Polytope of Type {16,16}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,16}*512e
if this polytope has a name.
Group : SmallGroup(512,30507)
Rank : 3
Schlafli Type : {16,16}
Number of vertices, edges, etc : 16, 128, 16
Order of s0s1s2 : 16
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
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 : {8,16}*256f, {16,8}*256f
4-fold quotients : {8,8}*128b, {4,16}*128b, {16,4}*128b
8-fold quotients : {4,8}*64a, {8,4}*64a
16-fold quotients : {4,4}*32, {2,8}*32, {8,2}*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, 70)( 6, 69)( 7, 72)( 8, 71)
( 9, 74)( 10, 73)( 11, 76)( 12, 75)( 13, 77)( 14, 78)( 15, 79)( 16, 80)
( 17, 87)( 18, 88)( 19, 85)( 20, 86)( 21, 83)( 22, 84)( 23, 81)( 24, 82)
( 25, 96)( 26, 95)( 27, 94)( 28, 93)( 29, 92)( 30, 91)( 31, 90)( 32, 89)
( 33,101)( 34,102)( 35,103)( 36,104)( 37, 97)( 38, 98)( 39, 99)( 40,100)
( 41,110)( 42,109)( 43,112)( 44,111)( 45,106)( 46,105)( 47,108)( 48,107)
( 49,116)( 50,115)( 51,114)( 52,113)( 53,119)( 54,120)( 55,117)( 56,118)
( 57,123)( 58,124)( 59,121)( 60,122)( 61,128)( 62,127)( 63,126)( 64,125)
(129,193)(130,194)(131,195)(132,196)(133,198)(134,197)(135,200)(136,199)
(137,202)(138,201)(139,204)(140,203)(141,205)(142,206)(143,207)(144,208)
(145,215)(146,216)(147,213)(148,214)(149,211)(150,212)(151,209)(152,210)
(153,224)(154,223)(155,222)(156,221)(157,220)(158,219)(159,218)(160,217)
(161,229)(162,230)(163,231)(164,232)(165,225)(166,226)(167,227)(168,228)
(169,238)(170,237)(171,240)(172,239)(173,234)(174,233)(175,236)(176,235)
(177,244)(178,243)(179,242)(180,241)(181,247)(182,248)(183,245)(184,246)
(185,251)(186,252)(187,249)(188,250)(189,256)(190,255)(191,254)(192,253)
(257,321)(258,322)(259,323)(260,324)(261,326)(262,325)(263,328)(264,327)
(265,330)(266,329)(267,332)(268,331)(269,333)(270,334)(271,335)(272,336)
(273,343)(274,344)(275,341)(276,342)(277,339)(278,340)(279,337)(280,338)
(281,352)(282,351)(283,350)(284,349)(285,348)(286,347)(287,346)(288,345)
(289,357)(290,358)(291,359)(292,360)(293,353)(294,354)(295,355)(296,356)
(297,366)(298,365)(299,368)(300,367)(301,362)(302,361)(303,364)(304,363)
(305,372)(306,371)(307,370)(308,369)(309,375)(310,376)(311,373)(312,374)
(313,379)(314,380)(315,377)(316,378)(317,384)(318,383)(319,382)(320,381)
(385,449)(386,450)(387,451)(388,452)(389,454)(390,453)(391,456)(392,455)
(393,458)(394,457)(395,460)(396,459)(397,461)(398,462)(399,463)(400,464)
(401,471)(402,472)(403,469)(404,470)(405,467)(406,468)(407,465)(408,466)
(409,480)(410,479)(411,478)(412,477)(413,476)(414,475)(415,474)(416,473)
(417,485)(418,486)(419,487)(420,488)(421,481)(422,482)(423,483)(424,484)
(425,494)(426,493)(427,496)(428,495)(429,490)(430,489)(431,492)(432,491)
(433,500)(434,499)(435,498)(436,497)(437,503)(438,504)(439,501)(440,502)
(441,507)(442,508)(443,505)(444,506)(445,512)(446,511)(447,510)(448,509);;
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)
( 17,279)( 18,280)( 19,277)( 20,278)( 21,275)( 22,276)( 23,273)( 24,274)
( 25,285)( 26,286)( 27,287)( 28,288)( 29,281)( 30,282)( 31,283)( 32,284)
( 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)
( 49,319)( 50,320)( 51,317)( 52,318)( 53,315)( 54,316)( 55,313)( 56,314)
( 57,311)( 58,312)( 59,309)( 60,310)( 61,307)( 62,308)( 63,305)( 64,306)
( 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)
(145,439)(146,440)(147,437)(148,438)(149,435)(150,436)(151,433)(152,434)
(153,445)(154,446)(155,447)(156,448)(157,441)(158,442)(159,443)(160,444)
(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)
(177,407)(178,408)(179,405)(180,406)(181,403)(182,404)(183,401)(184,402)
(185,413)(186,414)(187,415)(188,416)(189,409)(190,410)(191,411)(192,412)
(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 := ( 1,193)( 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)
( 17,211)( 18,212)( 19,209)( 20,210)( 21,215)( 22,216)( 23,213)( 24,214)
( 25,218)( 26,217)( 27,220)( 28,219)( 29,222)( 30,221)( 31,224)( 32,223)
( 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)
( 49,256)( 50,255)( 51,254)( 52,253)( 53,251)( 54,252)( 55,249)( 56,250)
( 57,247)( 58,248)( 59,245)( 60,246)( 61,244)( 62,243)( 63,242)( 64,241)
( 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)
( 81,147)( 82,148)( 83,145)( 84,146)( 85,151)( 86,152)( 87,149)( 88,150)
( 89,154)( 90,153)( 91,156)( 92,155)( 93,158)( 94,157)( 95,160)( 96,159)
( 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)
(113,192)(114,191)(115,190)(116,189)(117,187)(118,188)(119,185)(120,186)
(121,183)(122,184)(123,181)(124,182)(125,180)(126,179)(127,178)(128,177)
(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)
(273,467)(274,468)(275,465)(276,466)(277,471)(278,472)(279,469)(280,470)
(281,474)(282,473)(283,476)(284,475)(285,478)(286,477)(287,480)(288,479)
(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)
(305,512)(306,511)(307,510)(308,509)(309,507)(310,508)(311,505)(312,506)
(313,503)(314,504)(315,501)(316,502)(317,500)(318,499)(319,498)(320,497)
(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)
(337,403)(338,404)(339,401)(340,402)(341,407)(342,408)(343,405)(344,406)
(345,410)(346,409)(347,412)(348,411)(349,414)(350,413)(351,416)(352,415)
(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)
(369,448)(370,447)(371,446)(372,445)(373,443)(374,444)(375,441)(376,442)
(377,439)(378,440)(379,437)(380,438)(381,436)(382,435)(383,434)(384,433);;
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,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(512)!( 1, 65)( 2, 66)( 3, 67)( 4, 68)( 5, 70)( 6, 69)( 7, 72)
( 8, 71)( 9, 74)( 10, 73)( 11, 76)( 12, 75)( 13, 77)( 14, 78)( 15, 79)
( 16, 80)( 17, 87)( 18, 88)( 19, 85)( 20, 86)( 21, 83)( 22, 84)( 23, 81)
( 24, 82)( 25, 96)( 26, 95)( 27, 94)( 28, 93)( 29, 92)( 30, 91)( 31, 90)
( 32, 89)( 33,101)( 34,102)( 35,103)( 36,104)( 37, 97)( 38, 98)( 39, 99)
( 40,100)( 41,110)( 42,109)( 43,112)( 44,111)( 45,106)( 46,105)( 47,108)
( 48,107)( 49,116)( 50,115)( 51,114)( 52,113)( 53,119)( 54,120)( 55,117)
( 56,118)( 57,123)( 58,124)( 59,121)( 60,122)( 61,128)( 62,127)( 63,126)
( 64,125)(129,193)(130,194)(131,195)(132,196)(133,198)(134,197)(135,200)
(136,199)(137,202)(138,201)(139,204)(140,203)(141,205)(142,206)(143,207)
(144,208)(145,215)(146,216)(147,213)(148,214)(149,211)(150,212)(151,209)
(152,210)(153,224)(154,223)(155,222)(156,221)(157,220)(158,219)(159,218)
(160,217)(161,229)(162,230)(163,231)(164,232)(165,225)(166,226)(167,227)
(168,228)(169,238)(170,237)(171,240)(172,239)(173,234)(174,233)(175,236)
(176,235)(177,244)(178,243)(179,242)(180,241)(181,247)(182,248)(183,245)
(184,246)(185,251)(186,252)(187,249)(188,250)(189,256)(190,255)(191,254)
(192,253)(257,321)(258,322)(259,323)(260,324)(261,326)(262,325)(263,328)
(264,327)(265,330)(266,329)(267,332)(268,331)(269,333)(270,334)(271,335)
(272,336)(273,343)(274,344)(275,341)(276,342)(277,339)(278,340)(279,337)
(280,338)(281,352)(282,351)(283,350)(284,349)(285,348)(286,347)(287,346)
(288,345)(289,357)(290,358)(291,359)(292,360)(293,353)(294,354)(295,355)
(296,356)(297,366)(298,365)(299,368)(300,367)(301,362)(302,361)(303,364)
(304,363)(305,372)(306,371)(307,370)(308,369)(309,375)(310,376)(311,373)
(312,374)(313,379)(314,380)(315,377)(316,378)(317,384)(318,383)(319,382)
(320,381)(385,449)(386,450)(387,451)(388,452)(389,454)(390,453)(391,456)
(392,455)(393,458)(394,457)(395,460)(396,459)(397,461)(398,462)(399,463)
(400,464)(401,471)(402,472)(403,469)(404,470)(405,467)(406,468)(407,465)
(408,466)(409,480)(410,479)(411,478)(412,477)(413,476)(414,475)(415,474)
(416,473)(417,485)(418,486)(419,487)(420,488)(421,481)(422,482)(423,483)
(424,484)(425,494)(426,493)(427,496)(428,495)(429,490)(430,489)(431,492)
(432,491)(433,500)(434,499)(435,498)(436,497)(437,503)(438,504)(439,501)
(440,502)(441,507)(442,508)(443,505)(444,506)(445,512)(446,511)(447,510)
(448,509);
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)( 17,279)( 18,280)( 19,277)( 20,278)( 21,275)( 22,276)( 23,273)
( 24,274)( 25,285)( 26,286)( 27,287)( 28,288)( 29,281)( 30,282)( 31,283)
( 32,284)( 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)( 49,319)( 50,320)( 51,317)( 52,318)( 53,315)( 54,316)( 55,313)
( 56,314)( 57,311)( 58,312)( 59,309)( 60,310)( 61,307)( 62,308)( 63,305)
( 64,306)( 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)(145,439)(146,440)(147,437)(148,438)(149,435)(150,436)(151,433)
(152,434)(153,445)(154,446)(155,447)(156,448)(157,441)(158,442)(159,443)
(160,444)(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)(177,407)(178,408)(179,405)(180,406)(181,403)(182,404)(183,401)
(184,402)(185,413)(186,414)(187,415)(188,416)(189,409)(190,410)(191,411)
(192,412)(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)!( 1,193)( 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)( 17,211)( 18,212)( 19,209)( 20,210)( 21,215)( 22,216)( 23,213)
( 24,214)( 25,218)( 26,217)( 27,220)( 28,219)( 29,222)( 30,221)( 31,224)
( 32,223)( 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)( 49,256)( 50,255)( 51,254)( 52,253)( 53,251)( 54,252)( 55,249)
( 56,250)( 57,247)( 58,248)( 59,245)( 60,246)( 61,244)( 62,243)( 63,242)
( 64,241)( 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)( 81,147)( 82,148)( 83,145)( 84,146)( 85,151)( 86,152)( 87,149)
( 88,150)( 89,154)( 90,153)( 91,156)( 92,155)( 93,158)( 94,157)( 95,160)
( 96,159)( 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)(113,192)(114,191)(115,190)(116,189)(117,187)(118,188)(119,185)
(120,186)(121,183)(122,184)(123,181)(124,182)(125,180)(126,179)(127,178)
(128,177)(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)(273,467)(274,468)(275,465)(276,466)(277,471)(278,472)(279,469)
(280,470)(281,474)(282,473)(283,476)(284,475)(285,478)(286,477)(287,480)
(288,479)(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)(305,512)(306,511)(307,510)(308,509)(309,507)(310,508)(311,505)
(312,506)(313,503)(314,504)(315,501)(316,502)(317,500)(318,499)(319,498)
(320,497)(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)(337,403)(338,404)(339,401)(340,402)(341,407)(342,408)(343,405)
(344,406)(345,410)(346,409)(347,412)(348,411)(349,414)(350,413)(351,416)
(352,415)(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)(369,448)(370,447)(371,446)(372,445)(373,443)(374,444)(375,441)
(376,442)(377,439)(378,440)(379,437)(380,438)(381,436)(382,435)(383,434)
(384,433);
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,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope