Polytope of Type {20,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,12}*1920c
if this polytope has a name.
Group : SmallGroup(1920,238871)
Rank : 3
Schlafli Type : {20,12}
Number of vertices, edges, etc : 80, 480, 48
Order of s₀s₁s₂ : 60
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {20,12}*960b, {20,6}*960e, {20,12}*960c
   4-fold quotients : {20,12}*480, {20,6}*480c
   5-fold quotients : {4,12}*384d
   8-fold quotients : {10,12}*240, {20,6}*240a, {20,6}*240b
   10-fold quotients : {4,12}*192b, {4,6}*192b, {4,12}*192c
   12-fold quotients : {20,4}*160
   16-fold quotients : {10,6}*120
   20-fold quotients : {4,12}*96a, {4,12}*96b, {4,12}*96c, {4,6}*96
   24-fold quotients : {20,2}*80, {10,4}*80
   40-fold quotients : {2,12}*48, {4,6}*48a, {4,3}*48, {4,6}*48b, {4,6}*48c
   48-fold quotients : {10,2}*40
   60-fold quotients : {4,4}*32
   80-fold quotients : {4,3}*24, {2,6}*24
   96-fold quotients : {5,2}*20
   120-fold quotients : {2,4}*16, {4,2}*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)
(121,365)(122,366)(123,368)(124,367)(125,361)(126,362)(127,364)(128,363)
(129,377)(130,378)(131,380)(132,379)(133,373)(134,374)(135,376)(136,375)
(137,369)(138,370)(139,372)(140,371)(141,405)(142,406)(143,408)(144,407)
(145,401)(146,402)(147,404)(148,403)(149,417)(150,418)(151,420)(152,419)
(153,413)(154,414)(155,416)(156,415)(157,409)(158,410)(159,412)(160,411)
(161,385)(162,386)(163,388)(164,387)(165,381)(166,382)(167,384)(168,383)
(169,397)(170,398)(171,400)(172,399)(173,393)(174,394)(175,396)(176,395)
(177,389)(178,390)(179,392)(180,391)(181,425)(182,426)(183,428)(184,427)
(185,421)(186,422)(187,424)(188,423)(189,437)(190,438)(191,440)(192,439)
(193,433)(194,434)(195,436)(196,435)(197,429)(198,430)(199,432)(200,431)
(201,465)(202,466)(203,468)(204,467)(205,461)(206,462)(207,464)(208,463)
(209,477)(210,478)(211,480)(212,479)(213,473)(214,474)(215,476)(216,475)
(217,469)(218,470)(219,472)(220,471)(221,445)(222,446)(223,448)(224,447)
(225,441)(226,442)(227,444)(228,443)(229,457)(230,458)(231,460)(232,459)
(233,453)(234,454)(235,456)(236,455)(237,449)(238,450)(239,452)(240,451);;
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)(121,141)(122,144)(123,143)(124,142)(125,145)(126,148)
(127,147)(128,146)(129,149)(130,152)(131,151)(132,150)(133,153)(134,156)
(135,155)(136,154)(137,157)(138,160)(139,159)(140,158)(162,164)(166,168)
(170,172)(174,176)(178,180)(181,201)(182,204)(183,203)(184,202)(185,205)
(186,208)(187,207)(188,206)(189,209)(190,212)(191,211)(192,210)(193,213)
(194,216)(195,215)(196,214)(197,217)(198,220)(199,219)(200,218)(222,224)
(226,228)(230,232)(234,236)(238,240)(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, 
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*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)!(  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)(121,365)(122,366)(123,368)(124,367)(125,361)(126,362)(127,364)
(128,363)(129,377)(130,378)(131,380)(132,379)(133,373)(134,374)(135,376)
(136,375)(137,369)(138,370)(139,372)(140,371)(141,405)(142,406)(143,408)
(144,407)(145,401)(146,402)(147,404)(148,403)(149,417)(150,418)(151,420)
(152,419)(153,413)(154,414)(155,416)(156,415)(157,409)(158,410)(159,412)
(160,411)(161,385)(162,386)(163,388)(164,387)(165,381)(166,382)(167,384)
(168,383)(169,397)(170,398)(171,400)(172,399)(173,393)(174,394)(175,396)
(176,395)(177,389)(178,390)(179,392)(180,391)(181,425)(182,426)(183,428)
(184,427)(185,421)(186,422)(187,424)(188,423)(189,437)(190,438)(191,440)
(192,439)(193,433)(194,434)(195,436)(196,435)(197,429)(198,430)(199,432)
(200,431)(201,465)(202,466)(203,468)(204,467)(205,461)(206,462)(207,464)
(208,463)(209,477)(210,478)(211,480)(212,479)(213,473)(214,474)(215,476)
(216,475)(217,469)(218,470)(219,472)(220,471)(221,445)(222,446)(223,448)
(224,447)(225,441)(226,442)(227,444)(228,443)(229,457)(230,458)(231,460)
(232,459)(233,453)(234,454)(235,456)(236,455)(237,449)(238,450)(239,452)
(240,451);
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)(121,141)(122,144)(123,143)(124,142)(125,145)
(126,148)(127,147)(128,146)(129,149)(130,152)(131,151)(132,150)(133,153)
(134,156)(135,155)(136,154)(137,157)(138,160)(139,159)(140,158)(162,164)
(166,168)(170,172)(174,176)(178,180)(181,201)(182,204)(183,203)(184,202)
(185,205)(186,208)(187,207)(188,206)(189,209)(190,212)(191,211)(192,210)
(193,213)(194,216)(195,215)(196,214)(197,217)(198,220)(199,219)(200,218)
(222,224)(226,228)(230,232)(234,236)(238,240)(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, 
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*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