(430,494)(431,495)
(432,496)(433,499)(434,500)(435,497)(436,498)(437,503)(438,504)(439,501)
(440,502)(441,507)(442,508)(443,505)(444,506)(445,511)(446,512)(447,509)
(448,510);
s3 := Sym(512)!( 1,180)( 2,179)( 3,178)( 4,177)( 5,184)( 6,183)( 7,182)
( 8,181)( 9,188)( 10,187)( 11,186)( 12,185)( 13,192)( 14,191)( 15,190)
( 16,189)( 17,163)( 18,164)( 19,161)( 20,162)( 21,167)( 22,168)( 23,165)
( 24,166)( 25,171)( 26,172)( 27,169)( 28,170)( 29,175)( 30,176)( 31,173)
( 32,174)( 33,147)( 34,148)( 35,145)( 36,146)( 37,151)( 38,152)( 39,149)
( 40,150)( 41,155)( 42,156)( 43,153)( 44,154)( 45,159)( 46,160)( 47,157)
( 48,158)( 49,132)( 50,131)( 51,130)( 52,129)( 53,136)( 54,135)( 55,134)
( 56,133)( 57,140)( 58,139)( 59,138)( 60,137)( 61,144)( 62,143)( 63,142)
( 64,141)( 65,248)( 66,247)( 67,246)( 68,245)( 69,244)( 70,243)( 71,242)
( 72,241)( 73,256)( 74,255)( 75,254)( 76,253)( 77,252)( 78,251)( 79,250)
( 80,249)( 81,231)( 82,232)( 83,229)( 84,230)( 85,227)( 86,228)( 87,225)
( 88,226)( 89,239)( 90,240)( 91,237)( 92,238)( 93,235)( 94,236)( 95,233)
( 96,234)( 97,215)( 98,216)( 99,213)(100,214)(101,211)(102,212)(103,209)
(104,210)(105,223)(106,224)(107,221)(108,222)(109,219)(110,220)(111,217)
(112,218)(113,200)(114,199)(115,198)(116,197)(117,196)(118,195)(119,194)
(120,193)(121,208)(122,207)(123,206)(124,205)(125,204)(126,203)(127,202)
(128,201)(257,436)(258,435)(259,434)(260,433)(261,440)(262,439)(263,438)
(264,437)(265,444)(266,443)(267,442)(268,441)(269,448)(270,447)(271,446)
(272,445)(273,419)(274,420)(275,417)(276,418)(277,423)(278,424)(279,421)
(280,422)(281,427)(282,428)(283,425)(284,426)(285,431)(286,432)(287,429)
(288,430)(289,403)(290,404)(291,401)(292,402)(293,407)(294,408)(295,405)
(296,406)(297,411)(298,412)(299,409)(300,410)(301,415)(302,416)(303,413)
(304,414)(305,388)(306,387)(307,386)(308,385)(309,392)(310,391)(311,390)
(312,389)(313,396)(314,395)(315,394)(316,393)(317,400)(318,399)(319,398)
(320,397)(321,504)(322,503)(323,502)(324,501)(325,500)(326,499)(327,498)
(328,497)(329,512)(330,511)(331,510)(332,509)(333,508)(334,507)(335,506)
(336,505)(337,487)(338,488)(339,485)(340,486)(341,483)(342,484)(343,481)
(344,482)(345,495)(346,496)(347,493)(348,494)(349,491)(350,492)(351,489)
(352,490)(353,471)(354,472)(355,469)(356,470)(357,467)(358,468)(359,465)
(360,466)(361,479)(362,480)(363,477)(364,478)(365,475)(366,476)(367,473)
(368,474)(369,456)(370,455)(371,454)(372,453)(373,452)(374,451)(375,450)
(376,449)(377,464)(378,463)(379,462)(380,461)(381,460)(382,459)(383,458)
(384,457);
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*s3*s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1 >;
References : None.
to this polytope