Polytope of Type {20,24}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,24}*1920d
if this polytope has a name.
Group : SmallGroup(1920,238609)
Rank : 3
Schlafli Type : {20,24}
Number of vertices, edges, etc : 40, 480, 48
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 : {20,12}*960b
4-fold quotients : {20,6}*480c
5-fold quotients : {4,24}*384d
8-fold quotients : {10,12}*240, {20,6}*240b
10-fold quotients : {4,12}*192b
16-fold quotients : {10,6}*120
20-fold quotients : {4,12}*96b, {4,12}*96c, {4,6}*96
24-fold quotients : {10,4}*80
40-fold quotients : {2,12}*48, {4,3}*48, {4,6}*48b, {4,6}*48c
48-fold quotients : {10,2}*40
80-fold quotients : {4,3}*24, {2,6}*24
96-fold quotients : {5,2}*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, 19)( 6, 20)( 7, 17)( 8, 18)( 9, 15)( 10, 16)
( 11, 13)( 12, 14)( 21, 23)( 22, 24)( 25, 39)( 26, 40)( 27, 37)( 28, 38)
( 29, 35)( 30, 36)( 31, 33)( 32, 34)( 41, 43)( 42, 44)( 45, 59)( 46, 60)
( 47, 57)( 48, 58)( 49, 55)( 50, 56)( 51, 53)( 52, 54)( 61, 63)( 62, 64)
( 65, 79)( 66, 80)( 67, 77)( 68, 78)( 69, 75)( 70, 76)( 71, 73)( 72, 74)
( 81, 83)( 82, 84)( 85, 99)( 86,100)( 87, 97)( 88, 98)( 89, 95)( 90, 96)
( 91, 93)( 92, 94)(101,103)(102,104)(105,119)(106,120)(107,117)(108,118)
(109,115)(110,116)(111,113)(112,114)(121,123)(122,124)(125,139)(126,140)
(127,137)(128,138)(129,135)(130,136)(131,133)(132,134)(141,143)(142,144)
(145,159)(146,160)(147,157)(148,158)(149,155)(150,156)(151,153)(152,154)
(161,163)(162,164)(165,179)(166,180)(167,177)(168,178)(169,175)(170,176)
(171,173)(172,174)(181,183)(182,184)(185,199)(186,200)(187,197)(188,198)
(189,195)(190,196)(191,193)(192,194)(201,203)(202,204)(205,219)(206,220)
(207,217)(208,218)(209,215)(210,216)(211,213)(212,214)(221,223)(222,224)
(225,239)(226,240)(227,237)(228,238)(229,235)(230,236)(231,233)(232,234)
(241,303)(242,304)(243,301)(244,302)(245,319)(246,320)(247,317)(248,318)
(249,315)(250,316)(251,313)(252,314)(253,311)(254,312)(255,309)(256,310)
(257,307)(258,308)(259,305)(260,306)(261,323)(262,324)(263,321)(264,322)
(265,339)(266,340)(267,337)(268,338)(269,335)(270,336)(271,333)(272,334)
(273,331)(274,332)(275,329)(276,330)(277,327)(278,328)(279,325)(280,326)
(281,343)(282,344)(283,341)(284,342)(285,359)(286,360)(287,357)(288,358)
(289,355)(290,356)(291,353)(292,354)(293,351)(294,352)(295,349)(296,350)
(297,347)(298,348)(299,345)(300,346)(361,423)(362,424)(363,421)(364,422)
(365,439)(366,440)(367,437)(368,438)(369,435)(370,436)(371,433)(372,434)
(373,431)(374,432)(375,429)(376,430)(377,427)(378,428)(379,425)(380,426)
(381,443)(382,444)(383,441)(384,442)(385,459)(386,460)(387,457)(388,458)
(389,455)(390,456)(391,453)(392,454)(393,451)(394,452)(395,449)(396,450)
(397,447)(398,448)(399,445)(400,446)(401,463)(402,464)(403,461)(404,462)
(405,479)(406,480)(407,477)(408,478)(409,475)(410,476)(411,473)(412,474)
(413,471)(414,472)(415,469)(416,470)(417,467)(418,468)(419,465)(420,466);;
s1 := ( 1,245)( 2,246)( 3,248)( 4,247)( 5,241)( 6,242)( 7,244)( 8,243)
( 9,257)( 10,258)( 11,260)( 12,259)( 13,253)( 14,254)( 15,256)( 16,255)
( 17,249)( 18,250)( 19,252)( 20,251)( 21,285)( 22,286)( 23,288)( 24,287)
( 25,281)( 26,282)( 27,284)( 28,283)( 29,297)( 30,298)( 31,300)( 32,299)
( 33,293)( 34,294)( 35,296)( 36,295)( 37,289)( 38,290)( 39,292)( 40,291)
( 41,265)( 42,266)( 43,268)( 44,267)( 45,261)( 46,262)( 47,264)( 48,263)
( 49,277)( 50,278)( 51,280)( 52,279)( 53,273)( 54,274)( 55,276)( 56,275)
( 57,269)( 58,270)( 59,272)( 60,271)( 61,305)( 62,306)( 63,308)( 64,307)
( 65,301)( 66,302)( 67,304)( 68,303)( 69,317)( 70,318)( 71,320)( 72,319)
( 73,313)( 74,314)( 75,316)( 76,315)( 77,309)( 78,310)( 79,312)( 80,311)
( 81,345)( 82,346)( 83,348)( 84,347)( 85,341)( 86,342)( 87,344)( 88,343)
( 89,357)( 90,358)( 91,360)( 92,359)( 93,353)( 94,354)( 95,356)( 96,355)
( 97,349)( 98,350)( 99,352)(100,351)(101,325)(102,326)(103,328)(104,327)
(105,321)(106,322)(107,324)(108,323)(109,337)(110,338)(111,340)(112,339)
(113,333)(114,334)(115,336)(116,335)(117,329)(118,330)(119,332)(120,331)
(121,425)(122,426)(123,428)(124,427)(125,421)(126,422)(127,424)(128,423)
(129,437)(130,438)(131,440)(132,439)(133,433)(134,434)(135,436)(136,435)
(137,429)(138,430)(139,432)(140,431)(141,465)(142,466)(143,468)(144,467)
(145,461)(146,462)(147,464)(148,463)(149,477)(150,478)(151,480)(152,479)
(153,473)(154,474)(155,476)(156,475)(157,469)(158,470)(159,472)(160,471)
(161,445)(162,446)(163,448)(164,447)(165,441)(166,442)(167,444)(168,443)
(169,457)(170,458)(171,460)(172,459)(173,453)(174,454)(175,456)(176,455)
(177,449)(178,450)(179,452)(180,451)(181,365)(182,366)(183,368)(184,367)
(185,361)(186,362)(187,364)(188,363)(189,377)(190,378)(191,380)(192,379)
(193,373)(194,374)(195,376)(196,375)(197,369)(198,370)(199,372)(200,371)
(201,405)(202,406)(203,408)(204,407)(205,401)(206,402)(207,404)(208,403)
(209,417)(210,418)(211,420)(212,419)(213,413)(214,414)(215,416)(216,415)
(217,409)(218,410)(219,412)(220,411)(221,385)(222,386)(223,388)(224,387)
(225,381)(226,382)(227,384)(228,383)(229,397)(230,398)(231,400)(232,399)
(233,393)(234,394)(235,396)(236,395)(237,389)(238,390)(239,392)(240,391);;
s2 := ( 1, 21)( 2, 24)( 3, 23)( 4, 22)( 5, 25)( 6, 28)( 7, 27)( 8, 26)
( 9, 29)( 10, 32)( 11, 31)( 12, 30)( 13, 33)( 14, 36)( 15, 35)( 16, 34)
( 17, 37)( 18, 40)( 19, 39)( 20, 38)( 42, 44)( 46, 48)( 50, 52)( 54, 56)
( 58, 60)( 61, 81)( 62, 84)( 63, 83)( 64, 82)( 65, 85)( 66, 88)( 67, 87)
( 68, 86)( 69, 89)( 70, 92)( 71, 91)( 72, 90)( 73, 93)( 74, 96)( 75, 95)
( 76, 94)( 77, 97)( 78,100)( 79, 99)( 80, 98)(102,104)(106,108)(110,112)
(114,116)(118,120)(121,201)(122,204)(123,203)(124,202)(125,205)(126,208)
(127,207)(128,206)(129,209)(130,212)(131,211)(132,210)(133,213)(134,216)
(135,215)(136,214)(137,217)(138,220)(139,219)(140,218)(141,181)(142,184)
(143,183)(144,182)(145,185)(146,188)(147,187)(148,186)(149,189)(150,192)
(151,191)(152,190)(153,193)(154,196)(155,195)(156,194)(157,197)(158,200)
(159,199)(160,198)(161,221)(162,224)(163,223)(164,222)(165,225)(166,228)
(167,227)(168,226)(169,229)(170,232)(171,231)(172,230)(173,233)(174,236)
(175,235)(176,234)(177,237)(178,240)(179,239)(180,238)(241,381)(242,384)
(243,383)(244,382)(245,385)(246,388)(247,387)(248,386)(249,389)(250,392)
(251,391)(252,390)(253,393)(254,396)(255,395)(256,394)(257,397)(258,400)
(259,399)(260,398)(261,361)(262,364)(263,363)(264,362)(265,365)(266,368)
(267,367)(268,366)(269,369)(270,372)(271,371)(272,370)(273,373)(274,376)
(275,375)(276,374)(277,377)(278,380)(279,379)(280,378)(281,401)(282,404)
(283,403)(284,402)(285,405)(286,408)(287,407)(288,406)(289,409)(290,412)
(291,411)(292,410)(293,413)(294,416)(295,415)(296,414)(297,417)(298,420)
(299,419)(300,418)(301,441)(302,444)(303,443)(304,442)(305,445)(306,448)
(307,447)(308,446)(309,449)(310,452)(311,451)(312,450)(313,453)(314,456)
(315,455)(316,454)(317,457)(318,460)(319,459)(320,458)(321,421)(322,424)
(323,423)(324,422)(325,425)(326,428)(327,427)(328,426)(329,429)(330,432)
(331,431)(332,430)(333,433)(334,436)(335,435)(336,434)(337,437)(338,440)
(339,439)(340,438)(341,461)(342,464)(343,463)(344,462)(345,465)(346,468)
(347,467)(348,466)(349,469)(350,472)(351,471)(352,470)(353,473)(354,476)
(355,475)(356,474)(357,477)(358,480)(359,479)(360,478);;
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*s2*s1*s0*s1*s0*s1*s0*s1*s2*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*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(480)!( 1, 3)( 2, 4)( 5, 19)( 6, 20)( 7, 17)( 8, 18)( 9, 15)
( 10, 16)( 11, 13)( 12, 14)( 21, 23)( 22, 24)( 25, 39)( 26, 40)( 27, 37)
( 28, 38)( 29, 35)( 30, 36)( 31, 33)( 32, 34)( 41, 43)( 42, 44)( 45, 59)
( 46, 60)( 47, 57)( 48, 58)( 49, 55)( 50, 56)( 51, 53)( 52, 54)( 61, 63)
( 62, 64)( 65, 79)( 66, 80)( 67, 77)( 68, 78)( 69, 75)( 70, 76)( 71, 73)
( 72, 74)( 81, 83)( 82, 84)( 85, 99)( 86,100)( 87, 97)( 88, 98)( 89, 95)
( 90, 96)( 91, 93)( 92, 94)(101,103)(102,104)(105,119)(106,120)(107,117)
(108,118)(109,115)(110,116)(111,113)(112,114)(121,123)(122,124)(125,139)
(126,140)(127,137)(128,138)(129,135)(130,136)(131,133)(132,134)(141,143)
(142,144)(145,159)(146,160)(147,157)(148,158)(149,155)(150,156)(151,153)
(152,154)(161,163)(162,164)(165,179)(166,180)(167,177)(168,178)(169,175)
(170,176)(171,173)(172,174)(181,183)(182,184)(185,199)(186,200)(187,197)
(188,198)(189,195)(190,196)(191,193)(192,194)(201,203)(202,204)(205,219)
(206,220)(207,217)(208,218)(209,215)(210,216)(211,213)(212,214)(221,223)
(222,224)(225,239)(226,240)(227,237)(228,238)(229,235)(230,236)(231,233)
(232,234)(241,303)(242,304)(243,301)(244,302)(245,319)(246,320)(247,317)
(248,318)(249,315)(250,316)(251,313)(252,314)(253,311)(254,312)(255,309)
(256,310)(257,307)(258,308)(259,305)(260,306)(261,323)(262,324)(263,321)
(264,322)(265,339)(266,340)(267,337)(268,338)(269,335)(270,336)(271,333)
(272,334)(273,331)(274,332)(275,329)(276,330)(277,327)(278,328)(279,325)
(280,326)(281,343)(282,344)(283,341)(284,342)(285,359)(286,360)(287,357)
(288,358)(289,355)(290,356)(291,353)(292,354)(293,351)(294,352)(295,349)
(296,350)(297,347)(298,348)(299,345)(300,346)(361,423)(362,424)(363,421)
(364,422)(365,439)(366,440)(367,437)(368,438)(369,435)(370,436)(371,433)
(372,434)(373,431)(374,432)(375,429)(376,430)(377,427)(378,428)(379,425)
(380,426)(381,443)(382,444)(383,441)(384,442)(385,459)(386,460)(387,457)
(388,458)(389,455)(390,456)(391,453)(392,454)(393,451)(394,452)(395,449)
(396,450)(397,447)(398,448)(399,445)(400,446)(401,463)(402,464)(403,461)
(404,462)(405,479)(406,480)(407,477)(408,478)(409,475)(410,476)(411,473)
(412,474)(413,471)(414,472)(415,469)(416,470)(417,467)(418,468)(419,465)
(420,466);
s1 := Sym(480)!( 1,245)( 2,246)( 3,248)( 4,247)( 5,241)( 6,242)( 7,244)
( 8,243)( 9,257)( 10,258)( 11,260)( 12,259)( 13,253)( 14,254)( 15,256)
( 16,255)( 17,249)( 18,250)( 19,252)( 20,251)( 21,285)( 22,286)( 23,288)
( 24,287)( 25,281)( 26,282)( 27,284)( 28,283)( 29,297)( 30,298)( 31,300)
( 32,299)( 33,293)( 34,294)( 35,296)( 36,295)( 37,289)( 38,290)( 39,292)
( 40,291)( 41,265)( 42,266)( 43,268)( 44,267)( 45,261)( 46,262)( 47,264)
( 48,263)( 49,277)( 50,278)( 51,280)( 52,279)( 53,273)( 54,274)( 55,276)
( 56,275)( 57,269)( 58,270)( 59,272)( 60,271)( 61,305)( 62,306)( 63,308)
( 64,307)( 65,301)( 66,302)( 67,304)( 68,303)( 69,317)( 70,318)( 71,320)
( 72,319)( 73,313)( 74,314)( 75,316)( 76,315)( 77,309)( 78,310)( 79,312)
( 80,311)( 81,345)( 82,346)( 83,348)( 84,347)( 85,341)( 86,342)( 87,344)
( 88,343)( 89,357)( 90,358)( 91,360)( 92,359)( 93,353)( 94,354)( 95,356)
( 96,355)( 97,349)( 98,350)( 99,352)(100,351)(101,325)(102,326)(103,328)
(104,327)(105,321)(106,322)(107,324)(108,323)(109,337)(110,338)(111,340)
(112,339)(113,333)(114,334)(115,336)(116,335)(117,329)(118,330)(119,332)
(120,331)(121,425)(122,426)(123,428)(124,427)(125,421)(126,422)(127,424)
(128,423)(129,437)(130,438)(131,440)(132,439)(133,433)(134,434)(135,436)
(136,435)(137,429)(138,430)(139,432)(140,431)(141,465)(142,466)(143,468)
(144,467)(145,461)(146,462)(147,464)(148,463)(149,477)(150,478)(151,480)
(152,479)(153,473)(154,474)(155,476)(156,475)(157,469)(158,470)(159,472)
(160,471)(161,445)(162,446)(163,448)(164,447)(165,441)(166,442)(167,444)
(168,443)(169,457)(170,458)(171,460)(172,459)(173,453)(174,454)(175,456)
(176,455)(177,449)(178,450)(179,452)(180,451)(181,365)(182,366)(183,368)
(184,367)(185,361)(186,362)(187,364)(188,363)(189,377)(190,378)(191,380)
(192,379)(193,373)(194,374)(195,376)(196,375)(197,369)(198,370)(199,372)
(200,371)(201,405)(202,406)(203,408)(204,407)(205,401)(206,402)(207,404)
(208,403)(209,417)(210,418)(211,420)(212,419)(213,413)(214,414)(215,416)
(216,415)(217,409)(218,410)(219,412)(220,411)(221,385)(222,386)(223,388)
(224,387)(225,381)(226,382)(227,384)(228,383)(229,397)(230,398)(231,400)
(232,399)(233,393)(234,394)(235,396)(236,395)(237,389)(238,390)(239,392)
(240,391);
s2 := Sym(480)!( 1, 21)( 2, 24)( 3, 23)( 4, 22)( 5, 25)( 6, 28)( 7, 27)
( 8, 26)( 9, 29)( 10, 32)( 11, 31)( 12, 30)( 13, 33)( 14, 36)( 15, 35)
( 16, 34)( 17, 37)( 18, 40)( 19, 39)( 20, 38)( 42, 44)( 46, 48)( 50, 52)
( 54, 56)( 58, 60)( 61, 81)( 62, 84)( 63, 83)( 64, 82)( 65, 85)( 66, 88)
( 67, 87)( 68, 86)( 69, 89)( 70, 92)( 71, 91)( 72, 90)( 73, 93)( 74, 96)
( 75, 95)( 76, 94)( 77, 97)( 78,100)( 79, 99)( 80, 98)(102,104)(106,108)
(110,112)(114,116)(118,120)(121,201)(122,204)(123,203)(124,202)(125,205)
(126,208)(127,207)(128,206)(129,209)(130,212)(131,211)(132,210)(133,213)
(134,216)(135,215)(136,214)(137,217)(138,220)(139,219)(140,218)(141,181)
(142,184)(143,183)(144,182)(145,185)(146,188)(147,187)(148,186)(149,189)
(150,192)(151,191)(152,190)(153,193)(154,196)(155,195)(156,194)(157,197)
(158,200)(159,199)(160,198)(161,221)(162,224)(163,223)(164,222)(165,225)
(166,228)(167,227)(168,226)(169,229)(170,232)(171,231)(172,230)(173,233)
(174,236)(175,235)(176,234)(177,237)(178,240)(179,239)(180,238)(241,381)
(242,384)(243,383)(244,382)(245,385)(246,388)(247,387)(248,386)(249,389)
(250,392)(251,391)(252,390)(253,393)(254,396)(255,395)(256,394)(257,397)
(258,400)(259,399)(260,398)(261,361)(262,364)(263,363)(264,362)(265,365)
(266,368)(267,367)(268,366)(269,369)(270,372)(271,371)(272,370)(273,373)
(274,376)(275,375)(276,374)(277,377)(278,380)(279,379)(280,378)(281,401)
(282,404)(283,403)(284,402)(285,405)(286,408)(287,407)(288,406)(289,409)
(290,412)(291,411)(292,410)(293,413)(294,416)(295,415)(296,414)(297,417)
(298,420)(299,419)(300,418)(301,441)(302,444)(303,443)(304,442)(305,445)
(306,448)(307,447)(308,446)(309,449)(310,452)(311,451)(312,450)(313,453)
(314,456)(315,455)(316,454)(317,457)(318,460)(319,459)(320,458)(321,421)
(322,424)(323,423)(324,422)(325,425)(326,428)(327,427)(328,426)(329,429)
(330,432)(331,431)(332,430)(333,433)(334,436)(335,435)(336,434)(337,437)
(338,440)(339,439)(340,438)(341,461)(342,464)(343,463)(344,462)(345,465)
(346,468)(347,467)(348,466)(349,469)(350,472)(351,471)(352,470)(353,473)
(354,476)(355,475)(356,474)(357,477)(358,480)(359,479)(360,478);
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*s2*s1*s0*s1*s0*s1*s0*s1*s2*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*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1 >;
References : None.
to this polytope