Polytope of Type {16,16}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,16}*512l
if this polytope has a name.
Group : SmallGroup(512,30527)
Rank : 3
Schlafli Type : {16,16}
Number of vertices, edges, etc : 16, 128, 16
Order of s0s1s2 : 16
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
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 : {16,8}*256b, {8,16}*256e
4-fold quotients : {8,8}*128a, {4,16}*128b
8-fold quotients : {4,8}*64a, {8,4}*64b
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 := ( 1,193)( 2,194)( 3,195)( 4,196)( 5,197)( 6,198)( 7,199)( 8,200)
( 9,204)( 10,203)( 11,202)( 12,201)( 13,208)( 14,207)( 15,206)( 16,205)
( 17,210)( 18,209)( 19,212)( 20,211)( 21,214)( 22,213)( 23,216)( 24,215)
( 25,219)( 26,220)( 27,217)( 28,218)( 29,223)( 30,224)( 31,221)( 32,222)
( 33,238)( 34,237)( 35,240)( 36,239)( 37,233)( 38,234)( 39,235)( 40,236)
( 41,229)( 42,230)( 43,231)( 44,232)( 45,226)( 46,225)( 47,228)( 48,227)
( 49,253)( 50,254)( 51,255)( 52,256)( 53,250)( 54,249)( 55,252)( 56,251)
( 57,246)( 58,245)( 59,248)( 60,247)( 61,241)( 62,242)( 63,243)( 64,244)
( 65,129)( 66,130)( 67,131)( 68,132)( 69,133)( 70,134)( 71,135)( 72,136)
( 73,140)( 74,139)( 75,138)( 76,137)( 77,144)( 78,143)( 79,142)( 80,141)
( 81,146)( 82,145)( 83,148)( 84,147)( 85,150)( 86,149)( 87,152)( 88,151)
( 89,155)( 90,156)( 91,153)( 92,154)( 93,159)( 94,160)( 95,157)( 96,158)
( 97,174)( 98,173)( 99,176)(100,175)(101,169)(102,170)(103,171)(104,172)
(105,165)(106,166)(107,167)(108,168)(109,162)(110,161)(111,164)(112,163)
(113,189)(114,190)(115,191)(116,192)(117,186)(118,185)(119,188)(120,187)
(121,182)(122,181)(123,184)(124,183)(125,177)(126,178)(127,179)(128,180)
(257,449)(258,450)(259,451)(260,452)(261,453)(262,454)(263,455)(264,456)
(265,460)(266,459)(267,458)(268,457)(269,464)(270,463)(271,462)(272,461)
(273,466)(274,465)(275,468)(276,467)(277,470)(278,469)(279,472)(280,471)
(281,475)(282,476)(283,473)(284,474)(285,479)(286,480)(287,477)(288,478)
(289,494)(290,493)(291,496)(292,495)(293,489)(294,490)(295,491)(296,492)
(297,485)(298,486)(299,487)(300,488)(301,482)(302,481)(303,484)(304,483)
(305,509)(306,510)(307,511)(308,512)(309,506)(310,505)(311,508)(312,507)
(313,502)(314,501)(315,504)(316,503)(317,497)(318,498)(319,499)(320,500)
(321,385)(322,386)(323,387)(324,388)(325,389)(326,390)(327,391)(328,392)
(329,396)(330,395)(331,394)(332,393)(333,400)(334,399)(335,398)(336,397)
(337,402)(338,401)(339,404)(340,403)(341,406)(342,405)(343,408)(344,407)
(345,411)(346,412)(347,409)(348,410)(349,415)(350,416)(351,413)(352,414)
(353,430)(354,429)(355,432)(356,431)(357,425)(358,426)(359,427)(360,428)
(361,421)(362,422)(363,423)(364,424)(365,418)(366,417)(367,420)(368,419)
(369,445)(370,446)(371,447)(372,448)(373,442)(374,441)(375,444)(376,443)
(377,438)(378,437)(379,440)(380,439)(381,433)(382,434)(383,435)(384,436);;
s1 := ( 1,257)( 2,258)( 3,259)( 4,260)( 5,262)( 6,261)( 7,264)( 8,263)
( 9,267)( 10,268)( 11,265)( 12,266)( 13,272)( 14,271)( 15,270)( 16,269)
( 17,278)( 18,277)( 19,280)( 20,279)( 21,274)( 22,273)( 23,276)( 24,275)
( 25,288)( 26,287)( 27,286)( 28,285)( 29,284)( 30,283)( 31,282)( 32,281)
( 33,297)( 34,298)( 35,299)( 36,300)( 37,302)( 38,301)( 39,304)( 40,303)
( 41,289)( 42,290)( 43,291)( 44,292)( 45,294)( 46,293)( 47,296)( 48,295)
( 49,318)( 50,317)( 51,320)( 52,319)( 53,314)( 54,313)( 55,316)( 56,315)
( 57,310)( 58,309)( 59,312)( 60,311)( 61,306)( 62,305)( 63,308)( 64,307)
( 65,337)( 66,338)( 67,339)( 68,340)( 69,342)( 70,341)( 71,344)( 72,343)
( 73,347)( 74,348)( 75,345)( 76,346)( 77,352)( 78,351)( 79,350)( 80,349)
( 81,321)( 82,322)( 83,323)( 84,324)( 85,326)( 86,325)( 87,328)( 88,327)
( 89,331)( 90,332)( 91,329)( 92,330)( 93,336)( 94,335)( 95,334)( 96,333)
( 97,377)( 98,378)( 99,379)(100,380)(101,382)(102,381)(103,384)(104,383)
(105,369)(106,370)(107,371)(108,372)(109,374)(110,373)(111,376)(112,375)
(113,361)(114,362)(115,363)(116,364)(117,366)(118,365)(119,368)(120,367)
(121,353)(122,354)(123,355)(124,356)(125,358)(126,357)(127,360)(128,359)
(129,417)(130,418)(131,419)(132,420)(133,422)(134,421)(135,424)(136,423)
(137,427)(138,428)(139,425)(140,426)(141,432)(142,431)(143,430)(144,429)
(145,438)(146,437)(147,440)(148,439)(149,434)(150,433)(151,436)(152,435)
(153,448)(154,447)(155,446)(156,445)(157,444)(158,443)(159,442)(160,441)
(161,385)(162,386)(163,387)(164,388)(165,390)(166,389)(167,392)(168,391)
(169,395)(170,396)(171,393)(172,394)(173,400)(174,399)(175,398)(176,397)
(177,406)(178,405)(179,408)(180,407)(181,402)(182,401)(183,404)(184,403)
(185,416)(186,415)(187,414)(188,413)(189,412)(190,411)(191,410)(192,409)
(193,501)(194,502)(195,503)(196,504)(197,497)(198,498)(199,499)(200,500)
(201,511)(202,512)(203,509)(204,510)(205,507)(206,508)(207,505)(208,506)
(209,485)(210,486)(211,487)(212,488)(213,481)(214,482)(215,483)(216,484)
(217,495)(218,496)(219,493)(220,494)(221,491)(222,492)(223,489)(224,490)
(225,469)(226,470)(227,471)(228,472)(229,465)(230,466)(231,467)(232,468)
(233,479)(234,480)(235,477)(236,478)(237,475)(238,476)(239,473)(240,474)
(241,453)(242,454)(243,455)(244,456)(245,449)(246,450)(247,451)(248,452)
(249,463)(250,464)(251,461)(252,462)(253,459)(254,460)(255,457)(256,458);;
s2 := ( 1,129)( 2,130)( 3,131)( 4,132)( 5,134)( 6,133)( 7,136)( 8,135)
( 9,139)( 10,140)( 11,137)( 12,138)( 13,144)( 14,143)( 15,142)( 16,141)
( 17,149)( 18,150)( 19,151)( 20,152)( 21,145)( 22,146)( 23,147)( 24,148)
( 25,159)( 26,160)( 27,157)( 28,158)( 29,155)( 30,156)( 31,153)( 32,154)
( 33,169)( 34,170)( 35,171)( 36,172)( 37,174)( 38,173)( 39,176)( 40,175)
( 41,161)( 42,162)( 43,163)( 44,164)( 45,166)( 46,165)( 47,168)( 48,167)
( 49,189)( 50,190)( 51,191)( 52,192)( 53,185)( 54,186)( 55,187)( 56,188)
( 57,181)( 58,182)( 59,183)( 60,184)( 61,177)( 62,178)( 63,179)( 64,180)
( 65,193)( 66,194)( 67,195)( 68,196)( 69,198)( 70,197)( 71,200)( 72,199)
( 73,203)( 74,204)( 75,201)( 76,202)( 77,208)( 78,207)( 79,206)( 80,205)
( 81,213)( 82,214)( 83,215)( 84,216)( 85,209)( 86,210)( 87,211)( 88,212)
( 89,223)( 90,224)( 91,221)( 92,222)( 93,219)( 94,220)( 95,217)( 96,218)
( 97,233)( 98,234)( 99,235)(100,236)(101,238)(102,237)(103,240)(104,239)
(105,225)(106,226)(107,227)(108,228)(109,230)(110,229)(111,232)(112,231)
(113,253)(114,254)(115,255)(116,256)(117,249)(118,250)(119,251)(120,252)
(121,245)(122,246)(123,247)(124,248)(125,241)(126,242)(127,243)(128,244)
(257,385)(258,386)(259,387)(260,388)(261,390)(262,389)(263,392)(264,391)
(265,395)(266,396)(267,393)(268,394)(269,400)(270,399)(271,398)(272,397)
(273,405)(274,406)(275,407)(276,408)(277,401)(278,402)(279,403)(280,404)
(281,415)(282,416)(283,413)(284,414)(285,411)(286,412)(287,409)(288,410)
(289,425)(290,426)(291,427)(292,428)(293,430)(294,429)(295,432)(296,431)
(297,417)(298,418)(299,419)(300,420)(301,422)(302,421)(303,424)(304,423)
(305,445)(306,446)(307,447)(308,448)(309,441)(310,442)(311,443)(312,444)
(313,437)(314,438)(315,439)(316,440)(317,433)(318,434)(319,435)(320,436)
(321,449)(322,450)(323,451)(324,452)(325,454)(326,453)(327,456)(328,455)
(329,459)(330,460)(331,457)(332,458)(333,464)(334,463)(335,462)(336,461)
(337,469)(338,470)(339,471)(340,472)(341,465)(342,466)(343,467)(344,468)
(345,479)(346,480)(347,477)(348,478)(349,475)(350,476)(351,473)(352,474)
(353,489)(354,490)(355,491)(356,492)(357,494)(358,493)(359,496)(360,495)
(361,481)(362,482)(363,483)(364,484)(365,486)(366,485)(367,488)(368,487)
(369,509)(370,510)(371,511)(372,512)(373,505)(374,506)(375,507)(376,508)
(377,501)(378,502)(379,503)(380,504)(381,497)(382,498)(383,499)(384,500);;
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s0*s2*s1*s0*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(512)!( 1,193)( 2,194)( 3,195)( 4,196)( 5,197)( 6,198)( 7,199)
( 8,200)( 9,204)( 10,203)( 11,202)( 12,201)( 13,208)( 14,207)( 15,206)
( 16,205)( 17,210)( 18,209)( 19,212)( 20,211)( 21,214)( 22,213)( 23,216)
( 24,215)( 25,219)( 26,220)( 27,217)( 28,218)( 29,223)( 30,224)( 31,221)
( 32,222)( 33,238)( 34,237)( 35,240)( 36,239)( 37,233)( 38,234)( 39,235)
( 40,236)( 41,229)( 42,230)( 43,231)( 44,232)( 45,226)( 46,225)( 47,228)
( 48,227)( 49,253)( 50,254)( 51,255)( 52,256)( 53,250)( 54,249)( 55,252)
( 56,251)( 57,246)( 58,245)( 59,248)( 60,247)( 61,241)( 62,242)( 63,243)
( 64,244)( 65,129)( 66,130)( 67,131)( 68,132)( 69,133)( 70,134)( 71,135)
( 72,136)( 73,140)( 74,139)( 75,138)( 76,137)( 77,144)( 78,143)( 79,142)
( 80,141)( 81,146)( 82,145)( 83,148)( 84,147)( 85,150)( 86,149)( 87,152)
( 88,151)( 89,155)( 90,156)( 91,153)( 92,154)( 93,159)( 94,160)( 95,157)
( 96,158)( 97,174)( 98,173)( 99,176)(100,175)(101,169)(102,170)(103,171)
(104,172)(105,165)(106,166)(107,167)(108,168)(109,162)(110,161)(111,164)
(112,163)(113,189)(114,190)(115,191)(116,192)(117,186)(118,185)(119,188)
(120,187)(121,182)(122,181)(123,184)(124,183)(125,177)(126,178)(127,179)
(128,180)(257,449)(258,450)(259,451)(260,452)(261,453)(262,454)(263,455)
(264,456)(265,460)(266,459)(267,458)(268,457)(269,464)(270,463)(271,462)
(272,461)(273,466)(274,465)(275,468)(276,467)(277,470)(278,469)(279,472)
(280,471)(281,475)(282,476)(283,473)(284,474)(285,479)(286,480)(287,477)
(288,478)(289,494)(290,493)(291,496)(292,495)(293,489)(294,490)(295,491)
(296,492)(297,485)(298,486)(299,487)(300,488)(301,482)(302,481)(303,484)
(304,483)(305,509)(306,510)(307,511)(308,512)(309,506)(310,505)(311,508)
(312,507)(313,502)(314,501)(315,504)(316,503)(317,497)(318,498)(319,499)
(320,500)(321,385)(322,386)(323,387)(324,388)(325,389)(326,390)(327,391)
(328,392)(329,396)(330,395)(331,394)(332,393)(333,400)(334,399)(335,398)
(336,397)(337,402)(338,401)(339,404)(340,403)(341,406)(342,405)(343,408)
(344,407)(345,411)(346,412)(347,409)(348,410)(349,415)(350,416)(351,413)
(352,414)(353,430)(354,429)(355,432)(356,431)(357,425)(358,426)(359,427)
(360,428)(361,421)(362,422)(363,423)(364,424)(365,418)(366,417)(367,420)
(368,419)(369,445)(370,446)(371,447)(372,448)(373,442)(374,441)(375,444)
(376,443)(377,438)(378,437)(379,440)(380,439)(381,433)(382,434)(383,435)
(384,436);
s1 := Sym(512)!( 1,257)( 2,258)( 3,259)( 4,260)( 5,262)( 6,261)( 7,264)
( 8,263)( 9,267)( 10,268)( 11,265)( 12,266)( 13,272)( 14,271)( 15,270)
( 16,269)( 17,278)( 18,277)( 19,280)( 20,279)( 21,274)( 22,273)( 23,276)
( 24,275)( 25,288)( 26,287)( 27,286)( 28,285)( 29,284)( 30,283)( 31,282)
( 32,281)( 33,297)( 34,298)( 35,299)( 36,300)( 37,302)( 38,301)( 39,304)
( 40,303)( 41,289)( 42,290)( 43,291)( 44,292)( 45,294)( 46,293)( 47,296)
( 48,295)( 49,318)( 50,317)( 51,320)( 52,319)( 53,314)( 54,313)( 55,316)
( 56,315)( 57,310)( 58,309)( 59,312)( 60,311)( 61,306)( 62,305)( 63,308)
( 64,307)( 65,337)( 66,338)( 67,339)( 68,340)( 69,342)( 70,341)( 71,344)
( 72,343)( 73,347)( 74,348)( 75,345)( 76,346)( 77,352)( 78,351)( 79,350)
( 80,349)( 81,321)( 82,322)( 83,323)( 84,324)( 85,326)( 86,325)( 87,328)
( 88,327)( 89,331)( 90,332)( 91,329)( 92,330)( 93,336)( 94,335)( 95,334)
( 96,333)( 97,377)( 98,378)( 99,379)(100,380)(101,382)(102,381)(103,384)
(104,383)(105,369)(106,370)(107,371)(108,372)(109,374)(110,373)(111,376)
(112,375)(113,361)(114,362)(115,363)(116,364)(117,366)(118,365)(119,368)
(120,367)(121,353)(122,354)(123,355)(124,356)(125,358)(126,357)(127,360)
(128,359)(129,417)(130,418)(131,419)(132,420)(133,422)(134,421)(135,424)
(136,423)(137,427)(138,428)(139,425)(140,426)(141,432)(142,431)(143,430)
(144,429)(145,438)(146,437)(147,440)(148,439)(149,434)(150,433)(151,436)
(152,435)(153,448)(154,447)(155,446)(156,445)(157,444)(158,443)(159,442)
(160,441)(161,385)(162,386)(163,387)(164,388)(165,390)(166,389)(167,392)
(168,391)(169,395)(170,396)(171,393)(172,394)(173,400)(174,399)(175,398)
(176,397)(177,406)(178,405)(179,408)(180,407)(181,402)(182,401)(183,404)
(184,403)(185,416)(186,415)(187,414)(188,413)(189,412)(190,411)(191,410)
(192,409)(193,501)(194,502)(195,503)(196,504)(197,497)(198,498)(199,499)
(200,500)(201,511)(202,512)(203,509)(204,510)(205,507)(206,508)(207,505)
(208,506)(209,485)(210,486)(211,487)(212,488)(213,481)(214,482)(215,483)
(216,484)(217,495)(218,496)(219,493)(220,494)(221,491)(222,492)(223,489)
(224,490)(225,469)(226,470)(227,471)(228,472)(229,465)(230,466)(231,467)
(232,468)(233,479)(234,480)(235,477)(236,478)(237,475)(238,476)(239,473)
(240,474)(241,453)(242,454)(243,455)(244,456)(245,449)(246,450)(247,451)
(248,452)(249,463)(250,464)(251,461)(252,462)(253,459)(254,460)(255,457)
(256,458);
s2 := Sym(512)!( 1,129)( 2,130)( 3,131)( 4,132)( 5,134)( 6,133)( 7,136)
( 8,135)( 9,139)( 10,140)( 11,137)( 12,138)( 13,144)( 14,143)( 15,142)
( 16,141)( 17,149)( 18,150)( 19,151)( 20,152)( 21,145)( 22,146)( 23,147)
( 24,148)( 25,159)( 26,160)( 27,157)( 28,158)( 29,155)( 30,156)( 31,153)
( 32,154)( 33,169)( 34,170)( 35,171)( 36,172)( 37,174)( 38,173)( 39,176)
( 40,175)( 41,161)( 42,162)( 43,163)( 44,164)( 45,166)( 46,165)( 47,168)
( 48,167)( 49,189)( 50,190)( 51,191)( 52,192)( 53,185)( 54,186)( 55,187)
( 56,188)( 57,181)( 58,182)( 59,183)( 60,184)( 61,177)( 62,178)( 63,179)
( 64,180)( 65,193)( 66,194)( 67,195)( 68,196)( 69,198)( 70,197)( 71,200)
( 72,199)( 73,203)( 74,204)( 75,201)( 76,202)( 77,208)( 78,207)( 79,206)
( 80,205)( 81,213)( 82,214)( 83,215)( 84,216)( 85,209)( 86,210)( 87,211)
( 88,212)( 89,223)( 90,224)( 91,221)( 92,222)( 93,219)( 94,220)( 95,217)
( 96,218)( 97,233)( 98,234)( 99,235)(100,236)(101,238)(102,237)(103,240)
(104,239)(105,225)(106,226)(107,227)(108,228)(109,230)(110,229)(111,232)
(112,231)(113,253)(114,254)(115,255)(116,256)(117,249)(118,250)(119,251)
(120,252)(121,245)(122,246)(123,247)(124,248)(125,241)(126,242)(127,243)
(128,244)(257,385)(258,386)(259,387)(260,388)(261,390)(262,389)(263,392)
(264,391)(265,395)(266,396)(267,393)(268,394)(269,400)(270,399)(271,398)
(272,397)(273,405)(274,406)(275,407)(276,408)(277,401)(278,402)(279,403)
(280,404)(281,415)(282,416)(283,413)(284,414)(285,411)(286,412)(287,409)
(288,410)(289,425)(290,426)(291,427)(292,428)(293,430)(294,429)(295,432)
(296,431)(297,417)(298,418)(299,419)(300,420)(301,422)(302,421)(303,424)
(304,423)(305,445)(306,446)(307,447)(308,448)(309,441)(310,442)(311,443)
(312,444)(313,437)(314,438)(315,439)(316,440)(317,433)(318,434)(319,435)
(320,436)(321,449)(322,450)(323,451)(324,452)(325,454)(326,453)(327,456)
(328,455)(329,459)(330,460)(331,457)(332,458)(333,464)(334,463)(335,462)
(336,461)(337,469)(338,470)(339,471)(340,472)(341,465)(342,466)(343,467)
(344,468)(345,479)(346,480)(347,477)(348,478)(349,475)(350,476)(351,473)
(352,474)(353,489)(354,490)(355,491)(356,492)(357,494)(358,493)(359,496)
(360,495)(361,481)(362,482)(363,483)(364,484)(365,486)(366,485)(367,488)
(368,487)(369,509)(370,510)(371,511)(372,512)(373,505)(374,506)(375,507)
(376,508)(377,501)(378,502)(379,503)(380,504)(381,497)(382,498)(383,499)
(384,500);
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s0*s2*s1*s0*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope