Polytope of Type {60,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {60,12}*1920c
if this polytope has a name.
Group : SmallGroup(1920,238871)
Rank : 3
Schlafli Type : {60,12}
Number of vertices, edges, etc : 80, 480, 16
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 6
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 : {60,6}*960a, {30,12}*960b
   4-fold quotients : {30,6}*480
   5-fold quotients : {12,12}*384a
   8-fold quotients : {15,6}*240
   10-fold quotients : {6,12}*192a, {12,6}*192a
   12-fold quotients : {20,4}*160
   20-fold quotients : {6,6}*96
   24-fold quotients : {20,2}*80, {10,4}*80
   40-fold quotients : {3,6}*48, {6,3}*48
   48-fold quotients : {10,2}*40
   60-fold quotients : {4,4}*32
   80-fold quotients : {3,3}*24
   96-fold quotients : {5,2}*20
   120-fold quotients : {2,4}*16, {4,2}*16
   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)(123,124)(125,137)(126,138)(127,140)(128,139)(129,133)
(130,134)(131,136)(132,135)(141,161)(142,162)(143,164)(144,163)(145,177)
(146,178)(147,180)(148,179)(149,173)(150,174)(151,176)(152,175)(153,169)
(154,170)(155,172)(156,171)(157,165)(158,166)(159,168)(160,167)(183,184)
(185,197)(186,198)(187,200)(188,199)(189,193)(190,194)(191,196)(192,195)
(201,221)(202,222)(203,224)(204,223)(205,237)(206,238)(207,240)(208,239)
(209,233)(210,234)(211,236)(212,235)(213,229)(214,230)(215,232)(216,231)
(217,225)(218,226)(219,228)(220,227)(241,421)(242,422)(243,424)(244,423)
(245,437)(246,438)(247,440)(248,439)(249,433)(250,434)(251,436)(252,435)
(253,429)(254,430)(255,432)(256,431)(257,425)(258,426)(259,428)(260,427)
(261,461)(262,462)(263,464)(264,463)(265,477)(266,478)(267,480)(268,479)
(269,473)(270,474)(271,476)(272,475)(273,469)(274,470)(275,472)(276,471)
(277,465)(278,466)(279,468)(280,467)(281,441)(282,442)(283,444)(284,443)
(285,457)(286,458)(287,460)(288,459)(289,453)(290,454)(291,456)(292,455)
(293,449)(294,450)(295,452)(296,451)(297,445)(298,446)(299,448)(300,447)
(301,361)(302,362)(303,364)(304,363)(305,377)(306,378)(307,380)(308,379)
(309,373)(310,374)(311,376)(312,375)(313,369)(314,370)(315,372)(316,371)
(317,365)(318,366)(319,368)(320,367)(321,401)(322,402)(323,404)(324,403)
(325,417)(326,418)(327,420)(328,419)(329,413)(330,414)(331,416)(332,415)
(333,409)(334,410)(335,412)(336,411)(337,405)(338,406)(339,408)(340,407)
(341,381)(342,382)(343,384)(344,383)(345,397)(346,398)(347,400)(348,399)
(349,393)(350,394)(351,396)(352,395)(353,389)(354,390)(355,392)(356,391)
(357,385)(358,386)(359,388)(360,387);;
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)
(121,385)(122,388)(123,387)(124,386)(125,381)(126,384)(127,383)(128,382)
(129,397)(130,400)(131,399)(132,398)(133,393)(134,396)(135,395)(136,394)
(137,389)(138,392)(139,391)(140,390)(141,365)(142,368)(143,367)(144,366)
(145,361)(146,364)(147,363)(148,362)(149,377)(150,380)(151,379)(152,378)
(153,373)(154,376)(155,375)(156,374)(157,369)(158,372)(159,371)(160,370)
(161,405)(162,408)(163,407)(164,406)(165,401)(166,404)(167,403)(168,402)
(169,417)(170,420)(171,419)(172,418)(173,413)(174,416)(175,415)(176,414)
(177,409)(178,412)(179,411)(180,410)(181,445)(182,448)(183,447)(184,446)
(185,441)(186,444)(187,443)(188,442)(189,457)(190,460)(191,459)(192,458)
(193,453)(194,456)(195,455)(196,454)(197,449)(198,452)(199,451)(200,450)
(201,425)(202,428)(203,427)(204,426)(205,421)(206,424)(207,423)(208,422)
(209,437)(210,440)(211,439)(212,438)(213,433)(214,436)(215,435)(216,434)
(217,429)(218,432)(219,431)(220,430)(221,465)(222,468)(223,467)(224,466)
(225,461)(226,464)(227,463)(228,462)(229,477)(230,480)(231,479)(232,478)
(233,473)(234,476)(235,475)(236,474)(237,469)(238,472)(239,471)(240,470);;
s2 := (  1,  2)(  5,  6)(  9, 10)( 13, 14)( 17, 18)( 21, 42)( 22, 41)( 23, 43)
( 24, 44)( 25, 46)( 26, 45)( 27, 47)( 28, 48)( 29, 50)( 30, 49)( 31, 51)
( 32, 52)( 33, 54)( 34, 53)( 35, 55)( 36, 56)( 37, 58)( 38, 57)( 39, 59)
( 40, 60)( 61, 62)( 65, 66)( 69, 70)( 73, 74)( 77, 78)( 81,102)( 82,101)
( 83,103)( 84,104)( 85,106)( 86,105)( 87,107)( 88,108)( 89,110)( 90,109)
( 91,111)( 92,112)( 93,114)( 94,113)( 95,115)( 96,116)( 97,118)( 98,117)
( 99,119)(100,120)(121,122)(125,126)(129,130)(133,134)(137,138)(141,162)
(142,161)(143,163)(144,164)(145,166)(146,165)(147,167)(148,168)(149,170)
(150,169)(151,171)(152,172)(153,174)(154,173)(155,175)(156,176)(157,178)
(158,177)(159,179)(160,180)(181,182)(185,186)(189,190)(193,194)(197,198)
(201,222)(202,221)(203,223)(204,224)(205,226)(206,225)(207,227)(208,228)
(209,230)(210,229)(211,231)(212,232)(213,234)(214,233)(215,235)(216,236)
(217,238)(218,237)(219,239)(220,240)(241,362)(242,361)(243,363)(244,364)
(245,366)(246,365)(247,367)(248,368)(249,370)(250,369)(251,371)(252,372)
(253,374)(254,373)(255,375)(256,376)(257,378)(258,377)(259,379)(260,380)
(261,402)(262,401)(263,403)(264,404)(265,406)(266,405)(267,407)(268,408)
(269,410)(270,409)(271,411)(272,412)(273,414)(274,413)(275,415)(276,416)
(277,418)(278,417)(279,419)(280,420)(281,382)(282,381)(283,383)(284,384)
(285,386)(286,385)(287,387)(288,388)(289,390)(290,389)(291,391)(292,392)
(293,394)(294,393)(295,395)(296,396)(297,398)(298,397)(299,399)(300,400)
(301,422)(302,421)(303,423)(304,424)(305,426)(306,425)(307,427)(308,428)
(309,430)(310,429)(311,431)(312,432)(313,434)(314,433)(315,435)(316,436)
(317,438)(318,437)(319,439)(320,440)(321,462)(322,461)(323,463)(324,464)
(325,466)(326,465)(327,467)(328,468)(329,470)(330,469)(331,471)(332,472)
(333,474)(334,473)(335,475)(336,476)(337,478)(338,477)(339,479)(340,480)
(341,442)(342,441)(343,443)(344,444)(345,446)(346,445)(347,447)(348,448)
(349,450)(350,449)(351,451)(352,452)(353,454)(354,453)(355,455)(356,456)
(357,458)(358,457)(359,459)(360,460);;
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, s2*s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*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)(123,124)(125,137)(126,138)(127,140)(128,139)
(129,133)(130,134)(131,136)(132,135)(141,161)(142,162)(143,164)(144,163)
(145,177)(146,178)(147,180)(148,179)(149,173)(150,174)(151,176)(152,175)
(153,169)(154,170)(155,172)(156,171)(157,165)(158,166)(159,168)(160,167)
(183,184)(185,197)(186,198)(187,200)(188,199)(189,193)(190,194)(191,196)
(192,195)(201,221)(202,222)(203,224)(204,223)(205,237)(206,238)(207,240)
(208,239)(209,233)(210,234)(211,236)(212,235)(213,229)(214,230)(215,232)
(216,231)(217,225)(218,226)(219,228)(220,227)(241,421)(242,422)(243,424)
(244,423)(245,437)(246,438)(247,440)(248,439)(249,433)(250,434)(251,436)
(252,435)(253,429)(254,430)(255,432)(256,431)(257,425)(258,426)(259,428)
(260,427)(261,461)(262,462)(263,464)(264,463)(265,477)(266,478)(267,480)
(268,479)(269,473)(270,474)(271,476)(272,475)(273,469)(274,470)(275,472)
(276,471)(277,465)(278,466)(279,468)(280,467)(281,441)(282,442)(283,444)
(284,443)(285,457)(286,458)(287,460)(288,459)(289,453)(290,454)(291,456)
(292,455)(293,449)(294,450)(295,452)(296,451)(297,445)(298,446)(299,448)
(300,447)(301,361)(302,362)(303,364)(304,363)(305,377)(306,378)(307,380)
(308,379)(309,373)(310,374)(311,376)(312,375)(313,369)(314,370)(315,372)
(316,371)(317,365)(318,366)(319,368)(320,367)(321,401)(322,402)(323,404)
(324,403)(325,417)(326,418)(327,420)(328,419)(329,413)(330,414)(331,416)
(332,415)(333,409)(334,410)(335,412)(336,411)(337,405)(338,406)(339,408)
(340,407)(341,381)(342,382)(343,384)(344,383)(345,397)(346,398)(347,400)
(348,399)(349,393)(350,394)(351,396)(352,395)(353,389)(354,390)(355,392)
(356,391)(357,385)(358,386)(359,388)(360,387);
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)(121,385)(122,388)(123,387)(124,386)(125,381)(126,384)(127,383)
(128,382)(129,397)(130,400)(131,399)(132,398)(133,393)(134,396)(135,395)
(136,394)(137,389)(138,392)(139,391)(140,390)(141,365)(142,368)(143,367)
(144,366)(145,361)(146,364)(147,363)(148,362)(149,377)(150,380)(151,379)
(152,378)(153,373)(154,376)(155,375)(156,374)(157,369)(158,372)(159,371)
(160,370)(161,405)(162,408)(163,407)(164,406)(165,401)(166,404)(167,403)
(168,402)(169,417)(170,420)(171,419)(172,418)(173,413)(174,416)(175,415)
(176,414)(177,409)(178,412)(179,411)(180,410)(181,445)(182,448)(183,447)
(184,446)(185,441)(186,444)(187,443)(188,442)(189,457)(190,460)(191,459)
(192,458)(193,453)(194,456)(195,455)(196,454)(197,449)(198,452)(199,451)
(200,450)(201,425)(202,428)(203,427)(204,426)(205,421)(206,424)(207,423)
(208,422)(209,437)(210,440)(211,439)(212,438)(213,433)(214,436)(215,435)
(216,434)(217,429)(218,432)(219,431)(220,430)(221,465)(222,468)(223,467)
(224,466)(225,461)(226,464)(227,463)(228,462)(229,477)(230,480)(231,479)
(232,478)(233,473)(234,476)(235,475)(236,474)(237,469)(238,472)(239,471)
(240,470);
s2 := Sym(480)!(  1,  2)(  5,  6)(  9, 10)( 13, 14)( 17, 18)( 21, 42)( 22, 41)
( 23, 43)( 24, 44)( 25, 46)( 26, 45)( 27, 47)( 28, 48)( 29, 50)( 30, 49)
( 31, 51)( 32, 52)( 33, 54)( 34, 53)( 35, 55)( 36, 56)( 37, 58)( 38, 57)
( 39, 59)( 40, 60)( 61, 62)( 65, 66)( 69, 70)( 73, 74)( 77, 78)( 81,102)
( 82,101)( 83,103)( 84,104)( 85,106)( 86,105)( 87,107)( 88,108)( 89,110)
( 90,109)( 91,111)( 92,112)( 93,114)( 94,113)( 95,115)( 96,116)( 97,118)
( 98,117)( 99,119)(100,120)(121,122)(125,126)(129,130)(133,134)(137,138)
(141,162)(142,161)(143,163)(144,164)(145,166)(146,165)(147,167)(148,168)
(149,170)(150,169)(151,171)(152,172)(153,174)(154,173)(155,175)(156,176)
(157,178)(158,177)(159,179)(160,180)(181,182)(185,186)(189,190)(193,194)
(197,198)(201,222)(202,221)(203,223)(204,224)(205,226)(206,225)(207,227)
(208,228)(209,230)(210,229)(211,231)(212,232)(213,234)(214,233)(215,235)
(216,236)(217,238)(218,237)(219,239)(220,240)(241,362)(242,361)(243,363)
(244,364)(245,366)(246,365)(247,367)(248,368)(249,370)(250,369)(251,371)
(252,372)(253,374)(254,373)(255,375)(256,376)(257,378)(258,377)(259,379)
(260,380)(261,402)(262,401)(263,403)(264,404)(265,406)(266,405)(267,407)
(268,408)(269,410)(270,409)(271,411)(272,412)(273,414)(274,413)(275,415)
(276,416)(277,418)(278,417)(279,419)(280,420)(281,382)(282,381)(283,383)
(284,384)(285,386)(286,385)(287,387)(288,388)(289,390)(290,389)(291,391)
(292,392)(293,394)(294,393)(295,395)(296,396)(297,398)(298,397)(299,399)
(300,400)(301,422)(302,421)(303,423)(304,424)(305,426)(306,425)(307,427)
(308,428)(309,430)(310,429)(311,431)(312,432)(313,434)(314,433)(315,435)
(316,436)(317,438)(318,437)(319,439)(320,440)(321,462)(322,461)(323,463)
(324,464)(325,466)(326,465)(327,467)(328,468)(329,470)(330,469)(331,471)
(332,472)(333,474)(334,473)(335,475)(336,476)(337,478)(338,477)(339,479)
(340,480)(341,442)(342,441)(343,443)(344,444)(345,446)(346,445)(347,447)
(348,448)(349,450)(350,449)(351,451)(352,452)(353,454)(354,453)(355,455)
(356,456)(357,458)(358,457)(359,459)(360,460);
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, s2*s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope