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