Polytope of Type {4,64}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,64}*512b
if this polytope has a name.
Group : SmallGroup(512,60803)
Rank : 3
Schlafli Type : {4,64}
Number of vertices, edges, etc : 4, 128, 64
Order of s0s1s2 : 64
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
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 : {4,32}*256a
4-fold quotients : {4,16}*128a, {2,32}*128
8-fold quotients : {4,8}*64a, {2,16}*64
16-fold quotients : {4,4}*32, {2,8}*32
32-fold quotients : {2,4}*16, {4,2}*16
64-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 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, 81)( 18, 82)( 19, 83)( 20, 84)( 21, 85)( 22, 86)( 23, 87)( 24, 88)
( 25, 89)( 26, 90)( 27, 91)( 28, 92)( 29, 93)( 30, 94)( 31, 95)( 32, 96)
( 33, 98)( 34, 97)( 35,100)( 36, 99)( 37,102)( 38,101)( 39,104)( 40,103)
( 41,106)( 42,105)( 43,108)( 44,107)( 45,110)( 46,109)( 47,112)( 48,111)
( 49,114)( 50,113)( 51,116)( 52,115)( 53,118)( 54,117)( 55,120)( 56,119)
( 57,122)( 58,121)( 59,124)( 60,123)( 61,126)( 62,125)( 63,128)( 64,127)
(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)
(145,209)(146,210)(147,211)(148,212)(149,213)(150,214)(151,215)(152,216)
(153,217)(154,218)(155,219)(156,220)(157,221)(158,222)(159,223)(160,224)
(161,226)(162,225)(163,228)(164,227)(165,230)(166,229)(167,232)(168,231)
(169,234)(170,233)(171,236)(172,235)(173,238)(174,237)(175,240)(176,239)
(177,242)(178,241)(179,244)(180,243)(181,246)(182,245)(183,248)(184,247)
(185,250)(186,249)(187,252)(188,251)(189,254)(190,253)(191,256)(192,255)
(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)
(273,337)(274,338)(275,339)(276,340)(277,341)(278,342)(279,343)(280,344)
(281,345)(282,346)(283,347)(284,348)(285,349)(286,350)(287,351)(288,352)
(289,354)(290,353)(291,356)(292,355)(293,358)(294,357)(295,360)(296,359)
(297,362)(298,361)(299,364)(300,363)(301,366)(302,365)(303,368)(304,367)
(305,370)(306,369)(307,372)(308,371)(309,374)(310,373)(311,376)(312,375)
(313,378)(314,377)(315,380)(316,379)(317,382)(318,381)(319,384)(320,383)
(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)
(401,465)(402,466)(403,467)(404,468)(405,469)(406,470)(407,471)(408,472)
(409,473)(410,474)(411,475)(412,476)(413,477)(414,478)(415,479)(416,480)
(417,482)(418,481)(419,484)(420,483)(421,486)(422,485)(423,488)(424,487)
(425,490)(426,489)(427,492)(428,491)(429,494)(430,493)(431,496)(432,495)
(433,498)(434,497)(435,500)(436,499)(437,502)(438,501)(439,504)(440,503)
(441,506)(442,505)(443,508)(444,507)(445,510)(446,509)(447,512)(448,511);;
s1 := ( 1,257)( 2,258)( 3,260)( 4,259)( 5,263)( 6,264)( 7,261)( 8,262)
( 9,269)( 10,270)( 11,272)( 12,271)( 13,265)( 14,266)( 15,268)( 16,267)
( 17,273)( 18,274)( 19,276)( 20,275)( 21,279)( 22,280)( 23,277)( 24,278)
( 25,285)( 26,286)( 27,288)( 28,287)( 29,281)( 30,282)( 31,284)( 32,283)
( 33,297)( 34,298)( 35,300)( 36,299)( 37,303)( 38,304)( 39,301)( 40,302)
( 41,289)( 42,290)( 43,292)( 44,291)( 45,295)( 46,296)( 47,293)( 48,294)
( 49,313)( 50,314)( 51,316)( 52,315)( 53,319)( 54,320)( 55,317)( 56,318)
( 57,305)( 58,306)( 59,308)( 60,307)( 61,311)( 62,312)( 63,309)( 64,310)
( 65,337)( 66,338)( 67,340)( 68,339)( 69,343)( 70,344)( 71,341)( 72,342)
( 73,349)( 74,350)( 75,352)( 76,351)( 77,345)( 78,346)( 79,348)( 80,347)
( 81,321)( 82,322)( 83,324)( 84,323)( 85,327)( 86,328)( 87,325)( 88,326)
( 89,333)( 90,334)( 91,336)( 92,335)( 93,329)( 94,330)( 95,332)( 96,331)
( 97,377)( 98,378)( 99,380)(100,379)(101,383)(102,384)(103,381)(104,382)
(105,369)(106,370)(107,372)(108,371)(109,375)(110,376)(111,373)(112,374)
(113,361)(114,362)(115,364)(116,363)(117,367)(118,368)(119,365)(120,366)
(121,353)(122,354)(123,356)(124,355)(125,359)(126,360)(127,357)(128,358)
(129,417)(130,418)(131,420)(132,419)(133,423)(134,424)(135,421)(136,422)
(137,429)(138,430)(139,432)(140,431)(141,425)(142,426)(143,428)(144,427)
(145,433)(146,434)(147,436)(148,435)(149,439)(150,440)(151,437)(152,438)
(153,445)(154,446)(155,448)(156,447)(157,441)(158,442)(159,444)(160,443)
(161,385)(162,386)(163,388)(164,387)(165,391)(166,392)(167,389)(168,390)
(169,397)(170,398)(171,400)(172,399)(173,393)(174,394)(175,396)(176,395)
(177,401)(178,402)(179,404)(180,403)(181,407)(182,408)(183,405)(184,406)
(185,413)(186,414)(187,416)(188,415)(189,409)(190,410)(191,412)(192,411)
(193,498)(194,497)(195,499)(196,500)(197,504)(198,503)(199,502)(200,501)
(201,510)(202,509)(203,511)(204,512)(205,506)(206,505)(207,507)(208,508)
(209,482)(210,481)(211,483)(212,484)(213,488)(214,487)(215,486)(216,485)
(217,494)(218,493)(219,495)(220,496)(221,490)(222,489)(223,491)(224,492)
(225,466)(226,465)(227,467)(228,468)(229,472)(230,471)(231,470)(232,469)
(233,478)(234,477)(235,479)(236,480)(237,474)(238,473)(239,475)(240,476)
(241,450)(242,449)(243,451)(244,452)(245,456)(246,455)(247,454)(248,453)
(249,462)(250,461)(251,463)(252,464)(253,458)(254,457)(255,459)(256,460);;
s2 := ( 1,129)( 2,130)( 3,132)( 4,131)( 5,135)( 6,136)( 7,133)( 8,134)
( 9,141)( 10,142)( 11,144)( 12,143)( 13,137)( 14,138)( 15,140)( 16,139)
( 17,146)( 18,145)( 19,147)( 20,148)( 21,152)( 22,151)( 23,150)( 24,149)
( 25,158)( 26,157)( 27,159)( 28,160)( 29,154)( 30,153)( 31,155)( 32,156)
( 33,169)( 34,170)( 35,172)( 36,171)( 37,175)( 38,176)( 39,173)( 40,174)
( 41,161)( 42,162)( 43,164)( 44,163)( 45,167)( 46,168)( 47,165)( 48,166)
( 49,186)( 50,185)( 51,187)( 52,188)( 53,192)( 54,191)( 55,190)( 56,189)
( 57,178)( 58,177)( 59,179)( 60,180)( 61,184)( 62,183)( 63,182)( 64,181)
( 65,193)( 66,194)( 67,196)( 68,195)( 69,199)( 70,200)( 71,197)( 72,198)
( 73,205)( 74,206)( 75,208)( 76,207)( 77,201)( 78,202)( 79,204)( 80,203)
( 81,210)( 82,209)( 83,211)( 84,212)( 85,216)( 86,215)( 87,214)( 88,213)
( 89,222)( 90,221)( 91,223)( 92,224)( 93,218)( 94,217)( 95,219)( 96,220)
( 97,233)( 98,234)( 99,236)(100,235)(101,239)(102,240)(103,237)(104,238)
(105,225)(106,226)(107,228)(108,227)(109,231)(110,232)(111,229)(112,230)
(113,250)(114,249)(115,251)(116,252)(117,256)(118,255)(119,254)(120,253)
(121,242)(122,241)(123,243)(124,244)(125,248)(126,247)(127,246)(128,245)
(257,385)(258,386)(259,388)(260,387)(261,391)(262,392)(263,389)(264,390)
(265,397)(266,398)(267,400)(268,399)(269,393)(270,394)(271,396)(272,395)
(273,402)(274,401)(275,403)(276,404)(277,408)(278,407)(279,406)(280,405)
(281,414)(282,413)(283,415)(284,416)(285,410)(286,409)(287,411)(288,412)
(289,425)(290,426)(291,428)(292,427)(293,431)(294,432)(295,429)(296,430)
(297,417)(298,418)(299,420)(300,419)(301,423)(302,424)(303,421)(304,422)
(305,442)(306,441)(307,443)(308,444)(309,448)(310,447)(311,446)(312,445)
(313,434)(314,433)(315,435)(316,436)(317,440)(318,439)(319,438)(320,437)
(321,449)(322,450)(323,452)(324,451)(325,455)(326,456)(327,453)(328,454)
(329,461)(330,462)(331,464)(332,463)(333,457)(334,458)(335,460)(336,459)
(337,466)(338,465)(339,467)(340,468)(341,472)(342,471)(343,470)(344,469)
(345,478)(346,477)(347,479)(348,480)(349,474)(350,473)(351,475)(352,476)
(353,489)(354,490)(355,492)(356,491)(357,495)(358,496)(359,493)(360,494)
(361,481)(362,482)(363,484)(364,483)(365,487)(366,488)(367,485)(368,486)
(369,506)(370,505)(371,507)(372,508)(373,512)(374,511)(375,510)(376,509)
(377,498)(378,497)(379,499)(380,500)(381,504)(382,503)(383,502)(384,501);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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, 81)( 18, 82)( 19, 83)( 20, 84)( 21, 85)( 22, 86)( 23, 87)
( 24, 88)( 25, 89)( 26, 90)( 27, 91)( 28, 92)( 29, 93)( 30, 94)( 31, 95)
( 32, 96)( 33, 98)( 34, 97)( 35,100)( 36, 99)( 37,102)( 38,101)( 39,104)
( 40,103)( 41,106)( 42,105)( 43,108)( 44,107)( 45,110)( 46,109)( 47,112)
( 48,111)( 49,114)( 50,113)( 51,116)( 52,115)( 53,118)( 54,117)( 55,120)
( 56,119)( 57,122)( 58,121)( 59,124)( 60,123)( 61,126)( 62,125)( 63,128)
( 64,127)(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)(145,209)(146,210)(147,211)(148,212)(149,213)(150,214)(151,215)
(152,216)(153,217)(154,218)(155,219)(156,220)(157,221)(158,222)(159,223)
(160,224)(161,226)(162,225)(163,228)(164,227)(165,230)(166,229)(167,232)
(168,231)(169,234)(170,233)(171,236)(172,235)(173,238)(174,237)(175,240)
(176,239)(177,242)(178,241)(179,244)(180,243)(181,246)(182,245)(183,248)
(184,247)(185,250)(186,249)(187,252)(188,251)(189,254)(190,253)(191,256)
(192,255)(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)(273,337)(274,338)(275,339)(276,340)(277,341)(278,342)(279,343)
(280,344)(281,345)(282,346)(283,347)(284,348)(285,349)(286,350)(287,351)
(288,352)(289,354)(290,353)(291,356)(292,355)(293,358)(294,357)(295,360)
(296,359)(297,362)(298,361)(299,364)(300,363)(301,366)(302,365)(303,368)
(304,367)(305,370)(306,369)(307,372)(308,371)(309,374)(310,373)(311,376)
(312,375)(313,378)(314,377)(315,380)(316,379)(317,382)(318,381)(319,384)
(320,383)(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)(401,465)(402,466)(403,467)(404,468)(405,469)(406,470)(407,471)
(408,472)(409,473)(410,474)(411,475)(412,476)(413,477)(414,478)(415,479)
(416,480)(417,482)(418,481)(419,484)(420,483)(421,486)(422,485)(423,488)
(424,487)(425,490)(426,489)(427,492)(428,491)(429,494)(430,493)(431,496)
(432,495)(433,498)(434,497)(435,500)(436,499)(437,502)(438,501)(439,504)
(440,503)(441,506)(442,505)(443,508)(444,507)(445,510)(446,509)(447,512)
(448,511);
s1 := Sym(512)!( 1,257)( 2,258)( 3,260)( 4,259)( 5,263)( 6,264)( 7,261)
( 8,262)( 9,269)( 10,270)( 11,272)( 12,271)( 13,265)( 14,266)( 15,268)
( 16,267)( 17,273)( 18,274)( 19,276)( 20,275)( 21,279)( 22,280)( 23,277)
( 24,278)( 25,285)( 26,286)( 27,288)( 28,287)( 29,281)( 30,282)( 31,284)
( 32,283)( 33,297)( 34,298)( 35,300)( 36,299)( 37,303)( 38,304)( 39,301)
( 40,302)( 41,289)( 42,290)( 43,292)( 44,291)( 45,295)( 46,296)( 47,293)
( 48,294)( 49,313)( 50,314)( 51,316)( 52,315)( 53,319)( 54,320)( 55,317)
( 56,318)( 57,305)( 58,306)( 59,308)( 60,307)( 61,311)( 62,312)( 63,309)
( 64,310)( 65,337)( 66,338)( 67,340)( 68,339)( 69,343)( 70,344)( 71,341)
( 72,342)( 73,349)( 74,350)( 75,352)( 76,351)( 77,345)( 78,346)( 79,348)
( 80,347)( 81,321)( 82,322)( 83,324)( 84,323)( 85,327)( 86,328)( 87,325)
( 88,326)( 89,333)( 90,334)( 91,336)( 92,335)( 93,329)( 94,330)( 95,332)
( 96,331)( 97,377)( 98,378)( 99,380)(100,379)(101,383)(102,384)(103,381)
(104,382)(105,369)(106,370)(107,372)(108,371)(109,375)(110,376)(111,373)
(112,374)(113,361)(114,362)(115,364)(116,363)(117,367)(118,368)(119,365)
(120,366)(121,353)(122,354)(123,356)(124,355)(125,359)(126,360)(127,357)
(128,358)(129,417)(130,418)(131,420)(132,419)(133,423)(134,424)(135,421)
(136,422)(137,429)(138,430)(139,432)(140,431)(141,425)(142,426)(143,428)
(144,427)(145,433)(146,434)(147,436)(148,435)(149,439)(150,440)(151,437)
(152,438)(153,445)(154,446)(155,448)(156,447)(157,441)(158,442)(159,444)
(160,443)(161,385)(162,386)(163,388)(164,387)(165,391)(166,392)(167,389)
(168,390)(169,397)(170,398)(171,400)(172,399)(173,393)(174,394)(175,396)
(176,395)(177,401)(178,402)(179,404)(180,403)(181,407)(182,408)(183,405)
(184,406)(185,413)(186,414)(187,416)(188,415)(189,409)(190,410)(191,412)
(192,411)(193,498)(194,497)(195,499)(196,500)(197,504)(198,503)(199,502)
(200,501)(201,510)(202,509)(203,511)(204,512)(205,506)(206,505)(207,507)
(208,508)(209,482)(210,481)(211,483)(212,484)(213,488)(214,487)(215,486)
(216,485)(217,494)(218,493)(219,495)(220,496)(221,490)(222,489)(223,491)
(224,492)(225,466)(226,465)(227,467)(228,468)(229,472)(230,471)(231,470)
(232,469)(233,478)(234,477)(235,479)(236,480)(237,474)(238,473)(239,475)
(240,476)(241,450)(242,449)(243,451)(244,452)(245,456)(246,455)(247,454)
(248,453)(249,462)(250,461)(251,463)(252,464)(253,458)(254,457)(255,459)
(256,460);
s2 := Sym(512)!( 1,129)( 2,130)( 3,132)( 4,131)( 5,135)( 6,136)( 7,133)
( 8,134)( 9,141)( 10,142)( 11,144)( 12,143)( 13,137)( 14,138)( 15,140)
( 16,139)( 17,146)( 18,145)( 19,147)( 20,148)( 21,152)( 22,151)( 23,150)
( 24,149)( 25,158)( 26,157)( 27,159)( 28,160)( 29,154)( 30,153)( 31,155)
( 32,156)( 33,169)( 34,170)( 35,172)( 36,171)( 37,175)( 38,176)( 39,173)
( 40,174)( 41,161)( 42,162)( 43,164)( 44,163)( 45,167)( 46,168)( 47,165)
( 48,166)( 49,186)( 50,185)( 51,187)( 52,188)( 53,192)( 54,191)( 55,190)
( 56,189)( 57,178)( 58,177)( 59,179)( 60,180)( 61,184)( 62,183)( 63,182)
( 64,181)( 65,193)( 66,194)( 67,196)( 68,195)( 69,199)( 70,200)( 71,197)
( 72,198)( 73,205)( 74,206)( 75,208)( 76,207)( 77,201)( 78,202)( 79,204)
( 80,203)( 81,210)( 82,209)( 83,211)( 84,212)( 85,216)( 86,215)( 87,214)
( 88,213)( 89,222)( 90,221)( 91,223)( 92,224)( 93,218)( 94,217)( 95,219)
( 96,220)( 97,233)( 98,234)( 99,236)(100,235)(101,239)(102,240)(103,237)
(104,238)(105,225)(106,226)(107,228)(108,227)(109,231)(110,232)(111,229)
(112,230)(113,250)(114,249)(115,251)(116,252)(117,256)(118,255)(119,254)
(120,253)(121,242)(122,241)(123,243)(124,244)(125,248)(126,247)(127,246)
(128,245)(257,385)(258,386)(259,388)(260,387)(261,391)(262,392)(263,389)
(264,390)(265,397)(266,398)(267,400)(268,399)(269,393)(270,394)(271,396)
(272,395)(273,402)(274,401)(275,403)(276,404)(277,408)(278,407)(279,406)
(280,405)(281,414)(282,413)(283,415)(284,416)(285,410)(286,409)(287,411)
(288,412)(289,425)(290,426)(291,428)(292,427)(293,431)(294,432)(295,429)
(296,430)(297,417)(298,418)(299,420)(300,419)(301,423)(302,424)(303,421)
(304,422)(305,442)(306,441)(307,443)(308,444)(309,448)(310,447)(311,446)
(312,445)(313,434)(314,433)(315,435)(316,436)(317,440)(318,439)(319,438)
(320,437)(321,449)(322,450)(323,452)(324,451)(325,455)(326,456)(327,453)
(328,454)(329,461)(330,462)(331,464)(332,463)(333,457)(334,458)(335,460)
(336,459)(337,466)(338,465)(339,467)(340,468)(341,472)(342,471)(343,470)
(344,469)(345,478)(346,477)(347,479)(348,480)(349,474)(350,473)(351,475)
(352,476)(353,489)(354,490)(355,492)(356,491)(357,495)(358,496)(359,493)
(360,494)(361,481)(362,482)(363,484)(364,483)(365,487)(366,488)(367,485)
(368,486)(369,506)(370,505)(371,507)(372,508)(373,512)(374,511)(375,510)
(376,509)(377,498)(378,497)(379,499)(380,500)(381,504)(382,503)(383,502)
(384,501);
poly := sub<Sym(512)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1 >;
References : None.
to this polytope