Polytope of Type {2,120,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,120,4}*1920d
if this polytope has a name.
Group : SmallGroup(1920,239539)
Rank : 4
Schlafli Type : {2,120,4}
Number of vertices, edges, etc : 2, 120, 240, 4
Order of s0s1s2s3 : 120
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-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
4-fold quotients : {2,30,4}*480b
5-fold quotients : {2,24,4}*384d
8-fold quotients : {2,15,4}*240
10-fold quotients : {2,12,4}*192b
20-fold quotients : {2,6,4}*96c
40-fold quotients : {2,3,4}*48
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)(243,363)(244,365)
(245,364)(246,366)(247,379)(248,381)(249,380)(250,382)(251,375)(252,377)
(253,376)(254,378)(255,371)(256,373)(257,372)(258,374)(259,367)(260,369)
(261,368)(262,370)(263,403)(264,405)(265,404)(266,406)(267,419)(268,421)
(269,420)(270,422)(271,415)(272,417)(273,416)(274,418)(275,411)(276,413)
(277,412)(278,414)(279,407)(280,409)(281,408)(282,410)(283,383)(284,385)
(285,384)(286,386)(287,399)(288,401)(289,400)(290,402)(291,395)(292,397)
(293,396)(294,398)(295,391)(296,393)(297,392)(298,394)(299,387)(300,389)
(301,388)(302,390)(303,423)(304,425)(305,424)(306,426)(307,439)(308,441)
(309,440)(310,442)(311,435)(312,437)(313,436)(314,438)(315,431)(316,433)
(317,432)(318,434)(319,427)(320,429)(321,428)(322,430)(323,463)(324,465)
(325,464)(326,466)(327,479)(328,481)(329,480)(330,482)(331,475)(332,477)
(333,476)(334,478)(335,471)(336,473)(337,472)(338,474)(339,467)(340,469)
(341,468)(342,470)(343,443)(344,445)(345,444)(346,446)(347,459)(348,461)
(349,460)(350,462)(351,455)(352,457)(353,456)(354,458)(355,451)(356,453)
(357,452)(358,454)(359,447)(360,449)(361,448)(362,450);;
s2 := ( 3,267)( 4,268)( 5,270)( 6,269)( 7,263)( 8,264)( 9,266)( 10,265)
( 11,279)( 12,280)( 13,282)( 14,281)( 15,275)( 16,276)( 17,278)( 18,277)
( 19,271)( 20,272)( 21,274)( 22,273)( 23,247)( 24,248)( 25,250)( 26,249)
( 27,243)( 28,244)( 29,246)( 30,245)( 31,259)( 32,260)( 33,262)( 34,261)
( 35,255)( 36,256)( 37,258)( 38,257)( 39,251)( 40,252)( 41,254)( 42,253)
( 43,287)( 44,288)( 45,290)( 46,289)( 47,283)( 48,284)( 49,286)( 50,285)
( 51,299)( 52,300)( 53,302)( 54,301)( 55,295)( 56,296)( 57,298)( 58,297)
( 59,291)( 60,292)( 61,294)( 62,293)( 63,327)( 64,328)( 65,330)( 66,329)
( 67,323)( 68,324)( 69,326)( 70,325)( 71,339)( 72,340)( 73,342)( 74,341)
( 75,335)( 76,336)( 77,338)( 78,337)( 79,331)( 80,332)( 81,334)( 82,333)
( 83,307)( 84,308)( 85,310)( 86,309)( 87,303)( 88,304)( 89,306)( 90,305)
( 91,319)( 92,320)( 93,322)( 94,321)( 95,315)( 96,316)( 97,318)( 98,317)
( 99,311)(100,312)(101,314)(102,313)(103,347)(104,348)(105,350)(106,349)
(107,343)(108,344)(109,346)(110,345)(111,359)(112,360)(113,362)(114,361)
(115,355)(116,356)(117,358)(118,357)(119,351)(120,352)(121,354)(122,353)
(123,447)(124,448)(125,450)(126,449)(127,443)(128,444)(129,446)(130,445)
(131,459)(132,460)(133,462)(134,461)(135,455)(136,456)(137,458)(138,457)
(139,451)(140,452)(141,454)(142,453)(143,427)(144,428)(145,430)(146,429)
(147,423)(148,424)(149,426)(150,425)(151,439)(152,440)(153,442)(154,441)
(155,435)(156,436)(157,438)(158,437)(159,431)(160,432)(161,434)(162,433)
(163,467)(164,468)(165,470)(166,469)(167,463)(168,464)(169,466)(170,465)
(171,479)(172,480)(173,482)(174,481)(175,475)(176,476)(177,478)(178,477)
(179,471)(180,472)(181,474)(182,473)(183,387)(184,388)(185,390)(186,389)
(187,383)(188,384)(189,386)(190,385)(191,399)(192,400)(193,402)(194,401)
(195,395)(196,396)(197,398)(198,397)(199,391)(200,392)(201,394)(202,393)
(203,367)(204,368)(205,370)(206,369)(207,363)(208,364)(209,366)(210,365)
(211,379)(212,380)(213,382)(214,381)(215,375)(216,376)(217,378)(218,377)
(219,371)(220,372)(221,374)(222,373)(223,407)(224,408)(225,410)(226,409)
(227,403)(228,404)(229,406)(230,405)(231,419)(232,420)(233,422)(234,421)
(235,415)(236,416)(237,418)(238,417)(239,411)(240,412)(241,414)(242,413);;
s3 := ( 3, 66)( 4, 65)( 5, 64)( 6, 63)( 7, 70)( 8, 69)( 9, 68)( 10, 67)
( 11, 74)( 12, 73)( 13, 72)( 14, 71)( 15, 78)( 16, 77)( 17, 76)( 18, 75)
( 19, 82)( 20, 81)( 21, 80)( 22, 79)( 23, 86)( 24, 85)( 25, 84)( 26, 83)
( 27, 90)( 28, 89)( 29, 88)( 30, 87)( 31, 94)( 32, 93)( 33, 92)( 34, 91)
( 35, 98)( 36, 97)( 37, 96)( 38, 95)( 39,102)( 40,101)( 41,100)( 42, 99)
( 43,106)( 44,105)( 45,104)( 46,103)( 47,110)( 48,109)( 49,108)( 50,107)
( 51,114)( 52,113)( 53,112)( 54,111)( 55,118)( 56,117)( 57,116)( 58,115)
( 59,122)( 60,121)( 61,120)( 62,119)(123,186)(124,185)(125,184)(126,183)
(127,190)(128,189)(129,188)(130,187)(131,194)(132,193)(133,192)(134,191)
(135,198)(136,197)(137,196)(138,195)(139,202)(140,201)(141,200)(142,199)
(143,206)(144,205)(145,204)(146,203)(147,210)(148,209)(149,208)(150,207)
(151,214)(152,213)(153,212)(154,211)(155,218)(156,217)(157,216)(158,215)
(159,222)(160,221)(161,220)(162,219)(163,226)(164,225)(165,224)(166,223)
(167,230)(168,229)(169,228)(170,227)(171,234)(172,233)(173,232)(174,231)
(175,238)(176,237)(177,236)(178,235)(179,242)(180,241)(181,240)(182,239)
(243,306)(244,305)(245,304)(246,303)(247,310)(248,309)(249,308)(250,307)
(251,314)(252,313)(253,312)(254,311)(255,318)(256,317)(257,316)(258,315)
(259,322)(260,321)(261,320)(262,319)(263,326)(264,325)(265,324)(266,323)
(267,330)(268,329)(269,328)(270,327)(271,334)(272,333)(273,332)(274,331)
(275,338)(276,337)(277,336)(278,335)(279,342)(280,341)(281,340)(282,339)
(283,346)(284,345)(285,344)(286,343)(287,350)(288,349)(289,348)(290,347)
(291,354)(292,353)(293,352)(294,351)(295,358)(296,357)(297,356)(298,355)
(299,362)(300,361)(301,360)(302,359)(363,426)(364,425)(365,424)(366,423)
(367,430)(368,429)(369,428)(370,427)(371,434)(372,433)(373,432)(374,431)
(375,438)(376,437)(377,436)(378,435)(379,442)(380,441)(381,440)(382,439)
(383,446)(384,445)(385,444)(386,443)(387,450)(388,449)(389,448)(390,447)
(391,454)(392,453)(393,452)(394,451)(395,458)(396,457)(397,456)(398,455)
(399,462)(400,461)(401,460)(402,459)(403,466)(404,465)(405,464)(406,463)
(407,470)(408,469)(409,468)(410,467)(411,474)(412,473)(413,472)(414,471)
(415,478)(416,477)(417,476)(418,475)(419,482)(420,481)(421,480)(422,479);;
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*s3*s1*s2*s3*s1*s2*s3*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)(243,363)
(244,365)(245,364)(246,366)(247,379)(248,381)(249,380)(250,382)(251,375)
(252,377)(253,376)(254,378)(255,371)(256,373)(257,372)(258,374)(259,367)
(260,369)(261,368)(262,370)(263,403)(264,405)(265,404)(266,406)(267,419)
(268,421)(269,420)(270,422)(271,415)(272,417)(273,416)(274,418)(275,411)
(276,413)(277,412)(278,414)(279,407)(280,409)(281,408)(282,410)(283,383)
(284,385)(285,384)(286,386)(287,399)(288,401)(289,400)(290,402)(291,395)
(292,397)(293,396)(294,398)(295,391)(296,393)(297,392)(298,394)(299,387)
(300,389)(301,388)(302,390)(303,423)(304,425)(305,424)(306,426)(307,439)
(308,441)(309,440)(310,442)(311,435)(312,437)(313,436)(314,438)(315,431)
(316,433)(317,432)(318,434)(319,427)(320,429)(321,428)(322,430)(323,463)
(324,465)(325,464)(326,466)(327,479)(328,481)(329,480)(330,482)(331,475)
(332,477)(333,476)(334,478)(335,471)(336,473)(337,472)(338,474)(339,467)
(340,469)(341,468)(342,470)(343,443)(344,445)(345,444)(346,446)(347,459)
(348,461)(349,460)(350,462)(351,455)(352,457)(353,456)(354,458)(355,451)
(356,453)(357,452)(358,454)(359,447)(360,449)(361,448)(362,450);
s2 := Sym(482)!( 3,267)( 4,268)( 5,270)( 6,269)( 7,263)( 8,264)( 9,266)
( 10,265)( 11,279)( 12,280)( 13,282)( 14,281)( 15,275)( 16,276)( 17,278)
( 18,277)( 19,271)( 20,272)( 21,274)( 22,273)( 23,247)( 24,248)( 25,250)
( 26,249)( 27,243)( 28,244)( 29,246)( 30,245)( 31,259)( 32,260)( 33,262)
( 34,261)( 35,255)( 36,256)( 37,258)( 38,257)( 39,251)( 40,252)( 41,254)
( 42,253)( 43,287)( 44,288)( 45,290)( 46,289)( 47,283)( 48,284)( 49,286)
( 50,285)( 51,299)( 52,300)( 53,302)( 54,301)( 55,295)( 56,296)( 57,298)
( 58,297)( 59,291)( 60,292)( 61,294)( 62,293)( 63,327)( 64,328)( 65,330)
( 66,329)( 67,323)( 68,324)( 69,326)( 70,325)( 71,339)( 72,340)( 73,342)
( 74,341)( 75,335)( 76,336)( 77,338)( 78,337)( 79,331)( 80,332)( 81,334)
( 82,333)( 83,307)( 84,308)( 85,310)( 86,309)( 87,303)( 88,304)( 89,306)
( 90,305)( 91,319)( 92,320)( 93,322)( 94,321)( 95,315)( 96,316)( 97,318)
( 98,317)( 99,311)(100,312)(101,314)(102,313)(103,347)(104,348)(105,350)
(106,349)(107,343)(108,344)(109,346)(110,345)(111,359)(112,360)(113,362)
(114,361)(115,355)(116,356)(117,358)(118,357)(119,351)(120,352)(121,354)
(122,353)(123,447)(124,448)(125,450)(126,449)(127,443)(128,444)(129,446)
(130,445)(131,459)(132,460)(133,462)(134,461)(135,455)(136,456)(137,458)
(138,457)(139,451)(140,452)(141,454)(142,453)(143,427)(144,428)(145,430)
(146,429)(147,423)(148,424)(149,426)(150,425)(151,439)(152,440)(153,442)
(154,441)(155,435)(156,436)(157,438)(158,437)(159,431)(160,432)(161,434)
(162,433)(163,467)(164,468)(165,470)(166,469)(167,463)(168,464)(169,466)
(170,465)(171,479)(172,480)(173,482)(174,481)(175,475)(176,476)(177,478)
(178,477)(179,471)(180,472)(181,474)(182,473)(183,387)(184,388)(185,390)
(186,389)(187,383)(188,384)(189,386)(190,385)(191,399)(192,400)(193,402)
(194,401)(195,395)(196,396)(197,398)(198,397)(199,391)(200,392)(201,394)
(202,393)(203,367)(204,368)(205,370)(206,369)(207,363)(208,364)(209,366)
(210,365)(211,379)(212,380)(213,382)(214,381)(215,375)(216,376)(217,378)
(218,377)(219,371)(220,372)(221,374)(222,373)(223,407)(224,408)(225,410)
(226,409)(227,403)(228,404)(229,406)(230,405)(231,419)(232,420)(233,422)
(234,421)(235,415)(236,416)(237,418)(238,417)(239,411)(240,412)(241,414)
(242,413);
s3 := Sym(482)!( 3, 66)( 4, 65)( 5, 64)( 6, 63)( 7, 70)( 8, 69)( 9, 68)
( 10, 67)( 11, 74)( 12, 73)( 13, 72)( 14, 71)( 15, 78)( 16, 77)( 17, 76)
( 18, 75)( 19, 82)( 20, 81)( 21, 80)( 22, 79)( 23, 86)( 24, 85)( 25, 84)
( 26, 83)( 27, 90)( 28, 89)( 29, 88)( 30, 87)( 31, 94)( 32, 93)( 33, 92)
( 34, 91)( 35, 98)( 36, 97)( 37, 96)( 38, 95)( 39,102)( 40,101)( 41,100)
( 42, 99)( 43,106)( 44,105)( 45,104)( 46,103)( 47,110)( 48,109)( 49,108)
( 50,107)( 51,114)( 52,113)( 53,112)( 54,111)( 55,118)( 56,117)( 57,116)
( 58,115)( 59,122)( 60,121)( 61,120)( 62,119)(123,186)(124,185)(125,184)
(126,183)(127,190)(128,189)(129,188)(130,187)(131,194)(132,193)(133,192)
(134,191)(135,198)(136,197)(137,196)(138,195)(139,202)(140,201)(141,200)
(142,199)(143,206)(144,205)(145,204)(146,203)(147,210)(148,209)(149,208)
(150,207)(151,214)(152,213)(153,212)(154,211)(155,218)(156,217)(157,216)
(158,215)(159,222)(160,221)(161,220)(162,219)(163,226)(164,225)(165,224)
(166,223)(167,230)(168,229)(169,228)(170,227)(171,234)(172,233)(173,232)
(174,231)(175,238)(176,237)(177,236)(178,235)(179,242)(180,241)(181,240)
(182,239)(243,306)(244,305)(245,304)(246,303)(247,310)(248,309)(249,308)
(250,307)(251,314)(252,313)(253,312)(254,311)(255,318)(256,317)(257,316)
(258,315)(259,322)(260,321)(261,320)(262,319)(263,326)(264,325)(265,324)
(266,323)(267,330)(268,329)(269,328)(270,327)(271,334)(272,333)(273,332)
(274,331)(275,338)(276,337)(277,336)(278,335)(279,342)(280,341)(281,340)
(282,339)(283,346)(284,345)(285,344)(286,343)(287,350)(288,349)(289,348)
(290,347)(291,354)(292,353)(293,352)(294,351)(295,358)(296,357)(297,356)
(298,355)(299,362)(300,361)(301,360)(302,359)(363,426)(364,425)(365,424)
(366,423)(367,430)(368,429)(369,428)(370,427)(371,434)(372,433)(373,432)
(374,431)(375,438)(376,437)(377,436)(378,435)(379,442)(380,441)(381,440)
(382,439)(383,446)(384,445)(385,444)(386,443)(387,450)(388,449)(389,448)
(390,447)(391,454)(392,453)(393,452)(394,451)(395,458)(396,457)(397,456)
(398,455)(399,462)(400,461)(401,460)(402,459)(403,466)(404,465)(405,464)
(406,463)(407,470)(408,469)(409,468)(410,467)(411,474)(412,473)(413,472)
(414,471)(415,478)(416,477)(417,476)(418,475)(419,482)(420,481)(421,480)
(422,479);
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*s3*s1*s2*s3*s1*s2*s3*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