Polytope of Type {4,60,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,60,2}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240289)
Rank : 4
Schlafli Type : {4,60,2}
Number of vertices, edges, etc : 8, 240, 120, 2
Order of s0s1s2s3 : 60
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
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 : {4,60,2}*960b, {4,60,2}*960c, {4,30,2}*960
4-fold quotients : {2,60,2}*480, {4,15,2}*480, {4,30,2}*480b, {4,30,2}*480c
5-fold quotients : {4,12,2}*384b
8-fold quotients : {4,15,2}*240, {2,30,2}*240
10-fold quotients : {4,12,2}*192b, {4,12,2}*192c, {4,6,2}*192
12-fold quotients : {2,20,2}*160
16-fold quotients : {2,15,2}*120
20-fold quotients : {2,12,2}*96, {4,3,2}*96, {4,6,2}*96b, {4,6,2}*96c
24-fold quotients : {2,10,2}*80
40-fold quotients : {4,3,2}*48, {2,6,2}*48
48-fold quotients : {2,5,2}*40
60-fold quotients : {2,4,2}*32
80-fold quotients : {2,3,2}*24
120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,243)( 2,244)( 3,241)( 4,242)( 5,247)( 6,248)( 7,245)( 8,246)( 9,251)( 10,252)( 11,249)( 12,250)( 13,255)( 14,256)( 15,253)( 16,254)( 17,259)( 18,260)( 19,257)( 20,258)( 21,263)( 22,264)( 23,261)( 24,262)( 25,267)( 26,268)( 27,265)( 28,266)( 29,271)( 30,272)( 31,269)( 32,270)( 33,275)( 34,276)( 35,273)( 36,274)( 37,279)( 38,280)( 39,277)( 40,278)( 41,283)( 42,284)( 43,281)( 44,282)( 45,287)( 46,288)( 47,285)( 48,286)( 49,291)( 50,292)( 51,289)( 52,290)( 53,295)( 54,296)( 55,293)( 56,294)( 57,299)( 58,300)( 59,297)( 60,298)( 61,303)( 62,304)( 63,301)( 64,302)( 65,307)( 66,308)( 67,305)( 68,306)( 69,311)( 70,312)( 71,309)( 72,310)( 73,315)( 74,316)( 75,313)( 76,314)( 77,319)( 78,320)( 79,317)( 80,318)( 81,323)( 82,324)( 83,321)( 84,322)( 85,327)( 86,328)( 87,325)( 88,326)( 89,331)( 90,332)( 91,329)( 92,330)( 93,335)( 94,336)( 95,333)( 96,334)( 97,339)( 98,340)( 99,337)(100,338)(101,343)(102,344)(103,341)(104,342)(105,347)(106,348)(107,345)(108,346)(109,351)(110,352)(111,349)(112,350)(113,355)(114,356)(115,353)(116,354)(117,359)(118,360)(119,357)(120,358)(121,363)(122,364)(123,361)(124,362)(125,367)(126,368)(127,365)(128,366)(129,371)(130,372)(131,369)(132,370)(133,375)(134,376)(135,373)(136,374)(137,379)(138,380)(139,377)(140,378)(141,383)(142,384)(143,381)(144,382)(145,387)(146,388)(147,385)(148,386)(149,391)(150,392)(151,389)(152,390)(153,395)(154,396)(155,393)(156,394)(157,399)(158,400)(159,397)(160,398)(161,403)(162,404)(163,401)(164,402)(165,407)(166,408)(167,405)(168,406)(169,411)(170,412)(171,409)(172,410)(173,415)(174,416)(175,413)(176,414)(177,419)(178,420)(179,417)(180,418)(181,423)(182,424)(183,421)(184,422)(185,427)(186,428)(187,425)(188,426)(189,431)(190,432)(191,429)(192,430)(193,435)(194,436)(195,433)(196,434)(197,439)(198,440)(199,437)(200,438)(201,443)(202,444)(203,441)(204,442)(205,447)(206,448)(207,445)(208,446)(209,451)(210,452)(211,449)(212,450)(213,455)(214,456)(215,453)(216,454)(217,459)(218,460)(219,457)(220,458)(221,463)(222,464)(223,461)(224,462)(225,467)(226,468)(227,465)(228,466)(229,471)(230,472)(231,469)(232,470)(233,475)(234,476)(235,473)(236,474)(237,479)(238,480)(239,477)(240,478);;
s1 := ( 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)(242,243)(245,257)(246,259)(247,258)(248,260)(249,253)(250,255)(251,254)(252,256)(261,281)(262,283)(263,282)(264,284)(265,297)(266,299)(267,298)(268,300)(269,293)(270,295)(271,294)(272,296)(273,289)(274,291)(275,290)(276,292)(277,285)(278,287)(279,286)(280,288)(302,303)(305,317)(306,319)(307,318)(308,320)(309,313)(310,315)(311,314)(312,316)(321,341)(322,343)(323,342)(324,344)(325,357)(326,359)(327,358)(328,360)(329,353)(330,355)(331,354)(332,356)(333,349)(334,351)(335,350)(336,352)(337,345)(338,347)(339,346)(340,348)(361,421)(362,423)(363,422)(364,424)(365,437)(366,439)(367,438)(368,440)(369,433)(370,435)(371,434)(372,436)(373,429)(374,431)(375,430)(376,432)(377,425)(378,427)(379,426)(380,428)(381,461)(382,463)(383,462)(384,464)(385,477)(386,479)(387,478)(388,480)(389,473)(390,475)(391,474)(392,476)(393,469)(394,471)(395,470)(396,472)(397,465)(398,467)(399,466)(400,468)(401,441)(402,443)(403,442)(404,444)(405,457)(406,459)(407,458)(408,460)(409,453)(410,455)(411,454)(412,456)(413,449)(414,451)(415,450)(416,452)(417,445)(418,447)(419,446)(420,448);;
s2 := ( 1,165)( 2,168)( 3,167)( 4,166)( 5,161)( 6,164)( 7,163)( 8,162)( 9,177)( 10,180)( 11,179)( 12,178)( 13,173)( 14,176)( 15,175)( 16,174)( 17,169)( 18,172)( 19,171)( 20,170)( 21,145)( 22,148)( 23,147)( 24,146)( 25,141)( 26,144)( 27,143)( 28,142)( 29,157)( 30,160)( 31,159)( 32,158)( 33,153)( 34,156)( 35,155)( 36,154)( 37,149)( 38,152)( 39,151)( 40,150)( 41,125)( 42,128)( 43,127)( 44,126)( 45,121)( 46,124)( 47,123)( 48,122)( 49,137)( 50,140)( 51,139)( 52,138)( 53,133)( 54,136)( 55,135)( 56,134)( 57,129)( 58,132)( 59,131)( 60,130)( 61,225)( 62,228)( 63,227)( 64,226)( 65,221)( 66,224)( 67,223)( 68,222)( 69,237)( 70,240)( 71,239)( 72,238)( 73,233)( 74,236)( 75,235)( 76,234)( 77,229)( 78,232)( 79,231)( 80,230)( 81,205)( 82,208)( 83,207)( 84,206)( 85,201)( 86,204)( 87,203)( 88,202)( 89,217)( 90,220)( 91,219)( 92,218)( 93,213)( 94,216)( 95,215)( 96,214)( 97,209)( 98,212)( 99,211)(100,210)(101,185)(102,188)(103,187)(104,186)(105,181)(106,184)(107,183)(108,182)(109,197)(110,200)(111,199)(112,198)(113,193)(114,196)(115,195)(116,194)(117,189)(118,192)(119,191)(120,190)(241,405)(242,408)(243,407)(244,406)(245,401)(246,404)(247,403)(248,402)(249,417)(250,420)(251,419)(252,418)(253,413)(254,416)(255,415)(256,414)(257,409)(258,412)(259,411)(260,410)(261,385)(262,388)(263,387)(264,386)(265,381)(266,384)(267,383)(268,382)(269,397)(270,400)(271,399)(272,398)(273,393)(274,396)(275,395)(276,394)(277,389)(278,392)(279,391)(280,390)(281,365)(282,368)(283,367)(284,366)(285,361)(286,364)(287,363)(288,362)(289,377)(290,380)(291,379)(292,378)(293,373)(294,376)(295,375)(296,374)(297,369)(298,372)(299,371)(300,370)(301,465)(302,468)(303,467)(304,466)(305,461)(306,464)(307,463)(308,462)(309,477)(310,480)(311,479)(312,478)(313,473)(314,476)(315,475)(316,474)(317,469)(318,472)(319,471)(320,470)(321,445)(322,448)(323,447)(324,446)(325,441)(326,444)(327,443)(328,442)(329,457)(330,460)(331,459)(332,458)(333,453)(334,456)(335,455)(336,454)(337,449)(338,452)(339,451)(340,450)(341,425)(342,428)(343,427)(344,426)(345,421)(346,424)(347,423)(348,422)(349,437)(350,440)(351,439)(352,438)(353,433)(354,436)(355,435)(356,434)(357,429)(358,432)(359,431)(360,430);;
s3 := (481,482);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
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*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*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(482)!( 1,243)( 2,244)( 3,241)( 4,242)( 5,247)( 6,248)( 7,245)( 8,246)( 9,251)( 10,252)( 11,249)( 12,250)( 13,255)( 14,256)( 15,253)( 16,254)( 17,259)( 18,260)( 19,257)( 20,258)( 21,263)( 22,264)( 23,261)( 24,262)( 25,267)( 26,268)( 27,265)( 28,266)( 29,271)( 30,272)( 31,269)( 32,270)( 33,275)( 34,276)( 35,273)( 36,274)( 37,279)( 38,280)( 39,277)( 40,278)( 41,283)( 42,284)( 43,281)( 44,282)( 45,287)( 46,288)( 47,285)( 48,286)( 49,291)( 50,292)( 51,289)( 52,290)( 53,295)( 54,296)( 55,293)( 56,294)( 57,299)( 58,300)( 59,297)( 60,298)( 61,303)( 62,304)( 63,301)( 64,302)( 65,307)( 66,308)( 67,305)( 68,306)( 69,311)( 70,312)( 71,309)( 72,310)( 73,315)( 74,316)( 75,313)( 76,314)( 77,319)( 78,320)( 79,317)( 80,318)( 81,323)( 82,324)( 83,321)( 84,322)( 85,327)( 86,328)( 87,325)( 88,326)( 89,331)( 90,332)( 91,329)( 92,330)( 93,335)( 94,336)( 95,333)( 96,334)( 97,339)( 98,340)( 99,337)(100,338)(101,343)(102,344)(103,341)(104,342)(105,347)(106,348)(107,345)(108,346)(109,351)(110,352)(111,349)(112,350)(113,355)(114,356)(115,353)(116,354)(117,359)(118,360)(119,357)(120,358)(121,363)(122,364)(123,361)(124,362)(125,367)(126,368)(127,365)(128,366)(129,371)(130,372)(131,369)(132,370)(133,375)(134,376)(135,373)(136,374)(137,379)(138,380)(139,377)(140,378)(141,383)(142,384)(143,381)(144,382)(145,387)(146,388)(147,385)(148,386)(149,391)(150,392)(151,389)(152,390)(153,395)(154,396)(155,393)(156,394)(157,399)(158,400)(159,397)(160,398)(161,403)(162,404)(163,401)(164,402)(165,407)(166,408)(167,405)(168,406)(169,411)(170,412)(171,409)(172,410)(173,415)(174,416)(175,413)(176,414)(177,419)(178,420)(179,417)(180,418)(181,423)(182,424)(183,421)(184,422)(185,427)(186,428)(187,425)(188,426)(189,431)(190,432)(191,429)(192,430)(193,435)(194,436)(195,433)(196,434)(197,439)(198,440)(199,437)(200,438)(201,443)(202,444)(203,441)(204,442)(205,447)(206,448)(207,445)(208,446)(209,451)(210,452)(211,449)(212,450)(213,455)(214,456)(215,453)(216,454)(217,459)(218,460)(219,457)(220,458)(221,463)(222,464)(223,461)(224,462)(225,467)(226,468)(227,465)(228,466)(229,471)(230,472)(231,469)(232,470)(233,475)(234,476)(235,473)(236,474)(237,479)(238,480)(239,477)(240,478);
s1 := Sym(482)!( 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)(242,243)(245,257)(246,259)(247,258)(248,260)(249,253)(250,255)(251,254)(252,256)(261,281)(262,283)(263,282)(264,284)(265,297)(266,299)(267,298)(268,300)(269,293)(270,295)(271,294)(272,296)(273,289)(274,291)(275,290)(276,292)(277,285)(278,287)(279,286)(280,288)(302,303)(305,317)(306,319)(307,318)(308,320)(309,313)(310,315)(311,314)(312,316)(321,341)(322,343)(323,342)(324,344)(325,357)(326,359)(327,358)(328,360)(329,353)(330,355)(331,354)(332,356)(333,349)(334,351)(335,350)(336,352)(337,345)(338,347)(339,346)(340,348)(361,421)(362,423)(363,422)(364,424)(365,437)(366,439)(367,438)(368,440)(369,433)(370,435)(371,434)(372,436)(373,429)(374,431)(375,430)(376,432)(377,425)(378,427)(379,426)(380,428)(381,461)(382,463)(383,462)(384,464)(385,477)(386,479)(387,478)(388,480)(389,473)(390,475)(391,474)(392,476)(393,469)(394,471)(395,470)(396,472)(397,465)(398,467)(399,466)(400,468)(401,441)(402,443)(403,442)(404,444)(405,457)(406,459)(407,458)(408,460)(409,453)(410,455)(411,454)(412,456)(413,449)(414,451)(415,450)(416,452)(417,445)(418,447)(419,446)(420,448);
s2 := Sym(482)!( 1,165)( 2,168)( 3,167)( 4,166)( 5,161)( 6,164)( 7,163)( 8,162)( 9,177)( 10,180)( 11,179)( 12,178)( 13,173)( 14,176)( 15,175)( 16,174)( 17,169)( 18,172)( 19,171)( 20,170)( 21,145)( 22,148)( 23,147)( 24,146)( 25,141)( 26,144)( 27,143)( 28,142)( 29,157)( 30,160)( 31,159)( 32,158)( 33,153)( 34,156)( 35,155)( 36,154)( 37,149)( 38,152)( 39,151)( 40,150)( 41,125)( 42,128)( 43,127)( 44,126)( 45,121)( 46,124)( 47,123)( 48,122)( 49,137)( 50,140)( 51,139)( 52,138)( 53,133)( 54,136)( 55,135)( 56,134)( 57,129)( 58,132)( 59,131)( 60,130)( 61,225)( 62,228)( 63,227)( 64,226)( 65,221)( 66,224)( 67,223)( 68,222)( 69,237)( 70,240)( 71,239)( 72,238)( 73,233)( 74,236)( 75,235)( 76,234)( 77,229)( 78,232)( 79,231)( 80,230)( 81,205)( 82,208)( 83,207)( 84,206)( 85,201)( 86,204)( 87,203)( 88,202)( 89,217)( 90,220)( 91,219)( 92,218)( 93,213)( 94,216)( 95,215)( 96,214)( 97,209)( 98,212)( 99,211)(100,210)(101,185)(102,188)(103,187)(104,186)(105,181)(106,184)(107,183)(108,182)(109,197)(110,200)(111,199)(112,198)(113,193)(114,196)(115,195)(116,194)(117,189)(118,192)(119,191)(120,190)(241,405)(242,408)(243,407)(244,406)(245,401)(246,404)(247,403)(248,402)(249,417)(250,420)(251,419)(252,418)(253,413)(254,416)(255,415)(256,414)(257,409)(258,412)(259,411)(260,410)(261,385)(262,388)(263,387)(264,386)(265,381)(266,384)(267,383)(268,382)(269,397)(270,400)(271,399)(272,398)(273,393)(274,396)(275,395)(276,394)(277,389)(278,392)(279,391)(280,390)(281,365)(282,368)(283,367)(284,366)(285,361)(286,364)(287,363)(288,362)(289,377)(290,380)(291,379)(292,378)(293,373)(294,376)(295,375)(296,374)(297,369)(298,372)(299,371)(300,370)(301,465)(302,468)(303,467)(304,466)(305,461)(306,464)(307,463)(308,462)(309,477)(310,480)(311,479)(312,478)(313,473)(314,476)(315,475)(316,474)(317,469)(318,472)(319,471)(320,470)(321,445)(322,448)(323,447)(324,446)(325,441)(326,444)(327,443)(328,442)(329,457)(330,460)(331,459)(332,458)(333,453)(334,456)(335,455)(336,454)(337,449)(338,452)(339,451)(340,450)(341,425)(342,428)(343,427)(344,426)(345,421)(346,424)(347,423)(348,422)(349,437)(350,440)(351,439)(352,438)(353,433)(354,436)(355,435)(356,434)(357,429)(358,432)(359,431)(360,430);
s3 := Sym(482)!(481,482);
poly := sub<Sym(482)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
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*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*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 >;
to this polytope