Polytope of Type {4,120}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,120}*1920f
if this polytope has a name.
Group : SmallGroup(1920,239570)
Rank : 3
Schlafli Type : {4,120}
Number of vertices, edges, etc : 8, 480, 240
Order of s0s1s2 : 30
Order of s0s1s2s1 : 8
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 : {4,60}*960c
   4-fold quotients : {4,30}*480
   5-fold quotients : {4,24}*384f
   8-fold quotients : {4,15}*240, {4,30}*240b, {4,30}*240c
   10-fold quotients : {4,12}*192c
   16-fold quotients : {4,15}*120, {2,30}*120
   20-fold quotients : {4,6}*96
   32-fold quotients : {2,15}*60
   40-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   48-fold quotients : {2,10}*40
   80-fold quotients : {4,3}*24, {2,6}*24
   96-fold quotients : {2,5}*20
   160-fold quotients : {2,3}*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=<s0*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 2.
      120 facets:
         120 of {4}*8
      4 vertex figures:
         4 of {120}*240

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

Twisty Puzzle