Polytope of Type {120,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {120,4}*1920d
if this polytope has a name.
Group : SmallGroup(1920,239543)
Rank : 3
Schlafli Type : {120,4}
Number of vertices, edges, etc : 240, 480, 8
Order of s0s1s2 : 120
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {60,4}*960b
   4-fold quotients : {60,4}*480b, {60,4}*480c, {30,4}*480
   5-fold quotients : {24,4}*384d
   8-fold quotients : {60,2}*240, {15,4}*240, {30,4}*240b, {30,4}*240c
   10-fold quotients : {12,4}*192b
   16-fold quotients : {15,4}*120, {30,2}*120
   20-fold quotients : {12,4}*96b, {12,4}*96c, {6,4}*96
   24-fold quotients : {20,2}*80
   32-fold quotients : {15,2}*60
   40-fold quotients : {12,2}*48, {3,4}*48, {6,4}*48b, {6,4}*48c
   48-fold quotients : {10,2}*40
   80-fold quotients : {3,4}*24, {6,2}*24
   96-fold quotients : {5,2}*20
   120-fold quotients : {4,2}*16
   160-fold quotients : {3,2}*12
   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=<s1*s0*s1*s2*s1*s0*s2*s1> of order 2.
      4 facets:
         4 of {120}*240
      160 vertex figures:
         80 of {4}*8
         80 of {2}*4
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s2> of order 2.
      4 facets:
         4 of {120}*240
      120 vertex figures:
         120 of {4}*8

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

Twisty Puzzle