Polytope of Type {16,16}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,16}*512i
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 : {8,16}*256b, {16,8}*256c
   4-fold quotients : {8,8}*128c, {16,4}*128a
   8-fold quotients : {8,4}*64a, {4,8}*64b, {16,2}*64
   16-fold quotients : {4,4}*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.
Irregular Quotients (of which this is a minimal cover):
   None.

Permutation Representation (GAP) : 
s0 := (  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);;
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, 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, 86)( 18, 85)( 19, 88)( 20, 87)( 21, 82)( 22, 81)( 23, 84)( 24, 83)( 25, 93)( 26, 94)( 27, 95)( 28, 96)( 29, 89)( 30, 90)( 31, 91)( 32, 92)( 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)( 49,113)( 50,114)( 51,115)( 52,116)( 53,118)( 54,117)( 55,120)( 56,119)( 57,122)( 58,121)( 59,124)( 60,123)( 61,125)( 62,126)( 63,127)( 64,128)(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)(145,214)(146,213)(147,216)(148,215)(149,210)(150,209)(151,212)(152,211)(153,221)(154,222)(155,223)(156,224)(157,217)(158,218)(159,219)(160,220)(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)(177,241)(178,242)(179,243)(180,244)(181,246)(182,245)(183,248)(184,247)(185,250)(186,249)(187,252)(188,251)(189,253)(190,254)(191,255)(192,256)(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)(273,342)(274,341)(275,344)(276,343)(277,338)(278,337)(279,340)(280,339)(281,349)(282,350)(283,351)(284,352)(285,345)(286,346)(287,347)(288,348)(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)(305,369)(306,370)(307,371)(308,372)(309,374)(310,373)(311,376)(312,375)(313,378)(314,377)(315,380)(316,379)(317,381)(318,382)(319,383)(320,384)(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)(401,470)(402,469)(403,472)(404,471)(405,466)(406,465)(407,468)(408,467)(409,477)(410,478)(411,479)(412,480)(413,473)(414,474)(415,475)(416,476)(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)(433,497)(434,498)(435,499)(436,500)(437,502)(438,501)(439,504)(440,503)(441,506)(442,505)(443,508)(444,507)(445,509)(446,510)(447,511)(448,512);;
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*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1, 
s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := 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);
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, 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, 86)( 18, 85)( 19, 88)( 20, 87)( 21, 82)( 22, 81)( 23, 84)( 24, 83)( 25, 93)( 26, 94)( 27, 95)( 28, 96)( 29, 89)( 30, 90)( 31, 91)( 32, 92)( 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)( 49,113)( 50,114)( 51,115)( 52,116)( 53,118)( 54,117)( 55,120)( 56,119)( 57,122)( 58,121)( 59,124)( 60,123)( 61,125)( 62,126)( 63,127)( 64,128)(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)(145,214)(146,213)(147,216)(148,215)(149,210)(150,209)(151,212)(152,211)(153,221)(154,222)(155,223)(156,224)(157,217)(158,218)(159,219)(160,220)(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)(177,241)(178,242)(179,243)(180,244)(181,246)(182,245)(183,248)(184,247)(185,250)(186,249)(187,252)(188,251)(189,253)(190,254)(191,255)(192,256)(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)(273,342)(274,341)(275,344)(276,343)(277,338)(278,337)(279,340)(280,339)(281,349)(282,350)(283,351)(284,352)(285,345)(286,346)(287,347)(288,348)(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)(305,369)(306,370)(307,371)(308,372)(309,374)(310,373)(311,376)(312,375)(313,378)(314,377)(315,380)(316,379)(317,381)(318,382)(319,383)(320,384)(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)(401,470)(402,469)(403,472)(404,471)(405,466)(406,465)(407,468)(408,467)(409,477)(410,478)(411,479)(412,480)(413,473)(414,474)(415,475)(416,476)(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)(433,497)(434,498)(435,499)(436,500)(437,502)(438,501)(439,504)(440,503)(441,506)(442,505)(443,508)(444,507)(445,509)(446,510)(447,511)(448,512);
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*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1, 
s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*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 >;
References : None.
to this polytope

Twisty Puzzle