Part of the Atlas of Small Regular Polytopes

Polytope of Type {120,4}

Atlas Canonical Name {120,4}*960d

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(960,6316)
Rank
3
Schläfli Type
{120,4}
Vertices, edges, …
120, 240, 4
Order of s0s1s2
120
Order of s0s1s2s1
4
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Non-Orientable
  • Flat
  • Self-Petrie

Quotients maximal quotients in bold

2-fold

4-fold

5-fold

8-fold

10-fold

20-fold

40-fold

Covers minimal covers in bold

2-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

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

References

None.

to this polytope.

Twisty Puzzle