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