Polytope of Type {6,60}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,60}*1920
if this polytope has a name.
Group : SmallGroup(1920,238596)
Rank : 3
Schlafli Type : {6,60}
Number of vertices, edges, etc : 16, 480, 160
Order of s0s1s2 : 40
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,60}*960a, {6,30}*960, {6,60}*960b
   4-fold quotients : {6,30}*480
   5-fold quotients : {6,12}*384
   8-fold quotients : {6,15}*240
   10-fold quotients : {6,12}*192a, {6,12}*192b, {6,6}*192b
   20-fold quotients : {3,12}*96, {6,6}*96
   24-fold quotients : {2,20}*80
   40-fold quotients : {3,6}*48, {6,3}*48
   48-fold quotients : {2,10}*40
   80-fold quotients : {3,3}*24
   96-fold quotients : {2,5}*20
   120-fold quotients : {2,4}*16
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1> of order 3.
      80 facets:
         40 of {2}*4
         40 of {6}*12
      8 vertex figures:
         4 of {60}*120
         4 of {20}*40

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

Twisty Puzzle