Polytope of Type {4,16,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,16,4}*512b
if this polytope has a name.
Group : SmallGroup(512,407099)
Rank : 4
Schlafli Type : {4,16,4}
Number of vertices, edges, etc : 4, 32, 32, 4
Order of s0s1s2s3 : 16
Order of s0s1s2s3s2s1 : 2
Special Properties :
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 : {4,8,4}*256d
4-fold quotients : {4,4,4}*128, {2,8,4}*128a, {4,8,2}*128a
8-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64, {2,8,2}*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, 42)( 10, 41)( 11, 44)( 12, 43)( 13, 46)( 14, 45)( 15, 48)( 16, 47)
( 17, 49)( 18, 50)( 19, 51)( 20, 52)( 21, 53)( 22, 54)( 23, 55)( 24, 56)
( 25, 58)( 26, 57)( 27, 60)( 28, 59)( 29, 62)( 30, 61)( 31, 64)( 32, 63)
( 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)
( 81,113)( 82,114)( 83,115)( 84,116)( 85,117)( 86,118)( 87,119)( 88,120)
( 89,122)( 90,121)( 91,124)( 92,123)( 93,126)( 94,125)( 95,128)( 96,127)
(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)
(145,177)(146,178)(147,179)(148,180)(149,181)(150,182)(151,183)(152,184)
(153,186)(154,185)(155,188)(156,187)(157,190)(158,189)(159,192)(160,191)
(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)
(209,241)(210,242)(211,243)(212,244)(213,245)(214,246)(215,247)(216,248)
(217,250)(218,249)(219,252)(220,251)(221,254)(222,253)(223,256)(224,255)
(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)
(273,305)(274,306)(275,307)(276,308)(277,309)(278,310)(279,311)(280,312)
(281,314)(282,313)(283,316)(284,315)(285,318)(286,317)(287,320)(288,319)
(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)
(337,369)(338,370)(339,371)(340,372)(341,373)(342,374)(343,375)(344,376)
(345,378)(346,377)(347,380)(348,379)(349,382)(350,381)(351,384)(352,383)
(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)
(401,433)(402,434)(403,435)(404,436)(405,437)(406,438)(407,439)(408,440)
(409,442)(410,441)(411,444)(412,443)(413,446)(414,445)(415,448)(416,447)
(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)
(465,497)(466,498)(467,499)(468,500)(469,501)(470,502)(471,503)(472,504)
(473,506)(474,505)(475,508)(476,507)(477,510)(478,509)(479,512)(480,511);;
s1 := ( 1,257)( 2,258)( 3,260)( 4,259)( 5,262)( 6,261)( 7,263)( 8,264)
( 9,267)( 10,268)( 11,265)( 12,266)( 13,272)( 14,271)( 15,270)( 16,269)
( 17,273)( 18,274)( 19,276)( 20,275)( 21,278)( 22,277)( 23,279)( 24,280)
( 25,283)( 26,284)( 27,281)( 28,282)( 29,288)( 30,287)( 31,286)( 32,285)
( 33,305)( 34,306)( 35,308)( 36,307)( 37,310)( 38,309)( 39,311)( 40,312)
( 41,315)( 42,316)( 43,313)( 44,314)( 45,320)( 46,319)( 47,318)( 48,317)
( 49,289)( 50,290)( 51,292)( 52,291)( 53,294)( 54,293)( 55,295)( 56,296)
( 57,299)( 58,300)( 59,297)( 60,298)( 61,304)( 62,303)( 63,302)( 64,301)
( 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)
( 97,378)( 98,377)( 99,379)(100,380)(101,381)(102,382)(103,384)(104,383)
(105,370)(106,369)(107,371)(108,372)(109,373)(110,374)(111,376)(112,375)
(113,362)(114,361)(115,363)(116,364)(117,365)(118,366)(119,368)(120,367)
(121,354)(122,353)(123,355)(124,356)(125,357)(126,358)(127,360)(128,359)
(129,401)(130,402)(131,404)(132,403)(133,406)(134,405)(135,407)(136,408)
(137,411)(138,412)(139,409)(140,410)(141,416)(142,415)(143,414)(144,413)
(145,385)(146,386)(147,388)(148,387)(149,390)(150,389)(151,391)(152,392)
(153,395)(154,396)(155,393)(156,394)(157,400)(158,399)(159,398)(160,397)
(161,417)(162,418)(163,420)(164,419)(165,422)(166,421)(167,423)(168,424)
(169,427)(170,428)(171,425)(172,426)(173,432)(174,431)(175,430)(176,429)
(177,433)(178,434)(179,436)(180,435)(181,438)(182,437)(183,439)(184,440)
(185,443)(186,444)(187,441)(188,442)(189,448)(190,447)(191,446)(192,445)
(193,474)(194,473)(195,475)(196,476)(197,477)(198,478)(199,480)(200,479)
(201,466)(202,465)(203,467)(204,468)(205,469)(206,470)(207,472)(208,471)
(209,458)(210,457)(211,459)(212,460)(213,461)(214,462)(215,464)(216,463)
(217,450)(218,449)(219,451)(220,452)(221,453)(222,454)(223,456)(224,455)
(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, 68)( 4, 67)( 5, 69)( 6, 70)( 7, 72)( 8, 71)
( 9, 75)( 10, 76)( 11, 73)( 12, 74)( 13, 79)( 14, 80)( 15, 77)( 16, 78)
( 17, 82)( 18, 81)( 19, 83)( 20, 84)( 21, 86)( 22, 85)( 23, 87)( 24, 88)
( 25, 92)( 26, 91)( 27, 90)( 28, 89)( 29, 96)( 30, 95)( 31, 94)( 32, 93)
( 33, 97)( 34, 98)( 35,100)( 36, 99)( 37,101)( 38,102)( 39,104)( 40,103)
( 41,107)( 42,108)( 43,105)( 44,106)( 45,111)( 46,112)( 47,109)( 48,110)
( 49,114)( 50,113)( 51,115)( 52,116)( 53,118)( 54,117)( 55,119)( 56,120)
( 57,124)( 58,123)( 59,122)( 60,121)( 61,128)( 62,127)( 63,126)( 64,125)
(129,193)(130,194)(131,196)(132,195)(133,197)(134,198)(135,200)(136,199)
(137,203)(138,204)(139,201)(140,202)(141,207)(142,208)(143,205)(144,206)
(145,210)(146,209)(147,211)(148,212)(149,214)(150,213)(151,215)(152,216)
(153,220)(154,219)(155,218)(156,217)(157,224)(158,223)(159,222)(160,221)
(161,225)(162,226)(163,228)(164,227)(165,229)(166,230)(167,232)(168,231)
(169,235)(170,236)(171,233)(172,234)(173,239)(174,240)(175,237)(176,238)
(177,242)(178,241)(179,243)(180,244)(181,246)(182,245)(183,247)(184,248)
(185,252)(186,251)(187,250)(188,249)(189,256)(190,255)(191,254)(192,253)
(257,321)(258,322)(259,324)(260,323)(261,325)(262,326)(263,328)(264,327)
(265,331)(266,332)(267,329)(268,330)(269,335)(270,336)(271,333)(272,334)
(273,338)(274,337)(275,339)(276,340)(277,342)(278,341)(279,343)(280,344)
(281,348)(282,347)(283,346)(284,345)(285,352)(286,351)(287,350)(288,349)
(289,353)(290,354)(291,356)(292,355)(293,357)(294,358)(295,360)(296,359)
(297,363)(298,364)(299,361)(300,362)(301,367)(302,368)(303,365)(304,366)
(305,370)(306,369)(307,371)(308,372)(309,374)(310,373)(311,375)(312,376)
(313,380)(314,379)(315,378)(316,377)(317,384)(318,383)(319,382)(320,381)
(385,449)(386,450)(387,452)(388,451)(389,453)(390,454)(391,456)(392,455)
(393,459)(394,460)(395,457)(396,458)(397,463)(398,464)(399,461)(400,462)
(401,466)(402,465)(403,467)(404,468)(405,470)(406,469)(407,471)(408,472)
(409,476)(410,475)(411,474)(412,473)(413,480)(414,479)(415,478)(416,477)
(417,481)(418,482)(419,484)(420,483)(421,485)(422,486)(423,488)(424,487)
(425,491)(426,492)(427,489)(428,490)(429,495)(430,496)(431,493)(432,494)
(433,498)(434,497)(435,499)(436,500)(437,502)(438,501)(439,503)(440,504)
(441,508)(442,507)(443,506)(444,505)(445,512)(446,511)(447,510)(448,509);;
s3 := ( 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);;
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*s3*s2*s1*s2*s3*s1*s0*s1*s2*s1,
s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*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, 42)( 10, 41)( 11, 44)( 12, 43)( 13, 46)( 14, 45)( 15, 48)
( 16, 47)( 17, 49)( 18, 50)( 19, 51)( 20, 52)( 21, 53)( 22, 54)( 23, 55)
( 24, 56)( 25, 58)( 26, 57)( 27, 60)( 28, 59)( 29, 62)( 30, 61)( 31, 64)
( 32, 63)( 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)( 81,113)( 82,114)( 83,115)( 84,116)( 85,117)( 86,118)( 87,119)
( 88,120)( 89,122)( 90,121)( 91,124)( 92,123)( 93,126)( 94,125)( 95,128)
( 96,127)(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)(145,177)(146,178)(147,179)(148,180)(149,181)(150,182)(151,183)
(152,184)(153,186)(154,185)(155,188)(156,187)(157,190)(158,189)(159,192)
(160,191)(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)(209,241)(210,242)(211,243)(212,244)(213,245)(214,246)(215,247)
(216,248)(217,250)(218,249)(219,252)(220,251)(221,254)(222,253)(223,256)
(224,255)(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)(273,305)(274,306)(275,307)(276,308)(277,309)(278,310)(279,311)
(280,312)(281,314)(282,313)(283,316)(284,315)(285,318)(286,317)(287,320)
(288,319)(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)(337,369)(338,370)(339,371)(340,372)(341,373)(342,374)(343,375)
(344,376)(345,378)(346,377)(347,380)(348,379)(349,382)(350,381)(351,384)
(352,383)(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)(401,433)(402,434)(403,435)(404,436)(405,437)(406,438)(407,439)
(408,440)(409,442)(410,441)(411,444)(412,443)(413,446)(414,445)(415,448)
(416,447)(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)(465,497)(466,498)(467,499)(468,500)(469,501)(470,502)(471,503)
(472,504)(473,506)(474,505)(475,508)(476,507)(477,510)(478,509)(479,512)
(480,511);
s1 := Sym(512)!( 1,257)( 2,258)( 3,260)( 4,259)( 5,262)( 6,261)( 7,263)
( 8,264)( 9,267)( 10,268)( 11,265)( 12,266)( 13,272)( 14,271)( 15,270)
( 16,269)( 17,273)( 18,274)( 19,276)( 20,275)( 21,278)( 22,277)( 23,279)
( 24,280)( 25,283)( 26,284)( 27,281)( 28,282)( 29,288)( 30,287)( 31,286)
( 32,285)( 33,305)( 34,306)( 35,308)( 36,307)( 37,310)( 38,309)( 39,311)
( 40,312)( 41,315)( 42,316)( 43,313)( 44,314)( 45,320)( 46,319)( 47,318)
( 48,317)( 49,289)( 50,290)( 51,292)( 52,291)( 53,294)( 54,293)( 55,295)
( 56,296)( 57,299)( 58,300)( 59,297)( 60,298)( 61,304)( 62,303)( 63,302)
( 64,301)( 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)( 97,378)( 98,377)( 99,379)(100,380)(101,381)(102,382)(103,384)
(104,383)(105,370)(106,369)(107,371)(108,372)(109,373)(110,374)(111,376)
(112,375)(113,362)(114,361)(115,363)(116,364)(117,365)(118,366)(119,368)
(120,367)(121,354)(122,353)(123,355)(124,356)(125,357)(126,358)(127,360)
(128,359)(129,401)(130,402)(131,404)(132,403)(133,406)(134,405)(135,407)
(136,408)(137,411)(138,412)(139,409)(140,410)(141,416)(142,415)(143,414)
(144,413)(145,385)(146,386)(147,388)(148,387)(149,390)(150,389)(151,391)
(152,392)(153,395)(154,396)(155,393)(156,394)(157,400)(158,399)(159,398)
(160,397)(161,417)(162,418)(163,420)(164,419)(165,422)(166,421)(167,423)
(168,424)(169,427)(170,428)(171,425)(172,426)(173,432)(174,431)(175,430)
(176,429)(177,433)(178,434)(179,436)(180,435)(181,438)(182,437)(183,439)
(184,440)(185,443)(186,444)(187,441)(188,442)(189,448)(190,447)(191,446)
(192,445)(193,474)(194,473)(195,475)(196,476)(197,477)(198,478)(199,480)
(200,479)(201,466)(202,465)(203,467)(204,468)(205,469)(206,470)(207,472)
(208,471)(209,458)(210,457)(211,459)(212,460)(213,461)(214,462)(215,464)
(216,463)(217,450)(218,449)(219,451)(220,452)(221,453)(222,454)(223,456)
(224,455)(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, 68)( 4, 67)( 5, 69)( 6, 70)( 7, 72)
( 8, 71)( 9, 75)( 10, 76)( 11, 73)( 12, 74)( 13, 79)( 14, 80)( 15, 77)
( 16, 78)( 17, 82)( 18, 81)( 19, 83)( 20, 84)( 21, 86)( 22, 85)( 23, 87)
( 24, 88)( 25, 92)( 26, 91)( 27, 90)( 28, 89)( 29, 96)( 30, 95)( 31, 94)
( 32, 93)( 33, 97)( 34, 98)( 35,100)( 36, 99)( 37,101)( 38,102)( 39,104)
( 40,103)( 41,107)( 42,108)( 43,105)( 44,106)( 45,111)( 46,112)( 47,109)
( 48,110)( 49,114)( 50,113)( 51,115)( 52,116)( 53,118)( 54,117)( 55,119)
( 56,120)( 57,124)( 58,123)( 59,122)( 60,121)( 61,128)( 62,127)( 63,126)
( 64,125)(129,193)(130,194)(131,196)(132,195)(133,197)(134,198)(135,200)
(136,199)(137,203)(138,204)(139,201)(140,202)(141,207)(142,208)(143,205)
(144,206)(145,210)(146,209)(147,211)(148,212)(149,214)(150,213)(151,215)
(152,216)(153,220)(154,219)(155,218)(156,217)(157,224)(158,223)(159,222)
(160,221)(161,225)(162,226)(163,228)(164,227)(165,229)(166,230)(167,232)
(168,231)(169,235)(170,236)(171,233)(172,234)(173,239)(174,240)(175,237)
(176,238)(177,242)(178,241)(179,243)(180,244)(181,246)(182,245)(183,247)
(184,248)(185,252)(186,251)(187,250)(188,249)(189,256)(190,255)(191,254)
(192,253)(257,321)(258,322)(259,324)(260,323)(261,325)(262,326)(263,328)
(264,327)(265,331)(266,332)(267,329)(268,330)(269,335)(270,336)(271,333)
(272,334)(273,338)(274,337)(275,339)(276,340)(277,342)(278,341)(279,343)
(280,344)(281,348)(282,347)(283,346)(284,345)(285,352)(286,351)(287,350)
(288,349)(289,353)(290,354)(291,356)(292,355)(293,357)(294,358)(295,360)
(296,359)(297,363)(298,364)(299,361)(300,362)(301,367)(302,368)(303,365)
(304,366)(305,370)(306,369)(307,371)(308,372)(309,374)(310,373)(311,375)
(312,376)(313,380)(314,379)(315,378)(316,377)(317,384)(318,383)(319,382)
(320,381)(385,449)(386,450)(387,452)(388,451)(389,453)(390,454)(391,456)
(392,455)(393,459)(394,460)(395,457)(396,458)(397,463)(398,464)(399,461)
(400,462)(401,466)(402,465)(403,467)(404,468)(405,470)(406,469)(407,471)
(408,472)(409,476)(410,475)(411,474)(412,473)(413,480)(414,479)(415,478)
(416,477)(417,481)(418,482)(419,484)(420,483)(421,485)(422,486)(423,488)
(424,487)(425,491)(426,492)(427,489)(428,490)(429,495)(430,496)(431,493)
(432,494)(433,498)(434,497)(435,499)(436,500)(437,502)(438,501)(439,503)
(440,504)(441,508)(442,507)(443,506)(444,505)(445,512)(446,511)(447,510)
(448,509);
s3 := 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);
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*s3*s2*s1*s2*s3*s1*s0*s1*s2*s1,
s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1 >;
References : None.
to this polytope