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Polytope of Type {16,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,16}*512a
if this polytope has a name.
Group : SmallGroup(512,30471)
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
   Self-Petrie
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}*256a, {8,16}*256c
   4-fold quotients : {8,8}*128a, {4,16}*128a
   8-fold quotients : {4,8}*64a, {8,4}*64b, {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, 70)(  6, 69)(  7, 72)(  8, 71)
(  9, 74)( 10, 73)( 11, 76)( 12, 75)( 13, 77)( 14, 78)( 15, 79)( 16, 80)
( 17, 85)( 18, 86)( 19, 87)( 20, 88)( 21, 81)( 22, 82)( 23, 83)( 24, 84)
( 25, 94)( 26, 93)( 27, 96)( 28, 95)( 29, 90)( 30, 89)( 31, 92)( 32, 91)
( 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)
( 49,114)( 50,113)( 51,116)( 52,115)( 53,117)( 54,118)( 55,119)( 56,120)
( 57,121)( 58,122)( 59,123)( 60,124)( 61,126)( 62,125)( 63,128)( 64,127)
(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)
(145,213)(146,214)(147,215)(148,216)(149,209)(150,210)(151,211)(152,212)
(153,222)(154,221)(155,224)(156,223)(157,218)(158,217)(159,220)(160,219)
(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)
(177,242)(178,241)(179,244)(180,243)(181,245)(182,246)(183,247)(184,248)
(185,249)(186,250)(187,251)(188,252)(189,254)(190,253)(191,256)(192,255)
(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)
(273,341)(274,342)(275,343)(276,344)(277,337)(278,338)(279,339)(280,340)
(281,350)(282,349)(283,352)(284,351)(285,346)(286,345)(287,348)(288,347)
(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)
(305,370)(306,369)(307,372)(308,371)(309,373)(310,374)(311,375)(312,376)
(313,377)(314,378)(315,379)(316,380)(317,382)(318,381)(319,384)(320,383)
(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)
(401,469)(402,470)(403,471)(404,472)(405,465)(406,466)(407,467)(408,468)
(409,478)(410,477)(411,480)(412,479)(413,474)(414,473)(415,476)(416,475)
(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)
(433,498)(434,497)(435,500)(436,499)(437,501)(438,502)(439,503)(440,504)
(441,505)(442,506)(443,507)(444,508)(445,510)(446,509)(447,512)(448,511);;
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)
( 17,277)( 18,278)( 19,279)( 20,280)( 21,273)( 22,274)( 23,275)( 24,276)
( 25,287)( 26,288)( 27,285)( 28,286)( 29,283)( 30,284)( 31,281)( 32,282)
( 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)
( 49,317)( 50,318)( 51,319)( 52,320)( 53,313)( 54,314)( 55,315)( 56,316)
( 57,309)( 58,310)( 59,311)( 60,312)( 61,305)( 62,306)( 63,307)( 64,308)
( 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)
(145,437)(146,438)(147,439)(148,440)(149,433)(150,434)(151,435)(152,436)
(153,447)(154,448)(155,445)(156,446)(157,443)(158,444)(159,441)(160,442)
(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)
(177,405)(178,406)(179,407)(180,408)(181,401)(182,402)(183,403)(184,404)
(185,415)(186,416)(187,413)(188,414)(189,411)(190,412)(191,409)(192,410)
(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*s0*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*s0*s1*s0*s1, 
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 ];;
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, 85)( 18, 86)( 19, 87)( 20, 88)( 21, 81)( 22, 82)( 23, 83)
( 24, 84)( 25, 94)( 26, 93)( 27, 96)( 28, 95)( 29, 90)( 30, 89)( 31, 92)
( 32, 91)( 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)( 49,114)( 50,113)( 51,116)( 52,115)( 53,117)( 54,118)( 55,119)
( 56,120)( 57,121)( 58,122)( 59,123)( 60,124)( 61,126)( 62,125)( 63,128)
( 64,127)(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)(145,213)(146,214)(147,215)(148,216)(149,209)(150,210)(151,211)
(152,212)(153,222)(154,221)(155,224)(156,223)(157,218)(158,217)(159,220)
(160,219)(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)(177,242)(178,241)(179,244)(180,243)(181,245)(182,246)(183,247)
(184,248)(185,249)(186,250)(187,251)(188,252)(189,254)(190,253)(191,256)
(192,255)(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)(273,341)(274,342)(275,343)(276,344)(277,337)(278,338)(279,339)
(280,340)(281,350)(282,349)(283,352)(284,351)(285,346)(286,345)(287,348)
(288,347)(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)(305,370)(306,369)(307,372)(308,371)(309,373)(310,374)(311,375)
(312,376)(313,377)(314,378)(315,379)(316,380)(317,382)(318,381)(319,384)
(320,383)(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)(401,469)(402,470)(403,471)(404,472)(405,465)(406,466)(407,467)
(408,468)(409,478)(410,477)(411,480)(412,479)(413,474)(414,473)(415,476)
(416,475)(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)(433,498)(434,497)(435,500)(436,499)(437,501)(438,502)(439,503)
(440,504)(441,505)(442,506)(443,507)(444,508)(445,510)(446,509)(447,512)
(448,511);
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)( 17,277)( 18,278)( 19,279)( 20,280)( 21,273)( 22,274)( 23,275)
( 24,276)( 25,287)( 26,288)( 27,285)( 28,286)( 29,283)( 30,284)( 31,281)
( 32,282)( 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)( 49,317)( 50,318)( 51,319)( 52,320)( 53,313)( 54,314)( 55,315)
( 56,316)( 57,309)( 58,310)( 59,311)( 60,312)( 61,305)( 62,306)( 63,307)
( 64,308)( 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)(145,437)(146,438)(147,439)(148,440)(149,433)(150,434)(151,435)
(152,436)(153,447)(154,448)(155,445)(156,446)(157,443)(158,444)(159,441)
(160,442)(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)(177,405)(178,406)(179,407)(180,408)(181,401)(182,402)(183,403)
(184,404)(185,415)(186,416)(187,413)(188,414)(189,411)(190,412)(191,409)
(192,410)(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*s0*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*s0*s1*s0*s1, 
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 >; 
 
References : None.
to this polytope