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