Polytope of Type {20,24}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,24}*1920c
if this polytope has a name.
Group : SmallGroup(1920,238608)
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 : {10,24}*480, {20,6}*480c
5-fold quotients : {4,24}*384c
8-fold quotients : {10,12}*240, {20,6}*240b
10-fold quotients : {4,24}*192c, {4,24}*192d, {4,12}*192b
12-fold quotients : {10,8}*160
16-fold quotients : {10,6}*120
20-fold quotients : {2,24}*96, {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
60-fold quotients : {2,8}*32
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)
(241,243)(242,244)(245,259)(246,260)(247,257)(248,258)(249,255)(250,256)
(251,253)(252,254)(261,263)(262,264)(265,279)(266,280)(267,277)(268,278)
(269,275)(270,276)(271,273)(272,274)(281,283)(282,284)(285,299)(286,300)
(287,297)(288,298)(289,295)(290,296)(291,293)(292,294)(301,303)(302,304)
(305,319)(306,320)(307,317)(308,318)(309,315)(310,316)(311,313)(312,314)
(321,323)(322,324)(325,339)(326,340)(327,337)(328,338)(329,335)(330,336)
(331,333)(332,334)(341,343)(342,344)(345,359)(346,360)(347,357)(348,358)
(349,355)(350,356)(351,353)(352,354)(361,363)(362,364)(365,379)(366,380)
(367,377)(368,378)(369,375)(370,376)(371,373)(372,374)(381,383)(382,384)
(385,399)(386,400)(387,397)(388,398)(389,395)(390,396)(391,393)(392,394)
(401,403)(402,404)(405,419)(406,420)(407,417)(408,418)(409,415)(410,416)
(411,413)(412,414)(421,423)(422,424)(425,439)(426,440)(427,437)(428,438)
(429,435)(430,436)(431,433)(432,434)(441,443)(442,444)(445,459)(446,460)
(447,457)(448,458)(449,455)(450,456)(451,453)(452,454)(461,463)(462,464)
(465,479)(466,480)(467,477)(468,478)(469,475)(470,476)(471,473)(472,474);;
s1 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 9, 17)( 10, 18)( 11, 20)( 12, 19)
( 15, 16)( 21, 45)( 22, 46)( 23, 48)( 24, 47)( 25, 41)( 26, 42)( 27, 44)
( 28, 43)( 29, 57)( 30, 58)( 31, 60)( 32, 59)( 33, 53)( 34, 54)( 35, 56)
( 36, 55)( 37, 49)( 38, 50)( 39, 52)( 40, 51)( 61, 65)( 62, 66)( 63, 68)
( 64, 67)( 69, 77)( 70, 78)( 71, 80)( 72, 79)( 75, 76)( 81,105)( 82,106)
( 83,108)( 84,107)( 85,101)( 86,102)( 87,104)( 88,103)( 89,117)( 90,118)
( 91,120)( 92,119)( 93,113)( 94,114)( 95,116)( 96,115)( 97,109)( 98,110)
( 99,112)(100,111)(121,185)(122,186)(123,188)(124,187)(125,181)(126,182)
(127,184)(128,183)(129,197)(130,198)(131,200)(132,199)(133,193)(134,194)
(135,196)(136,195)(137,189)(138,190)(139,192)(140,191)(141,225)(142,226)
(143,228)(144,227)(145,221)(146,222)(147,224)(148,223)(149,237)(150,238)
(151,240)(152,239)(153,233)(154,234)(155,236)(156,235)(157,229)(158,230)
(159,232)(160,231)(161,205)(162,206)(163,208)(164,207)(165,201)(166,202)
(167,204)(168,203)(169,217)(170,218)(171,220)(172,219)(173,213)(174,214)
(175,216)(176,215)(177,209)(178,210)(179,212)(180,211)(241,365)(242,366)
(243,368)(244,367)(245,361)(246,362)(247,364)(248,363)(249,377)(250,378)
(251,380)(252,379)(253,373)(254,374)(255,376)(256,375)(257,369)(258,370)
(259,372)(260,371)(261,405)(262,406)(263,408)(264,407)(265,401)(266,402)
(267,404)(268,403)(269,417)(270,418)(271,420)(272,419)(273,413)(274,414)
(275,416)(276,415)(277,409)(278,410)(279,412)(280,411)(281,385)(282,386)
(283,388)(284,387)(285,381)(286,382)(287,384)(288,383)(289,397)(290,398)
(291,400)(292,399)(293,393)(294,394)(295,396)(296,395)(297,389)(298,390)
(299,392)(300,391)(301,425)(302,426)(303,428)(304,427)(305,421)(306,422)
(307,424)(308,423)(309,437)(310,438)(311,440)(312,439)(313,433)(314,434)
(315,436)(316,435)(317,429)(318,430)(319,432)(320,431)(321,465)(322,466)
(323,468)(324,467)(325,461)(326,462)(327,464)(328,463)(329,477)(330,478)
(331,480)(332,479)(333,473)(334,474)(335,476)(336,475)(337,469)(338,470)
(339,472)(340,471)(341,445)(342,446)(343,448)(344,447)(345,441)(346,442)
(347,444)(348,443)(349,457)(350,458)(351,460)(352,459)(353,453)(354,454)
(355,456)(356,455)(357,449)(358,450)(359,452)(360,451);;
s2 := ( 1,261)( 2,264)( 3,263)( 4,262)( 5,265)( 6,268)( 7,267)( 8,266)
( 9,269)( 10,272)( 11,271)( 12,270)( 13,273)( 14,276)( 15,275)( 16,274)
( 17,277)( 18,280)( 19,279)( 20,278)( 21,241)( 22,244)( 23,243)( 24,242)
( 25,245)( 26,248)( 27,247)( 28,246)( 29,249)( 30,252)( 31,251)( 32,250)
( 33,253)( 34,256)( 35,255)( 36,254)( 37,257)( 38,260)( 39,259)( 40,258)
( 41,281)( 42,284)( 43,283)( 44,282)( 45,285)( 46,288)( 47,287)( 48,286)
( 49,289)( 50,292)( 51,291)( 52,290)( 53,293)( 54,296)( 55,295)( 56,294)
( 57,297)( 58,300)( 59,299)( 60,298)( 61,321)( 62,324)( 63,323)( 64,322)
( 65,325)( 66,328)( 67,327)( 68,326)( 69,329)( 70,332)( 71,331)( 72,330)
( 73,333)( 74,336)( 75,335)( 76,334)( 77,337)( 78,340)( 79,339)( 80,338)
( 81,301)( 82,304)( 83,303)( 84,302)( 85,305)( 86,308)( 87,307)( 88,306)
( 89,309)( 90,312)( 91,311)( 92,310)( 93,313)( 94,316)( 95,315)( 96,314)
( 97,317)( 98,320)( 99,319)(100,318)(101,341)(102,344)(103,343)(104,342)
(105,345)(106,348)(107,347)(108,346)(109,349)(110,352)(111,351)(112,350)
(113,353)(114,356)(115,355)(116,354)(117,357)(118,360)(119,359)(120,358)
(121,441)(122,444)(123,443)(124,442)(125,445)(126,448)(127,447)(128,446)
(129,449)(130,452)(131,451)(132,450)(133,453)(134,456)(135,455)(136,454)
(137,457)(138,460)(139,459)(140,458)(141,421)(142,424)(143,423)(144,422)
(145,425)(146,428)(147,427)(148,426)(149,429)(150,432)(151,431)(152,430)
(153,433)(154,436)(155,435)(156,434)(157,437)(158,440)(159,439)(160,438)
(161,461)(162,464)(163,463)(164,462)(165,465)(166,468)(167,467)(168,466)
(169,469)(170,472)(171,471)(172,470)(173,473)(174,476)(175,475)(176,474)
(177,477)(178,480)(179,479)(180,478)(181,381)(182,384)(183,383)(184,382)
(185,385)(186,388)(187,387)(188,386)(189,389)(190,392)(191,391)(192,390)
(193,393)(194,396)(195,395)(196,394)(197,397)(198,400)(199,399)(200,398)
(201,361)(202,364)(203,363)(204,362)(205,365)(206,368)(207,367)(208,366)
(209,369)(210,372)(211,371)(212,370)(213,373)(214,376)(215,375)(216,374)
(217,377)(218,380)(219,379)(220,378)(221,401)(222,404)(223,403)(224,402)
(225,405)(226,408)(227,407)(228,406)(229,409)(230,412)(231,411)(232,410)
(233,413)(234,416)(235,415)(236,414)(237,417)(238,420)(239,419)(240,418);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
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 ];;
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)(241,243)(242,244)(245,259)(246,260)(247,257)(248,258)(249,255)
(250,256)(251,253)(252,254)(261,263)(262,264)(265,279)(266,280)(267,277)
(268,278)(269,275)(270,276)(271,273)(272,274)(281,283)(282,284)(285,299)
(286,300)(287,297)(288,298)(289,295)(290,296)(291,293)(292,294)(301,303)
(302,304)(305,319)(306,320)(307,317)(308,318)(309,315)(310,316)(311,313)
(312,314)(321,323)(322,324)(325,339)(326,340)(327,337)(328,338)(329,335)
(330,336)(331,333)(332,334)(341,343)(342,344)(345,359)(346,360)(347,357)
(348,358)(349,355)(350,356)(351,353)(352,354)(361,363)(362,364)(365,379)
(366,380)(367,377)(368,378)(369,375)(370,376)(371,373)(372,374)(381,383)
(382,384)(385,399)(386,400)(387,397)(388,398)(389,395)(390,396)(391,393)
(392,394)(401,403)(402,404)(405,419)(406,420)(407,417)(408,418)(409,415)
(410,416)(411,413)(412,414)(421,423)(422,424)(425,439)(426,440)(427,437)
(428,438)(429,435)(430,436)(431,433)(432,434)(441,443)(442,444)(445,459)
(446,460)(447,457)(448,458)(449,455)(450,456)(451,453)(452,454)(461,463)
(462,464)(465,479)(466,480)(467,477)(468,478)(469,475)(470,476)(471,473)
(472,474);
s1 := Sym(480)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 9, 17)( 10, 18)( 11, 20)
( 12, 19)( 15, 16)( 21, 45)( 22, 46)( 23, 48)( 24, 47)( 25, 41)( 26, 42)
( 27, 44)( 28, 43)( 29, 57)( 30, 58)( 31, 60)( 32, 59)( 33, 53)( 34, 54)
( 35, 56)( 36, 55)( 37, 49)( 38, 50)( 39, 52)( 40, 51)( 61, 65)( 62, 66)
( 63, 68)( 64, 67)( 69, 77)( 70, 78)( 71, 80)( 72, 79)( 75, 76)( 81,105)
( 82,106)( 83,108)( 84,107)( 85,101)( 86,102)( 87,104)( 88,103)( 89,117)
( 90,118)( 91,120)( 92,119)( 93,113)( 94,114)( 95,116)( 96,115)( 97,109)
( 98,110)( 99,112)(100,111)(121,185)(122,186)(123,188)(124,187)(125,181)
(126,182)(127,184)(128,183)(129,197)(130,198)(131,200)(132,199)(133,193)
(134,194)(135,196)(136,195)(137,189)(138,190)(139,192)(140,191)(141,225)
(142,226)(143,228)(144,227)(145,221)(146,222)(147,224)(148,223)(149,237)
(150,238)(151,240)(152,239)(153,233)(154,234)(155,236)(156,235)(157,229)
(158,230)(159,232)(160,231)(161,205)(162,206)(163,208)(164,207)(165,201)
(166,202)(167,204)(168,203)(169,217)(170,218)(171,220)(172,219)(173,213)
(174,214)(175,216)(176,215)(177,209)(178,210)(179,212)(180,211)(241,365)
(242,366)(243,368)(244,367)(245,361)(246,362)(247,364)(248,363)(249,377)
(250,378)(251,380)(252,379)(253,373)(254,374)(255,376)(256,375)(257,369)
(258,370)(259,372)(260,371)(261,405)(262,406)(263,408)(264,407)(265,401)
(266,402)(267,404)(268,403)(269,417)(270,418)(271,420)(272,419)(273,413)
(274,414)(275,416)(276,415)(277,409)(278,410)(279,412)(280,411)(281,385)
(282,386)(283,388)(284,387)(285,381)(286,382)(287,384)(288,383)(289,397)
(290,398)(291,400)(292,399)(293,393)(294,394)(295,396)(296,395)(297,389)
(298,390)(299,392)(300,391)(301,425)(302,426)(303,428)(304,427)(305,421)
(306,422)(307,424)(308,423)(309,437)(310,438)(311,440)(312,439)(313,433)
(314,434)(315,436)(316,435)(317,429)(318,430)(319,432)(320,431)(321,465)
(322,466)(323,468)(324,467)(325,461)(326,462)(327,464)(328,463)(329,477)
(330,478)(331,480)(332,479)(333,473)(334,474)(335,476)(336,475)(337,469)
(338,470)(339,472)(340,471)(341,445)(342,446)(343,448)(344,447)(345,441)
(346,442)(347,444)(348,443)(349,457)(350,458)(351,460)(352,459)(353,453)
(354,454)(355,456)(356,455)(357,449)(358,450)(359,452)(360,451);
s2 := Sym(480)!( 1,261)( 2,264)( 3,263)( 4,262)( 5,265)( 6,268)( 7,267)
( 8,266)( 9,269)( 10,272)( 11,271)( 12,270)( 13,273)( 14,276)( 15,275)
( 16,274)( 17,277)( 18,280)( 19,279)( 20,278)( 21,241)( 22,244)( 23,243)
( 24,242)( 25,245)( 26,248)( 27,247)( 28,246)( 29,249)( 30,252)( 31,251)
( 32,250)( 33,253)( 34,256)( 35,255)( 36,254)( 37,257)( 38,260)( 39,259)
( 40,258)( 41,281)( 42,284)( 43,283)( 44,282)( 45,285)( 46,288)( 47,287)
( 48,286)( 49,289)( 50,292)( 51,291)( 52,290)( 53,293)( 54,296)( 55,295)
( 56,294)( 57,297)( 58,300)( 59,299)( 60,298)( 61,321)( 62,324)( 63,323)
( 64,322)( 65,325)( 66,328)( 67,327)( 68,326)( 69,329)( 70,332)( 71,331)
( 72,330)( 73,333)( 74,336)( 75,335)( 76,334)( 77,337)( 78,340)( 79,339)
( 80,338)( 81,301)( 82,304)( 83,303)( 84,302)( 85,305)( 86,308)( 87,307)
( 88,306)( 89,309)( 90,312)( 91,311)( 92,310)( 93,313)( 94,316)( 95,315)
( 96,314)( 97,317)( 98,320)( 99,319)(100,318)(101,341)(102,344)(103,343)
(104,342)(105,345)(106,348)(107,347)(108,346)(109,349)(110,352)(111,351)
(112,350)(113,353)(114,356)(115,355)(116,354)(117,357)(118,360)(119,359)
(120,358)(121,441)(122,444)(123,443)(124,442)(125,445)(126,448)(127,447)
(128,446)(129,449)(130,452)(131,451)(132,450)(133,453)(134,456)(135,455)
(136,454)(137,457)(138,460)(139,459)(140,458)(141,421)(142,424)(143,423)
(144,422)(145,425)(146,428)(147,427)(148,426)(149,429)(150,432)(151,431)
(152,430)(153,433)(154,436)(155,435)(156,434)(157,437)(158,440)(159,439)
(160,438)(161,461)(162,464)(163,463)(164,462)(165,465)(166,468)(167,467)
(168,466)(169,469)(170,472)(171,471)(172,470)(173,473)(174,476)(175,475)
(176,474)(177,477)(178,480)(179,479)(180,478)(181,381)(182,384)(183,383)
(184,382)(185,385)(186,388)(187,387)(188,386)(189,389)(190,392)(191,391)
(192,390)(193,393)(194,396)(195,395)(196,394)(197,397)(198,400)(199,399)
(200,398)(201,361)(202,364)(203,363)(204,362)(205,365)(206,368)(207,367)
(208,366)(209,369)(210,372)(211,371)(212,370)(213,373)(214,376)(215,375)
(216,374)(217,377)(218,380)(219,379)(220,378)(221,401)(222,404)(223,403)
(224,402)(225,405)(226,408)(227,407)(228,406)(229,409)(230,412)(231,411)
(232,410)(233,413)(234,416)(235,415)(236,414)(237,417)(238,420)(239,419)
(240,418);
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*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
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 >;
References : None.
to this polytope