Polytope of Type {2,4,120}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,120}*1920d
if this polytope has a name.
Group : SmallGroup(1920,239539)
Rank : 4
Schlafli Type : {2,4,120}
Number of vertices, edges, etc : 2, 4, 240, 120
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 : {2,4,60}*960b
4-fold quotients : {2,4,30}*480b
5-fold quotients : {2,4,24}*384d
8-fold quotients : {2,4,15}*240
10-fold quotients : {2,4,12}*192b
20-fold quotients : {2,4,6}*96c
40-fold quotients : {2,4,3}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3, 65)( 4, 66)( 5, 63)( 6, 64)( 7, 69)( 8, 70)( 9, 67)( 10, 68)
( 11, 73)( 12, 74)( 13, 71)( 14, 72)( 15, 77)( 16, 78)( 17, 75)( 18, 76)
( 19, 81)( 20, 82)( 21, 79)( 22, 80)( 23, 85)( 24, 86)( 25, 83)( 26, 84)
( 27, 89)( 28, 90)( 29, 87)( 30, 88)( 31, 93)( 32, 94)( 33, 91)( 34, 92)
( 35, 97)( 36, 98)( 37, 95)( 38, 96)( 39,101)( 40,102)( 41, 99)( 42,100)
( 43,105)( 44,106)( 45,103)( 46,104)( 47,109)( 48,110)( 49,107)( 50,108)
( 51,113)( 52,114)( 53,111)( 54,112)( 55,117)( 56,118)( 57,115)( 58,116)
( 59,121)( 60,122)( 61,119)( 62,120)(123,185)(124,186)(125,183)(126,184)
(127,189)(128,190)(129,187)(130,188)(131,193)(132,194)(133,191)(134,192)
(135,197)(136,198)(137,195)(138,196)(139,201)(140,202)(141,199)(142,200)
(143,205)(144,206)(145,203)(146,204)(147,209)(148,210)(149,207)(150,208)
(151,213)(152,214)(153,211)(154,212)(155,217)(156,218)(157,215)(158,216)
(159,221)(160,222)(161,219)(162,220)(163,225)(164,226)(165,223)(166,224)
(167,229)(168,230)(169,227)(170,228)(171,233)(172,234)(173,231)(174,232)
(175,237)(176,238)(177,235)(178,236)(179,241)(180,242)(181,239)(182,240)
(243,305)(244,306)(245,303)(246,304)(247,309)(248,310)(249,307)(250,308)
(251,313)(252,314)(253,311)(254,312)(255,317)(256,318)(257,315)(258,316)
(259,321)(260,322)(261,319)(262,320)(263,325)(264,326)(265,323)(266,324)
(267,329)(268,330)(269,327)(270,328)(271,333)(272,334)(273,331)(274,332)
(275,337)(276,338)(277,335)(278,336)(279,341)(280,342)(281,339)(282,340)
(283,345)(284,346)(285,343)(286,344)(287,349)(288,350)(289,347)(290,348)
(291,353)(292,354)(293,351)(294,352)(295,357)(296,358)(297,355)(298,356)
(299,361)(300,362)(301,359)(302,360)(363,425)(364,426)(365,423)(366,424)
(367,429)(368,430)(369,427)(370,428)(371,433)(372,434)(373,431)(374,432)
(375,437)(376,438)(377,435)(378,436)(379,441)(380,442)(381,439)(382,440)
(383,445)(384,446)(385,443)(386,444)(387,449)(388,450)(389,447)(390,448)
(391,453)(392,454)(393,451)(394,452)(395,457)(396,458)(397,455)(398,456)
(399,461)(400,462)(401,459)(402,460)(403,465)(404,466)(405,463)(406,464)
(407,469)(408,470)(409,467)(410,468)(411,473)(412,474)(413,471)(414,472)
(415,477)(416,478)(417,475)(418,476)(419,481)(420,482)(421,479)(422,480);;
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)(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);;
s3 := ( 3,287)( 4,290)( 5,289)( 6,288)( 7,283)( 8,286)( 9,285)( 10,284)
( 11,299)( 12,302)( 13,301)( 14,300)( 15,295)( 16,298)( 17,297)( 18,296)
( 19,291)( 20,294)( 21,293)( 22,292)( 23,267)( 24,270)( 25,269)( 26,268)
( 27,263)( 28,266)( 29,265)( 30,264)( 31,279)( 32,282)( 33,281)( 34,280)
( 35,275)( 36,278)( 37,277)( 38,276)( 39,271)( 40,274)( 41,273)( 42,272)
( 43,247)( 44,250)( 45,249)( 46,248)( 47,243)( 48,246)( 49,245)( 50,244)
( 51,259)( 52,262)( 53,261)( 54,260)( 55,255)( 56,258)( 57,257)( 58,256)
( 59,251)( 60,254)( 61,253)( 62,252)( 63,347)( 64,350)( 65,349)( 66,348)
( 67,343)( 68,346)( 69,345)( 70,344)( 71,359)( 72,362)( 73,361)( 74,360)
( 75,355)( 76,358)( 77,357)( 78,356)( 79,351)( 80,354)( 81,353)( 82,352)
( 83,327)( 84,330)( 85,329)( 86,328)( 87,323)( 88,326)( 89,325)( 90,324)
( 91,339)( 92,342)( 93,341)( 94,340)( 95,335)( 96,338)( 97,337)( 98,336)
( 99,331)(100,334)(101,333)(102,332)(103,307)(104,310)(105,309)(106,308)
(107,303)(108,306)(109,305)(110,304)(111,319)(112,322)(113,321)(114,320)
(115,315)(116,318)(117,317)(118,316)(119,311)(120,314)(121,313)(122,312)
(123,467)(124,470)(125,469)(126,468)(127,463)(128,466)(129,465)(130,464)
(131,479)(132,482)(133,481)(134,480)(135,475)(136,478)(137,477)(138,476)
(139,471)(140,474)(141,473)(142,472)(143,447)(144,450)(145,449)(146,448)
(147,443)(148,446)(149,445)(150,444)(151,459)(152,462)(153,461)(154,460)
(155,455)(156,458)(157,457)(158,456)(159,451)(160,454)(161,453)(162,452)
(163,427)(164,430)(165,429)(166,428)(167,423)(168,426)(169,425)(170,424)
(171,439)(172,442)(173,441)(174,440)(175,435)(176,438)(177,437)(178,436)
(179,431)(180,434)(181,433)(182,432)(183,407)(184,410)(185,409)(186,408)
(187,403)(188,406)(189,405)(190,404)(191,419)(192,422)(193,421)(194,420)
(195,415)(196,418)(197,417)(198,416)(199,411)(200,414)(201,413)(202,412)
(203,387)(204,390)(205,389)(206,388)(207,383)(208,386)(209,385)(210,384)
(211,399)(212,402)(213,401)(214,400)(215,395)(216,398)(217,397)(218,396)
(219,391)(220,394)(221,393)(222,392)(223,367)(224,370)(225,369)(226,368)
(227,363)(228,366)(229,365)(230,364)(231,379)(232,382)(233,381)(234,380)
(235,375)(236,378)(237,377)(238,376)(239,371)(240,374)(241,373)(242,372);;
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*s1*s3*s2*s1*s3*s2*s1*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, 65)( 4, 66)( 5, 63)( 6, 64)( 7, 69)( 8, 70)( 9, 67)
( 10, 68)( 11, 73)( 12, 74)( 13, 71)( 14, 72)( 15, 77)( 16, 78)( 17, 75)
( 18, 76)( 19, 81)( 20, 82)( 21, 79)( 22, 80)( 23, 85)( 24, 86)( 25, 83)
( 26, 84)( 27, 89)( 28, 90)( 29, 87)( 30, 88)( 31, 93)( 32, 94)( 33, 91)
( 34, 92)( 35, 97)( 36, 98)( 37, 95)( 38, 96)( 39,101)( 40,102)( 41, 99)
( 42,100)( 43,105)( 44,106)( 45,103)( 46,104)( 47,109)( 48,110)( 49,107)
( 50,108)( 51,113)( 52,114)( 53,111)( 54,112)( 55,117)( 56,118)( 57,115)
( 58,116)( 59,121)( 60,122)( 61,119)( 62,120)(123,185)(124,186)(125,183)
(126,184)(127,189)(128,190)(129,187)(130,188)(131,193)(132,194)(133,191)
(134,192)(135,197)(136,198)(137,195)(138,196)(139,201)(140,202)(141,199)
(142,200)(143,205)(144,206)(145,203)(146,204)(147,209)(148,210)(149,207)
(150,208)(151,213)(152,214)(153,211)(154,212)(155,217)(156,218)(157,215)
(158,216)(159,221)(160,222)(161,219)(162,220)(163,225)(164,226)(165,223)
(166,224)(167,229)(168,230)(169,227)(170,228)(171,233)(172,234)(173,231)
(174,232)(175,237)(176,238)(177,235)(178,236)(179,241)(180,242)(181,239)
(182,240)(243,305)(244,306)(245,303)(246,304)(247,309)(248,310)(249,307)
(250,308)(251,313)(252,314)(253,311)(254,312)(255,317)(256,318)(257,315)
(258,316)(259,321)(260,322)(261,319)(262,320)(263,325)(264,326)(265,323)
(266,324)(267,329)(268,330)(269,327)(270,328)(271,333)(272,334)(273,331)
(274,332)(275,337)(276,338)(277,335)(278,336)(279,341)(280,342)(281,339)
(282,340)(283,345)(284,346)(285,343)(286,344)(287,349)(288,350)(289,347)
(290,348)(291,353)(292,354)(293,351)(294,352)(295,357)(296,358)(297,355)
(298,356)(299,361)(300,362)(301,359)(302,360)(363,425)(364,426)(365,423)
(366,424)(367,429)(368,430)(369,427)(370,428)(371,433)(372,434)(373,431)
(374,432)(375,437)(376,438)(377,435)(378,436)(379,441)(380,442)(381,439)
(382,440)(383,445)(384,446)(385,443)(386,444)(387,449)(388,450)(389,447)
(390,448)(391,453)(392,454)(393,451)(394,452)(395,457)(396,458)(397,455)
(398,456)(399,461)(400,462)(401,459)(402,460)(403,465)(404,466)(405,463)
(406,464)(407,469)(408,470)(409,467)(410,468)(411,473)(412,474)(413,471)
(414,472)(415,477)(416,478)(417,475)(418,476)(419,481)(420,482)(421,479)
(422,480);
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)(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);
s3 := Sym(482)!( 3,287)( 4,290)( 5,289)( 6,288)( 7,283)( 8,286)( 9,285)
( 10,284)( 11,299)( 12,302)( 13,301)( 14,300)( 15,295)( 16,298)( 17,297)
( 18,296)( 19,291)( 20,294)( 21,293)( 22,292)( 23,267)( 24,270)( 25,269)
( 26,268)( 27,263)( 28,266)( 29,265)( 30,264)( 31,279)( 32,282)( 33,281)
( 34,280)( 35,275)( 36,278)( 37,277)( 38,276)( 39,271)( 40,274)( 41,273)
( 42,272)( 43,247)( 44,250)( 45,249)( 46,248)( 47,243)( 48,246)( 49,245)
( 50,244)( 51,259)( 52,262)( 53,261)( 54,260)( 55,255)( 56,258)( 57,257)
( 58,256)( 59,251)( 60,254)( 61,253)( 62,252)( 63,347)( 64,350)( 65,349)
( 66,348)( 67,343)( 68,346)( 69,345)( 70,344)( 71,359)( 72,362)( 73,361)
( 74,360)( 75,355)( 76,358)( 77,357)( 78,356)( 79,351)( 80,354)( 81,353)
( 82,352)( 83,327)( 84,330)( 85,329)( 86,328)( 87,323)( 88,326)( 89,325)
( 90,324)( 91,339)( 92,342)( 93,341)( 94,340)( 95,335)( 96,338)( 97,337)
( 98,336)( 99,331)(100,334)(101,333)(102,332)(103,307)(104,310)(105,309)
(106,308)(107,303)(108,306)(109,305)(110,304)(111,319)(112,322)(113,321)
(114,320)(115,315)(116,318)(117,317)(118,316)(119,311)(120,314)(121,313)
(122,312)(123,467)(124,470)(125,469)(126,468)(127,463)(128,466)(129,465)
(130,464)(131,479)(132,482)(133,481)(134,480)(135,475)(136,478)(137,477)
(138,476)(139,471)(140,474)(141,473)(142,472)(143,447)(144,450)(145,449)
(146,448)(147,443)(148,446)(149,445)(150,444)(151,459)(152,462)(153,461)
(154,460)(155,455)(156,458)(157,457)(158,456)(159,451)(160,454)(161,453)
(162,452)(163,427)(164,430)(165,429)(166,428)(167,423)(168,426)(169,425)
(170,424)(171,439)(172,442)(173,441)(174,440)(175,435)(176,438)(177,437)
(178,436)(179,431)(180,434)(181,433)(182,432)(183,407)(184,410)(185,409)
(186,408)(187,403)(188,406)(189,405)(190,404)(191,419)(192,422)(193,421)
(194,420)(195,415)(196,418)(197,417)(198,416)(199,411)(200,414)(201,413)
(202,412)(203,387)(204,390)(205,389)(206,388)(207,383)(208,386)(209,385)
(210,384)(211,399)(212,402)(213,401)(214,400)(215,395)(216,398)(217,397)
(218,396)(219,391)(220,394)(221,393)(222,392)(223,367)(224,370)(225,369)
(226,368)(227,363)(228,366)(229,365)(230,364)(231,379)(232,382)(233,381)
(234,380)(235,375)(236,378)(237,377)(238,376)(239,371)(240,374)(241,373)
(242,372);
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*s1*s3*s2*s1*s3*s2*s1*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