Polytope of Type {8,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,8}*512t
if this polytope has a name.
Group : SmallGroup(512,58358)
Rank : 3
Schlafli Type : {8,8}
Number of vertices, edges, etc : 32, 128, 32
Order of s0s1s2 : 8
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,8}*256c, {8,4}*256c
4-fold quotients : {4,4}*128
8-fold quotients : {4,4}*64
16-fold quotients : {4,4}*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 := ( 1,129)( 2,130)( 3,132)( 4,131)( 5,133)( 6,134)( 7,136)( 8,135)
( 9,137)( 10,138)( 11,140)( 12,139)( 13,141)( 14,142)( 15,144)( 16,143)
( 17,152)( 18,151)( 19,149)( 20,150)( 21,147)( 22,148)( 23,146)( 24,145)
( 25,160)( 26,159)( 27,157)( 28,158)( 29,155)( 30,156)( 31,154)( 32,153)
( 33,169)( 34,170)( 35,172)( 36,171)( 37,173)( 38,174)( 39,176)( 40,175)
( 41,161)( 42,162)( 43,164)( 44,163)( 45,165)( 46,166)( 47,168)( 48,167)
( 49,192)( 50,191)( 51,189)( 52,190)( 53,187)( 54,188)( 55,186)( 56,185)
( 57,184)( 58,183)( 59,181)( 60,182)( 61,179)( 62,180)( 63,178)( 64,177)
( 65,193)( 66,194)( 67,196)( 68,195)( 69,197)( 70,198)( 71,200)( 72,199)
( 73,201)( 74,202)( 75,204)( 76,203)( 77,205)( 78,206)( 79,208)( 80,207)
( 81,216)( 82,215)( 83,213)( 84,214)( 85,211)( 86,212)( 87,210)( 88,209)
( 89,224)( 90,223)( 91,221)( 92,222)( 93,219)( 94,220)( 95,218)( 96,217)
( 97,233)( 98,234)( 99,236)(100,235)(101,237)(102,238)(103,240)(104,239)
(105,225)(106,226)(107,228)(108,227)(109,229)(110,230)(111,232)(112,231)
(113,256)(114,255)(115,253)(116,254)(117,251)(118,252)(119,250)(120,249)
(121,248)(122,247)(123,245)(124,246)(125,243)(126,244)(127,242)(128,241)
(257,385)(258,386)(259,388)(260,387)(261,389)(262,390)(263,392)(264,391)
(265,393)(266,394)(267,396)(268,395)(269,397)(270,398)(271,400)(272,399)
(273,408)(274,407)(275,405)(276,406)(277,403)(278,404)(279,402)(280,401)
(281,416)(282,415)(283,413)(284,414)(285,411)(286,412)(287,410)(288,409)
(289,425)(290,426)(291,428)(292,427)(293,429)(294,430)(295,432)(296,431)
(297,417)(298,418)(299,420)(300,419)(301,421)(302,422)(303,424)(304,423)
(305,448)(306,447)(307,445)(308,446)(309,443)(310,444)(311,442)(312,441)
(313,440)(314,439)(315,437)(316,438)(317,435)(318,436)(319,434)(320,433)
(321,449)(322,450)(323,452)(324,451)(325,453)(326,454)(327,456)(328,455)
(329,457)(330,458)(331,460)(332,459)(333,461)(334,462)(335,464)(336,463)
(337,472)(338,471)(339,469)(340,470)(341,467)(342,468)(343,466)(344,465)
(345,480)(346,479)(347,477)(348,478)(349,475)(350,476)(351,474)(352,473)
(353,489)(354,490)(355,492)(356,491)(357,493)(358,494)(359,496)(360,495)
(361,481)(362,482)(363,484)(364,483)(365,485)(366,486)(367,488)(368,487)
(369,512)(370,511)(371,509)(372,510)(373,507)(374,508)(375,506)(376,505)
(377,504)(378,503)(379,501)(380,502)(381,499)(382,500)(383,498)(384,497);;
s1 := ( 1,257)( 2,258)( 3,259)( 4,260)( 5,263)( 6,264)( 7,261)( 8,262)
( 9,265)( 10,266)( 11,267)( 12,268)( 13,271)( 14,272)( 15,269)( 16,270)
( 17,276)( 18,275)( 19,274)( 20,273)( 21,278)( 22,277)( 23,280)( 24,279)
( 25,284)( 26,283)( 27,282)( 28,281)( 29,286)( 30,285)( 31,288)( 32,287)
( 33,297)( 34,298)( 35,299)( 36,300)( 37,303)( 38,304)( 39,301)( 40,302)
( 41,289)( 42,290)( 43,291)( 44,292)( 45,295)( 46,296)( 47,293)( 48,294)
( 49,316)( 50,315)( 51,314)( 52,313)( 53,318)( 54,317)( 55,320)( 56,319)
( 57,308)( 58,307)( 59,306)( 60,305)( 61,310)( 62,309)( 63,312)( 64,311)
( 65,337)( 66,338)( 67,339)( 68,340)( 69,343)( 70,344)( 71,341)( 72,342)
( 73,345)( 74,346)( 75,347)( 76,348)( 77,351)( 78,352)( 79,349)( 80,350)
( 81,321)( 82,322)( 83,323)( 84,324)( 85,327)( 86,328)( 87,325)( 88,326)
( 89,329)( 90,330)( 91,331)( 92,332)( 93,335)( 94,336)( 95,333)( 96,334)
( 97,379)( 98,380)( 99,377)(100,378)(101,381)(102,382)(103,383)(104,384)
(105,371)(106,372)(107,369)(108,370)(109,373)(110,374)(111,375)(112,376)
(113,363)(114,364)(115,361)(116,362)(117,365)(118,366)(119,367)(120,368)
(121,355)(122,356)(123,353)(124,354)(125,357)(126,358)(127,359)(128,360)
(129,417)(130,418)(131,419)(132,420)(133,423)(134,424)(135,421)(136,422)
(137,425)(138,426)(139,427)(140,428)(141,431)(142,432)(143,429)(144,430)
(145,436)(146,435)(147,434)(148,433)(149,438)(150,437)(151,440)(152,439)
(153,444)(154,443)(155,442)(156,441)(157,446)(158,445)(159,448)(160,447)
(161,385)(162,386)(163,387)(164,388)(165,391)(166,392)(167,389)(168,390)
(169,393)(170,394)(171,395)(172,396)(173,399)(174,400)(175,397)(176,398)
(177,404)(178,403)(179,402)(180,401)(181,406)(182,405)(183,408)(184,407)
(185,412)(186,411)(187,410)(188,409)(189,414)(190,413)(191,416)(192,415)
(193,501)(194,502)(195,503)(196,504)(197,500)(198,499)(199,498)(200,497)
(201,509)(202,510)(203,511)(204,512)(205,508)(206,507)(207,506)(208,505)
(209,485)(210,486)(211,487)(212,488)(213,484)(214,483)(215,482)(216,481)
(217,493)(218,494)(219,495)(220,496)(221,492)(222,491)(223,490)(224,489)
(225,472)(226,471)(227,470)(228,469)(229,465)(230,466)(231,467)(232,468)
(233,480)(234,479)(235,478)(236,477)(237,473)(238,474)(239,475)(240,476)
(241,456)(242,455)(243,454)(244,453)(245,449)(246,450)(247,451)(248,452)
(249,464)(250,463)(251,462)(252,461)(253,457)(254,458)(255,459)(256,460);;
s2 := ( 1,193)( 2,194)( 3,196)( 4,195)( 5,198)( 6,197)( 7,199)( 8,200)
( 9,201)( 10,202)( 11,204)( 12,203)( 13,206)( 14,205)( 15,207)( 16,208)
( 17,214)( 18,213)( 19,215)( 20,216)( 21,210)( 22,209)( 23,211)( 24,212)
( 25,222)( 26,221)( 27,223)( 28,224)( 29,218)( 30,217)( 31,219)( 32,220)
( 33,237)( 34,238)( 35,240)( 36,239)( 37,233)( 38,234)( 39,236)( 40,235)
( 41,229)( 42,230)( 43,232)( 44,231)( 45,225)( 46,226)( 47,228)( 48,227)
( 49,249)( 50,250)( 51,252)( 52,251)( 53,254)( 54,253)( 55,255)( 56,256)
( 57,241)( 58,242)( 59,244)( 60,243)( 61,246)( 62,245)( 63,247)( 64,248)
( 65,129)( 66,130)( 67,132)( 68,131)( 69,134)( 70,133)( 71,135)( 72,136)
( 73,137)( 74,138)( 75,140)( 76,139)( 77,142)( 78,141)( 79,143)( 80,144)
( 81,150)( 82,149)( 83,151)( 84,152)( 85,146)( 86,145)( 87,147)( 88,148)
( 89,158)( 90,157)( 91,159)( 92,160)( 93,154)( 94,153)( 95,155)( 96,156)
( 97,173)( 98,174)( 99,176)(100,175)(101,169)(102,170)(103,172)(104,171)
(105,165)(106,166)(107,168)(108,167)(109,161)(110,162)(111,164)(112,163)
(113,185)(114,186)(115,188)(116,187)(117,190)(118,189)(119,191)(120,192)
(121,177)(122,178)(123,180)(124,179)(125,182)(126,181)(127,183)(128,184)
(257,449)(258,450)(259,452)(260,451)(261,454)(262,453)(263,455)(264,456)
(265,457)(266,458)(267,460)(268,459)(269,462)(270,461)(271,463)(272,464)
(273,470)(274,469)(275,471)(276,472)(277,466)(278,465)(279,467)(280,468)
(281,478)(282,477)(283,479)(284,480)(285,474)(286,473)(287,475)(288,476)
(289,493)(290,494)(291,496)(292,495)(293,489)(294,490)(295,492)(296,491)
(297,485)(298,486)(299,488)(300,487)(301,481)(302,482)(303,484)(304,483)
(305,505)(306,506)(307,508)(308,507)(309,510)(310,509)(311,511)(312,512)
(313,497)(314,498)(315,500)(316,499)(317,502)(318,501)(319,503)(320,504)
(321,385)(322,386)(323,388)(324,387)(325,390)(326,389)(327,391)(328,392)
(329,393)(330,394)(331,396)(332,395)(333,398)(334,397)(335,399)(336,400)
(337,406)(338,405)(339,407)(340,408)(341,402)(342,401)(343,403)(344,404)
(345,414)(346,413)(347,415)(348,416)(349,410)(350,409)(351,411)(352,412)
(353,429)(354,430)(355,432)(356,431)(357,425)(358,426)(359,428)(360,427)
(361,421)(362,422)(363,424)(364,423)(365,417)(366,418)(367,420)(368,419)
(369,441)(370,442)(371,444)(372,443)(373,446)(374,445)(375,447)(376,448)
(377,433)(378,434)(379,436)(380,435)(381,438)(382,437)(383,439)(384,440);;
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*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(512)!( 1,129)( 2,130)( 3,132)( 4,131)( 5,133)( 6,134)( 7,136)
( 8,135)( 9,137)( 10,138)( 11,140)( 12,139)( 13,141)( 14,142)( 15,144)
( 16,143)( 17,152)( 18,151)( 19,149)( 20,150)( 21,147)( 22,148)( 23,146)
( 24,145)( 25,160)( 26,159)( 27,157)( 28,158)( 29,155)( 30,156)( 31,154)
( 32,153)( 33,169)( 34,170)( 35,172)( 36,171)( 37,173)( 38,174)( 39,176)
( 40,175)( 41,161)( 42,162)( 43,164)( 44,163)( 45,165)( 46,166)( 47,168)
( 48,167)( 49,192)( 50,191)( 51,189)( 52,190)( 53,187)( 54,188)( 55,186)
( 56,185)( 57,184)( 58,183)( 59,181)( 60,182)( 61,179)( 62,180)( 63,178)
( 64,177)( 65,193)( 66,194)( 67,196)( 68,195)( 69,197)( 70,198)( 71,200)
( 72,199)( 73,201)( 74,202)( 75,204)( 76,203)( 77,205)( 78,206)( 79,208)
( 80,207)( 81,216)( 82,215)( 83,213)( 84,214)( 85,211)( 86,212)( 87,210)
( 88,209)( 89,224)( 90,223)( 91,221)( 92,222)( 93,219)( 94,220)( 95,218)
( 96,217)( 97,233)( 98,234)( 99,236)(100,235)(101,237)(102,238)(103,240)
(104,239)(105,225)(106,226)(107,228)(108,227)(109,229)(110,230)(111,232)
(112,231)(113,256)(114,255)(115,253)(116,254)(117,251)(118,252)(119,250)
(120,249)(121,248)(122,247)(123,245)(124,246)(125,243)(126,244)(127,242)
(128,241)(257,385)(258,386)(259,388)(260,387)(261,389)(262,390)(263,392)
(264,391)(265,393)(266,394)(267,396)(268,395)(269,397)(270,398)(271,400)
(272,399)(273,408)(274,407)(275,405)(276,406)(277,403)(278,404)(279,402)
(280,401)(281,416)(282,415)(283,413)(284,414)(285,411)(286,412)(287,410)
(288,409)(289,425)(290,426)(291,428)(292,427)(293,429)(294,430)(295,432)
(296,431)(297,417)(298,418)(299,420)(300,419)(301,421)(302,422)(303,424)
(304,423)(305,448)(306,447)(307,445)(308,446)(309,443)(310,444)(311,442)
(312,441)(313,440)(314,439)(315,437)(316,438)(317,435)(318,436)(319,434)
(320,433)(321,449)(322,450)(323,452)(324,451)(325,453)(326,454)(327,456)
(328,455)(329,457)(330,458)(331,460)(332,459)(333,461)(334,462)(335,464)
(336,463)(337,472)(338,471)(339,469)(340,470)(341,467)(342,468)(343,466)
(344,465)(345,480)(346,479)(347,477)(348,478)(349,475)(350,476)(351,474)
(352,473)(353,489)(354,490)(355,492)(356,491)(357,493)(358,494)(359,496)
(360,495)(361,481)(362,482)(363,484)(364,483)(365,485)(366,486)(367,488)
(368,487)(369,512)(370,511)(371,509)(372,510)(373,507)(374,508)(375,506)
(376,505)(377,504)(378,503)(379,501)(380,502)(381,499)(382,500)(383,498)
(384,497);
s1 := Sym(512)!( 1,257)( 2,258)( 3,259)( 4,260)( 5,263)( 6,264)( 7,261)
( 8,262)( 9,265)( 10,266)( 11,267)( 12,268)( 13,271)( 14,272)( 15,269)
( 16,270)( 17,276)( 18,275)( 19,274)( 20,273)( 21,278)( 22,277)( 23,280)
( 24,279)( 25,284)( 26,283)( 27,282)( 28,281)( 29,286)( 30,285)( 31,288)
( 32,287)( 33,297)( 34,298)( 35,299)( 36,300)( 37,303)( 38,304)( 39,301)
( 40,302)( 41,289)( 42,290)( 43,291)( 44,292)( 45,295)( 46,296)( 47,293)
( 48,294)( 49,316)( 50,315)( 51,314)( 52,313)( 53,318)( 54,317)( 55,320)
( 56,319)( 57,308)( 58,307)( 59,306)( 60,305)( 61,310)( 62,309)( 63,312)
( 64,311)( 65,337)( 66,338)( 67,339)( 68,340)( 69,343)( 70,344)( 71,341)
( 72,342)( 73,345)( 74,346)( 75,347)( 76,348)( 77,351)( 78,352)( 79,349)
( 80,350)( 81,321)( 82,322)( 83,323)( 84,324)( 85,327)( 86,328)( 87,325)
( 88,326)( 89,329)( 90,330)( 91,331)( 92,332)( 93,335)( 94,336)( 95,333)
( 96,334)( 97,379)( 98,380)( 99,377)(100,378)(101,381)(102,382)(103,383)
(104,384)(105,371)(106,372)(107,369)(108,370)(109,373)(110,374)(111,375)
(112,376)(113,363)(114,364)(115,361)(116,362)(117,365)(118,366)(119,367)
(120,368)(121,355)(122,356)(123,353)(124,354)(125,357)(126,358)(127,359)
(128,360)(129,417)(130,418)(131,419)(132,420)(133,423)(134,424)(135,421)
(136,422)(137,425)(138,426)(139,427)(140,428)(141,431)(142,432)(143,429)
(144,430)(145,436)(146,435)(147,434)(148,433)(149,438)(150,437)(151,440)
(152,439)(153,444)(154,443)(155,442)(156,441)(157,446)(158,445)(159,448)
(160,447)(161,385)(162,386)(163,387)(164,388)(165,391)(166,392)(167,389)
(168,390)(169,393)(170,394)(171,395)(172,396)(173,399)(174,400)(175,397)
(176,398)(177,404)(178,403)(179,402)(180,401)(181,406)(182,405)(183,408)
(184,407)(185,412)(186,411)(187,410)(188,409)(189,414)(190,413)(191,416)
(192,415)(193,501)(194,502)(195,503)(196,504)(197,500)(198,499)(199,498)
(200,497)(201,509)(202,510)(203,511)(204,512)(205,508)(206,507)(207,506)
(208,505)(209,485)(210,486)(211,487)(212,488)(213,484)(214,483)(215,482)
(216,481)(217,493)(218,494)(219,495)(220,496)(221,492)(222,491)(223,490)
(224,489)(225,472)(226,471)(227,470)(228,469)(229,465)(230,466)(231,467)
(232,468)(233,480)(234,479)(235,478)(236,477)(237,473)(238,474)(239,475)
(240,476)(241,456)(242,455)(243,454)(244,453)(245,449)(246,450)(247,451)
(248,452)(249,464)(250,463)(251,462)(252,461)(253,457)(254,458)(255,459)
(256,460);
s2 := Sym(512)!( 1,193)( 2,194)( 3,196)( 4,195)( 5,198)( 6,197)( 7,199)
( 8,200)( 9,201)( 10,202)( 11,204)( 12,203)( 13,206)( 14,205)( 15,207)
( 16,208)( 17,214)( 18,213)( 19,215)( 20,216)( 21,210)( 22,209)( 23,211)
( 24,212)( 25,222)( 26,221)( 27,223)( 28,224)( 29,218)( 30,217)( 31,219)
( 32,220)( 33,237)( 34,238)( 35,240)( 36,239)( 37,233)( 38,234)( 39,236)
( 40,235)( 41,229)( 42,230)( 43,232)( 44,231)( 45,225)( 46,226)( 47,228)
( 48,227)( 49,249)( 50,250)( 51,252)( 52,251)( 53,254)( 54,253)( 55,255)
( 56,256)( 57,241)( 58,242)( 59,244)( 60,243)( 61,246)( 62,245)( 63,247)
( 64,248)( 65,129)( 66,130)( 67,132)( 68,131)( 69,134)( 70,133)( 71,135)
( 72,136)( 73,137)( 74,138)( 75,140)( 76,139)( 77,142)( 78,141)( 79,143)
( 80,144)( 81,150)( 82,149)( 83,151)( 84,152)( 85,146)( 86,145)( 87,147)
( 88,148)( 89,158)( 90,157)( 91,159)( 92,160)( 93,154)( 94,153)( 95,155)
( 96,156)( 97,173)( 98,174)( 99,176)(100,175)(101,169)(102,170)(103,172)
(104,171)(105,165)(106,166)(107,168)(108,167)(109,161)(110,162)(111,164)
(112,163)(113,185)(114,186)(115,188)(116,187)(117,190)(118,189)(119,191)
(120,192)(121,177)(122,178)(123,180)(124,179)(125,182)(126,181)(127,183)
(128,184)(257,449)(258,450)(259,452)(260,451)(261,454)(262,453)(263,455)
(264,456)(265,457)(266,458)(267,460)(268,459)(269,462)(270,461)(271,463)
(272,464)(273,470)(274,469)(275,471)(276,472)(277,466)(278,465)(279,467)
(280,468)(281,478)(282,477)(283,479)(284,480)(285,474)(286,473)(287,475)
(288,476)(289,493)(290,494)(291,496)(292,495)(293,489)(294,490)(295,492)
(296,491)(297,485)(298,486)(299,488)(300,487)(301,481)(302,482)(303,484)
(304,483)(305,505)(306,506)(307,508)(308,507)(309,510)(310,509)(311,511)
(312,512)(313,497)(314,498)(315,500)(316,499)(317,502)(318,501)(319,503)
(320,504)(321,385)(322,386)(323,388)(324,387)(325,390)(326,389)(327,391)
(328,392)(329,393)(330,394)(331,396)(332,395)(333,398)(334,397)(335,399)
(336,400)(337,406)(338,405)(339,407)(340,408)(341,402)(342,401)(343,403)
(344,404)(345,414)(346,413)(347,415)(348,416)(349,410)(350,409)(351,411)
(352,412)(353,429)(354,430)(355,432)(356,431)(357,425)(358,426)(359,428)
(360,427)(361,421)(362,422)(363,424)(364,423)(365,417)(366,418)(367,420)
(368,419)(369,441)(370,442)(371,444)(372,443)(373,446)(374,445)(375,447)
(376,448)(377,433)(378,434)(379,436)(380,435)(381,438)(382,437)(383,439)
(384,440);
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*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1 >;
References : None.
to this polytope