Polytope of Type {4,120}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,120}*1920d
if this polytope has a name.
Group : SmallGroup(1920,239543)
Rank : 3
Schlafli Type : {4,120}
Number of vertices, edges, etc : 8, 480, 240
Order of s0s1s2 : 120
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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}*960b
4-fold quotients : {4,60}*480b, {4,60}*480c, {4,30}*480
5-fold quotients : {4,24}*384d
8-fold quotients : {2,60}*240, {4,15}*240, {4,30}*240b, {4,30}*240c
10-fold quotients : {4,12}*192b
16-fold quotients : {4,15}*120, {2,30}*120
20-fold quotients : {4,12}*96b, {4,12}*96c, {4,6}*96
24-fold quotients : {2,20}*80
32-fold quotients : {2,15}*60
40-fold quotients : {2,12}*48, {4,3}*48, {4,6}*48b, {4,6}*48c
48-fold quotients : {2,10}*40
80-fold quotients : {4,3}*24, {2,6}*24
96-fold quotients : {2,5}*20
120-fold quotients : {2,4}*16
160-fold quotients : {2,3}*12
240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)( 14, 16)
( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)
( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)
( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)
( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)
( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)
( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)
(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)
(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)
(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)
(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)
(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)
(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)
(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)
(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240)
(241,303)(242,304)(243,301)(244,302)(245,307)(246,308)(247,305)(248,306)
(249,311)(250,312)(251,309)(252,310)(253,315)(254,316)(255,313)(256,314)
(257,319)(258,320)(259,317)(260,318)(261,323)(262,324)(263,321)(264,322)
(265,327)(266,328)(267,325)(268,326)(269,331)(270,332)(271,329)(272,330)
(273,335)(274,336)(275,333)(276,334)(277,339)(278,340)(279,337)(280,338)
(281,343)(282,344)(283,341)(284,342)(285,347)(286,348)(287,345)(288,346)
(289,351)(290,352)(291,349)(292,350)(293,355)(294,356)(295,353)(296,354)
(297,359)(298,360)(299,357)(300,358)(361,423)(362,424)(363,421)(364,422)
(365,427)(366,428)(367,425)(368,426)(369,431)(370,432)(371,429)(372,430)
(373,435)(374,436)(375,433)(376,434)(377,439)(378,440)(379,437)(380,438)
(381,443)(382,444)(383,441)(384,442)(385,447)(386,448)(387,445)(388,446)
(389,451)(390,452)(391,449)(392,450)(393,455)(394,456)(395,453)(396,454)
(397,459)(398,460)(399,457)(400,458)(401,463)(402,464)(403,461)(404,462)
(405,467)(406,468)(407,465)(408,466)(409,471)(410,472)(411,469)(412,470)
(413,475)(414,476)(415,473)(416,474)(417,479)(418,480)(419,477)(420,478);;
s1 := ( 1,241)( 2,242)( 3,244)( 4,243)( 5,257)( 6,258)( 7,260)( 8,259)
( 9,253)( 10,254)( 11,256)( 12,255)( 13,249)( 14,250)( 15,252)( 16,251)
( 17,245)( 18,246)( 19,248)( 20,247)( 21,281)( 22,282)( 23,284)( 24,283)
( 25,297)( 26,298)( 27,300)( 28,299)( 29,293)( 30,294)( 31,296)( 32,295)
( 33,289)( 34,290)( 35,292)( 36,291)( 37,285)( 38,286)( 39,288)( 40,287)
( 41,261)( 42,262)( 43,264)( 44,263)( 45,277)( 46,278)( 47,280)( 48,279)
( 49,273)( 50,274)( 51,276)( 52,275)( 53,269)( 54,270)( 55,272)( 56,271)
( 57,265)( 58,266)( 59,268)( 60,267)( 61,301)( 62,302)( 63,304)( 64,303)
( 65,317)( 66,318)( 67,320)( 68,319)( 69,313)( 70,314)( 71,316)( 72,315)
( 73,309)( 74,310)( 75,312)( 76,311)( 77,305)( 78,306)( 79,308)( 80,307)
( 81,341)( 82,342)( 83,344)( 84,343)( 85,357)( 86,358)( 87,360)( 88,359)
( 89,353)( 90,354)( 91,356)( 92,355)( 93,349)( 94,350)( 95,352)( 96,351)
( 97,345)( 98,346)( 99,348)(100,347)(101,321)(102,322)(103,324)(104,323)
(105,337)(106,338)(107,340)(108,339)(109,333)(110,334)(111,336)(112,335)
(113,329)(114,330)(115,332)(116,331)(117,325)(118,326)(119,328)(120,327)
(121,421)(122,422)(123,424)(124,423)(125,437)(126,438)(127,440)(128,439)
(129,433)(130,434)(131,436)(132,435)(133,429)(134,430)(135,432)(136,431)
(137,425)(138,426)(139,428)(140,427)(141,461)(142,462)(143,464)(144,463)
(145,477)(146,478)(147,480)(148,479)(149,473)(150,474)(151,476)(152,475)
(153,469)(154,470)(155,472)(156,471)(157,465)(158,466)(159,468)(160,467)
(161,441)(162,442)(163,444)(164,443)(165,457)(166,458)(167,460)(168,459)
(169,453)(170,454)(171,456)(172,455)(173,449)(174,450)(175,452)(176,451)
(177,445)(178,446)(179,448)(180,447)(181,361)(182,362)(183,364)(184,363)
(185,377)(186,378)(187,380)(188,379)(189,373)(190,374)(191,376)(192,375)
(193,369)(194,370)(195,372)(196,371)(197,365)(198,366)(199,368)(200,367)
(201,401)(202,402)(203,404)(204,403)(205,417)(206,418)(207,420)(208,419)
(209,413)(210,414)(211,416)(212,415)(213,409)(214,410)(215,412)(216,411)
(217,405)(218,406)(219,408)(220,407)(221,381)(222,382)(223,384)(224,383)
(225,397)(226,398)(227,400)(228,399)(229,393)(230,394)(231,396)(232,395)
(233,389)(234,390)(235,392)(236,391)(237,385)(238,386)(239,388)(240,387);;
s2 := ( 1, 25)( 2, 28)( 3, 27)( 4, 26)( 5, 21)( 6, 24)( 7, 23)( 8, 22)
( 9, 37)( 10, 40)( 11, 39)( 12, 38)( 13, 33)( 14, 36)( 15, 35)( 16, 34)
( 17, 29)( 18, 32)( 19, 31)( 20, 30)( 41, 45)( 42, 48)( 43, 47)( 44, 46)
( 49, 57)( 50, 60)( 51, 59)( 52, 58)( 54, 56)( 61, 85)( 62, 88)( 63, 87)
( 64, 86)( 65, 81)( 66, 84)( 67, 83)( 68, 82)( 69, 97)( 70,100)( 71, 99)
( 72, 98)( 73, 93)( 74, 96)( 75, 95)( 76, 94)( 77, 89)( 78, 92)( 79, 91)
( 80, 90)(101,105)(102,108)(103,107)(104,106)(109,117)(110,120)(111,119)
(112,118)(114,116)(121,205)(122,208)(123,207)(124,206)(125,201)(126,204)
(127,203)(128,202)(129,217)(130,220)(131,219)(132,218)(133,213)(134,216)
(135,215)(136,214)(137,209)(138,212)(139,211)(140,210)(141,185)(142,188)
(143,187)(144,186)(145,181)(146,184)(147,183)(148,182)(149,197)(150,200)
(151,199)(152,198)(153,193)(154,196)(155,195)(156,194)(157,189)(158,192)
(159,191)(160,190)(161,225)(162,228)(163,227)(164,226)(165,221)(166,224)
(167,223)(168,222)(169,237)(170,240)(171,239)(172,238)(173,233)(174,236)
(175,235)(176,234)(177,229)(178,232)(179,231)(180,230)(241,385)(242,388)
(243,387)(244,386)(245,381)(246,384)(247,383)(248,382)(249,397)(250,400)
(251,399)(252,398)(253,393)(254,396)(255,395)(256,394)(257,389)(258,392)
(259,391)(260,390)(261,365)(262,368)(263,367)(264,366)(265,361)(266,364)
(267,363)(268,362)(269,377)(270,380)(271,379)(272,378)(273,373)(274,376)
(275,375)(276,374)(277,369)(278,372)(279,371)(280,370)(281,405)(282,408)
(283,407)(284,406)(285,401)(286,404)(287,403)(288,402)(289,417)(290,420)
(291,419)(292,418)(293,413)(294,416)(295,415)(296,414)(297,409)(298,412)
(299,411)(300,410)(301,445)(302,448)(303,447)(304,446)(305,441)(306,444)
(307,443)(308,442)(309,457)(310,460)(311,459)(312,458)(313,453)(314,456)
(315,455)(316,454)(317,449)(318,452)(319,451)(320,450)(321,425)(322,428)
(323,427)(324,426)(325,421)(326,424)(327,423)(328,422)(329,437)(330,440)
(331,439)(332,438)(333,433)(334,436)(335,435)(336,434)(337,429)(338,432)
(339,431)(340,430)(341,465)(342,468)(343,467)(344,466)(345,461)(346,464)
(347,463)(348,462)(349,477)(350,480)(351,479)(352,478)(353,473)(354,476)
(355,475)(356,474)(357,469)(358,472)(359,471)(360,470);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1,
s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(480)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)
( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)
( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)
( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)
( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)
( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)
( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)
(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)
(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)
(142,144)(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)
(158,160)(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)
(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)
(190,192)(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)
(206,208)(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)
(222,224)(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)
(238,240)(241,303)(242,304)(243,301)(244,302)(245,307)(246,308)(247,305)
(248,306)(249,311)(250,312)(251,309)(252,310)(253,315)(254,316)(255,313)
(256,314)(257,319)(258,320)(259,317)(260,318)(261,323)(262,324)(263,321)
(264,322)(265,327)(266,328)(267,325)(268,326)(269,331)(270,332)(271,329)
(272,330)(273,335)(274,336)(275,333)(276,334)(277,339)(278,340)(279,337)
(280,338)(281,343)(282,344)(283,341)(284,342)(285,347)(286,348)(287,345)
(288,346)(289,351)(290,352)(291,349)(292,350)(293,355)(294,356)(295,353)
(296,354)(297,359)(298,360)(299,357)(300,358)(361,423)(362,424)(363,421)
(364,422)(365,427)(366,428)(367,425)(368,426)(369,431)(370,432)(371,429)
(372,430)(373,435)(374,436)(375,433)(376,434)(377,439)(378,440)(379,437)
(380,438)(381,443)(382,444)(383,441)(384,442)(385,447)(386,448)(387,445)
(388,446)(389,451)(390,452)(391,449)(392,450)(393,455)(394,456)(395,453)
(396,454)(397,459)(398,460)(399,457)(400,458)(401,463)(402,464)(403,461)
(404,462)(405,467)(406,468)(407,465)(408,466)(409,471)(410,472)(411,469)
(412,470)(413,475)(414,476)(415,473)(416,474)(417,479)(418,480)(419,477)
(420,478);
s1 := Sym(480)!( 1,241)( 2,242)( 3,244)( 4,243)( 5,257)( 6,258)( 7,260)
( 8,259)( 9,253)( 10,254)( 11,256)( 12,255)( 13,249)( 14,250)( 15,252)
( 16,251)( 17,245)( 18,246)( 19,248)( 20,247)( 21,281)( 22,282)( 23,284)
( 24,283)( 25,297)( 26,298)( 27,300)( 28,299)( 29,293)( 30,294)( 31,296)
( 32,295)( 33,289)( 34,290)( 35,292)( 36,291)( 37,285)( 38,286)( 39,288)
( 40,287)( 41,261)( 42,262)( 43,264)( 44,263)( 45,277)( 46,278)( 47,280)
( 48,279)( 49,273)( 50,274)( 51,276)( 52,275)( 53,269)( 54,270)( 55,272)
( 56,271)( 57,265)( 58,266)( 59,268)( 60,267)( 61,301)( 62,302)( 63,304)
( 64,303)( 65,317)( 66,318)( 67,320)( 68,319)( 69,313)( 70,314)( 71,316)
( 72,315)( 73,309)( 74,310)( 75,312)( 76,311)( 77,305)( 78,306)( 79,308)
( 80,307)( 81,341)( 82,342)( 83,344)( 84,343)( 85,357)( 86,358)( 87,360)
( 88,359)( 89,353)( 90,354)( 91,356)( 92,355)( 93,349)( 94,350)( 95,352)
( 96,351)( 97,345)( 98,346)( 99,348)(100,347)(101,321)(102,322)(103,324)
(104,323)(105,337)(106,338)(107,340)(108,339)(109,333)(110,334)(111,336)
(112,335)(113,329)(114,330)(115,332)(116,331)(117,325)(118,326)(119,328)
(120,327)(121,421)(122,422)(123,424)(124,423)(125,437)(126,438)(127,440)
(128,439)(129,433)(130,434)(131,436)(132,435)(133,429)(134,430)(135,432)
(136,431)(137,425)(138,426)(139,428)(140,427)(141,461)(142,462)(143,464)
(144,463)(145,477)(146,478)(147,480)(148,479)(149,473)(150,474)(151,476)
(152,475)(153,469)(154,470)(155,472)(156,471)(157,465)(158,466)(159,468)
(160,467)(161,441)(162,442)(163,444)(164,443)(165,457)(166,458)(167,460)
(168,459)(169,453)(170,454)(171,456)(172,455)(173,449)(174,450)(175,452)
(176,451)(177,445)(178,446)(179,448)(180,447)(181,361)(182,362)(183,364)
(184,363)(185,377)(186,378)(187,380)(188,379)(189,373)(190,374)(191,376)
(192,375)(193,369)(194,370)(195,372)(196,371)(197,365)(198,366)(199,368)
(200,367)(201,401)(202,402)(203,404)(204,403)(205,417)(206,418)(207,420)
(208,419)(209,413)(210,414)(211,416)(212,415)(213,409)(214,410)(215,412)
(216,411)(217,405)(218,406)(219,408)(220,407)(221,381)(222,382)(223,384)
(224,383)(225,397)(226,398)(227,400)(228,399)(229,393)(230,394)(231,396)
(232,395)(233,389)(234,390)(235,392)(236,391)(237,385)(238,386)(239,388)
(240,387);
s2 := Sym(480)!( 1, 25)( 2, 28)( 3, 27)( 4, 26)( 5, 21)( 6, 24)( 7, 23)
( 8, 22)( 9, 37)( 10, 40)( 11, 39)( 12, 38)( 13, 33)( 14, 36)( 15, 35)
( 16, 34)( 17, 29)( 18, 32)( 19, 31)( 20, 30)( 41, 45)( 42, 48)( 43, 47)
( 44, 46)( 49, 57)( 50, 60)( 51, 59)( 52, 58)( 54, 56)( 61, 85)( 62, 88)
( 63, 87)( 64, 86)( 65, 81)( 66, 84)( 67, 83)( 68, 82)( 69, 97)( 70,100)
( 71, 99)( 72, 98)( 73, 93)( 74, 96)( 75, 95)( 76, 94)( 77, 89)( 78, 92)
( 79, 91)( 80, 90)(101,105)(102,108)(103,107)(104,106)(109,117)(110,120)
(111,119)(112,118)(114,116)(121,205)(122,208)(123,207)(124,206)(125,201)
(126,204)(127,203)(128,202)(129,217)(130,220)(131,219)(132,218)(133,213)
(134,216)(135,215)(136,214)(137,209)(138,212)(139,211)(140,210)(141,185)
(142,188)(143,187)(144,186)(145,181)(146,184)(147,183)(148,182)(149,197)
(150,200)(151,199)(152,198)(153,193)(154,196)(155,195)(156,194)(157,189)
(158,192)(159,191)(160,190)(161,225)(162,228)(163,227)(164,226)(165,221)
(166,224)(167,223)(168,222)(169,237)(170,240)(171,239)(172,238)(173,233)
(174,236)(175,235)(176,234)(177,229)(178,232)(179,231)(180,230)(241,385)
(242,388)(243,387)(244,386)(245,381)(246,384)(247,383)(248,382)(249,397)
(250,400)(251,399)(252,398)(253,393)(254,396)(255,395)(256,394)(257,389)
(258,392)(259,391)(260,390)(261,365)(262,368)(263,367)(264,366)(265,361)
(266,364)(267,363)(268,362)(269,377)(270,380)(271,379)(272,378)(273,373)
(274,376)(275,375)(276,374)(277,369)(278,372)(279,371)(280,370)(281,405)
(282,408)(283,407)(284,406)(285,401)(286,404)(287,403)(288,402)(289,417)
(290,420)(291,419)(292,418)(293,413)(294,416)(295,415)(296,414)(297,409)
(298,412)(299,411)(300,410)(301,445)(302,448)(303,447)(304,446)(305,441)
(306,444)(307,443)(308,442)(309,457)(310,460)(311,459)(312,458)(313,453)
(314,456)(315,455)(316,454)(317,449)(318,452)(319,451)(320,450)(321,425)
(322,428)(323,427)(324,426)(325,421)(326,424)(327,423)(328,422)(329,437)
(330,440)(331,439)(332,438)(333,433)(334,436)(335,435)(336,434)(337,429)
(338,432)(339,431)(340,430)(341,465)(342,468)(343,467)(344,466)(345,461)
(346,464)(347,463)(348,462)(349,477)(350,480)(351,479)(352,478)(353,473)
(354,476)(355,475)(356,474)(357,469)(358,472)(359,471)(360,470);
poly := sub<Sym(480)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1,
s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1 >;
References : None.
to this polytope