Polytope of Type {60,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {60,6}*1920
if this polytope has a name.
Group : SmallGroup(1920,238596)
Rank : 3
Schlafli Type : {60,6}
Number of vertices, edges, etc : 160, 480, 16
Order of s0s1s2 : 40
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {60,6}*960a, {30,6}*960, {60,6}*960b
   4-fold quotients : {30,6}*480
   5-fold quotients : {12,6}*384
   8-fold quotients : {15,6}*240
   10-fold quotients : {12,6}*192a, {12,6}*192b, {6,6}*192b
   20-fold quotients : {12,3}*96, {6,6}*96
   24-fold quotients : {20,2}*80
   40-fold quotients : {3,6}*48, {6,3}*48
   48-fold quotients : {10,2}*40
   80-fold quotients : {3,3}*24
   96-fold quotients : {5,2}*20
   120-fold quotients : {4,2}*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=<s2*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 3.
      8 facets:
         4 of {20}*40
         4 of {60}*120
      80 vertex figures:
         40 of {6}*12
         40 of {2}*4

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

Twisty Puzzle