Polytope of Type {120,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {120,4}*1920d
if this polytope has a name.
Group : SmallGroup(1920,239543)
Rank : 3
Schlafli Type : {120,4}
Number of vertices, edges, etc : 240, 480, 8
Order of s₀s₁s₂ : 120
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {60,4}*960b
   4-fold quotients : {60,4}*480b, {60,4}*480c, {30,4}*480
   5-fold quotients : {24,4}*384d
   8-fold quotients : {60,2}*240, {15,4}*240, {30,4}*240b, {30,4}*240c
   10-fold quotients : {12,4}*192b
   16-fold quotients : {15,4}*120, {30,2}*120
   20-fold quotients : {12,4}*96b, {12,4}*96c, {6,4}*96
   24-fold quotients : {20,2}*80
   32-fold quotients : {15,2}*60
   40-fold quotients : {12,2}*48, {3,4}*48, {6,4}*48b, {6,4}*48c
   48-fold quotients : {10,2}*40
   80-fold quotients : {3,4}*24, {6,2}*24
   96-fold quotients : {5,2}*20
   120-fold quotients : {4,2}*16
   160-fold quotients : {3,2}*12
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope