Polytope of Type {6,120}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,120}*1920b
if this polytope has a name.
Group : SmallGroup(1920,238657)
Rank : 3
Schlafli Type : {6,120}
Number of vertices, edges, etc : 8, 480, 160
Order of s0s1s2 : 20
Order of s0s1s2s1 : 12
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 : {6,60}*960a
4-fold quotients : {6,30}*480
5-fold quotients : {6,24}*384b
8-fold quotients : {6,15}*240
10-fold quotients : {6,12}*192a
20-fold quotients : {6,6}*96
24-fold quotients : {2,20}*80
40-fold quotients : {3,6}*48, {6,3}*48
48-fold quotients : {2,10}*40
80-fold quotients : {3,3}*24
96-fold quotients : {2,5}*20
120-fold quotients : {2,4}*16
240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 7)( 6, 8)( 11, 12)( 13, 15)( 14, 16)( 19, 20)( 21, 23)
( 22, 24)( 27, 28)( 29, 31)( 30, 32)( 35, 36)( 37, 39)( 38, 40)( 41, 81)
( 42, 82)( 43, 84)( 44, 83)( 45, 87)( 46, 88)( 47, 85)( 48, 86)( 49, 89)
( 50, 90)( 51, 92)( 52, 91)( 53, 95)( 54, 96)( 55, 93)( 56, 94)( 57, 97)
( 58, 98)( 59,100)( 60, 99)( 61,103)( 62,104)( 63,101)( 64,102)( 65,105)
( 66,106)( 67,108)( 68,107)( 69,111)( 70,112)( 71,109)( 72,110)( 73,113)
( 74,114)( 75,116)( 76,115)( 77,119)( 78,120)( 79,117)( 80,118)(123,124)
(125,127)(126,128)(131,132)(133,135)(134,136)(139,140)(141,143)(142,144)
(147,148)(149,151)(150,152)(155,156)(157,159)(158,160)(161,201)(162,202)
(163,204)(164,203)(165,207)(166,208)(167,205)(168,206)(169,209)(170,210)
(171,212)(172,211)(173,215)(174,216)(175,213)(176,214)(177,217)(178,218)
(179,220)(180,219)(181,223)(182,224)(183,221)(184,222)(185,225)(186,226)
(187,228)(188,227)(189,231)(190,232)(191,229)(192,230)(193,233)(194,234)
(195,236)(196,235)(197,239)(198,240)(199,237)(200,238)(241,242)(245,248)
(246,247)(249,250)(253,256)(254,255)(257,258)(261,264)(262,263)(265,266)
(269,272)(270,271)(273,274)(277,280)(278,279)(281,322)(282,321)(283,323)
(284,324)(285,328)(286,327)(287,326)(288,325)(289,330)(290,329)(291,331)
(292,332)(293,336)(294,335)(295,334)(296,333)(297,338)(298,337)(299,339)
(300,340)(301,344)(302,343)(303,342)(304,341)(305,346)(306,345)(307,347)
(308,348)(309,352)(310,351)(311,350)(312,349)(313,354)(314,353)(315,355)
(316,356)(317,360)(318,359)(319,358)(320,357)(361,362)(365,368)(366,367)
(369,370)(373,376)(374,375)(377,378)(381,384)(382,383)(385,386)(389,392)
(390,391)(393,394)(397,400)(398,399)(401,442)(402,441)(403,443)(404,444)
(405,448)(406,447)(407,446)(408,445)(409,450)(410,449)(411,451)(412,452)
(413,456)(414,455)(415,454)(416,453)(417,458)(418,457)(419,459)(420,460)
(421,464)(422,463)(423,462)(424,461)(425,466)(426,465)(427,467)(428,468)
(429,472)(430,471)(431,470)(432,469)(433,474)(434,473)(435,475)(436,476)
(437,480)(438,479)(439,478)(440,477);;
s1 := ( 1, 41)( 2, 42)( 3, 47)( 4, 48)( 5, 46)( 6, 45)( 7, 43)( 8, 44)
( 9, 73)( 10, 74)( 11, 79)( 12, 80)( 13, 78)( 14, 77)( 15, 75)( 16, 76)
( 17, 65)( 18, 66)( 19, 71)( 20, 72)( 21, 70)( 22, 69)( 23, 67)( 24, 68)
( 25, 57)( 26, 58)( 27, 63)( 28, 64)( 29, 62)( 30, 61)( 31, 59)( 32, 60)
( 33, 49)( 34, 50)( 35, 55)( 36, 56)( 37, 54)( 38, 53)( 39, 51)( 40, 52)
( 83, 87)( 84, 88)( 85, 86)( 89,113)( 90,114)( 91,119)( 92,120)( 93,118)
( 94,117)( 95,115)( 96,116)( 97,105)( 98,106)( 99,111)(100,112)(101,110)
(102,109)(103,107)(104,108)(121,162)(122,161)(123,168)(124,167)(125,165)
(126,166)(127,164)(128,163)(129,194)(130,193)(131,200)(132,199)(133,197)
(134,198)(135,196)(136,195)(137,186)(138,185)(139,192)(140,191)(141,189)
(142,190)(143,188)(144,187)(145,178)(146,177)(147,184)(148,183)(149,181)
(150,182)(151,180)(152,179)(153,170)(154,169)(155,176)(156,175)(157,173)
(158,174)(159,172)(160,171)(201,202)(203,208)(204,207)(209,234)(210,233)
(211,240)(212,239)(213,237)(214,238)(215,236)(216,235)(217,226)(218,225)
(219,232)(220,231)(221,229)(222,230)(223,228)(224,227)(241,402)(242,401)
(243,408)(244,407)(245,405)(246,406)(247,404)(248,403)(249,434)(250,433)
(251,440)(252,439)(253,437)(254,438)(255,436)(256,435)(257,426)(258,425)
(259,432)(260,431)(261,429)(262,430)(263,428)(264,427)(265,418)(266,417)
(267,424)(268,423)(269,421)(270,422)(271,420)(272,419)(273,410)(274,409)
(275,416)(276,415)(277,413)(278,414)(279,412)(280,411)(281,362)(282,361)
(283,368)(284,367)(285,365)(286,366)(287,364)(288,363)(289,394)(290,393)
(291,400)(292,399)(293,397)(294,398)(295,396)(296,395)(297,386)(298,385)
(299,392)(300,391)(301,389)(302,390)(303,388)(304,387)(305,378)(306,377)
(307,384)(308,383)(309,381)(310,382)(311,380)(312,379)(313,370)(314,369)
(315,376)(316,375)(317,373)(318,374)(319,372)(320,371)(321,442)(322,441)
(323,448)(324,447)(325,445)(326,446)(327,444)(328,443)(329,474)(330,473)
(331,480)(332,479)(333,477)(334,478)(335,476)(336,475)(337,466)(338,465)
(339,472)(340,471)(341,469)(342,470)(343,468)(344,467)(345,458)(346,457)
(347,464)(348,463)(349,461)(350,462)(351,460)(352,459)(353,450)(354,449)
(355,456)(356,455)(357,453)(358,454)(359,452)(360,451);;
s2 := ( 1,251)( 2,252)( 3,249)( 4,250)( 5,254)( 6,253)( 7,255)( 8,256)
( 9,243)( 10,244)( 11,241)( 12,242)( 13,246)( 14,245)( 15,247)( 16,248)
( 17,275)( 18,276)( 19,273)( 20,274)( 21,278)( 22,277)( 23,279)( 24,280)
( 25,267)( 26,268)( 27,265)( 28,266)( 29,270)( 30,269)( 31,271)( 32,272)
( 33,259)( 34,260)( 35,257)( 36,258)( 37,262)( 38,261)( 39,263)( 40,264)
( 41,331)( 42,332)( 43,329)( 44,330)( 45,334)( 46,333)( 47,335)( 48,336)
( 49,323)( 50,324)( 51,321)( 52,322)( 53,326)( 54,325)( 55,327)( 56,328)
( 57,355)( 58,356)( 59,353)( 60,354)( 61,358)( 62,357)( 63,359)( 64,360)
( 65,347)( 66,348)( 67,345)( 68,346)( 69,350)( 70,349)( 71,351)( 72,352)
( 73,339)( 74,340)( 75,337)( 76,338)( 77,342)( 78,341)( 79,343)( 80,344)
( 81,291)( 82,292)( 83,289)( 84,290)( 85,294)( 86,293)( 87,295)( 88,296)
( 89,283)( 90,284)( 91,281)( 92,282)( 93,286)( 94,285)( 95,287)( 96,288)
( 97,315)( 98,316)( 99,313)(100,314)(101,318)(102,317)(103,319)(104,320)
(105,307)(106,308)(107,305)(108,306)(109,310)(110,309)(111,311)(112,312)
(113,299)(114,300)(115,297)(116,298)(117,302)(118,301)(119,303)(120,304)
(121,372)(122,371)(123,370)(124,369)(125,373)(126,374)(127,376)(128,375)
(129,364)(130,363)(131,362)(132,361)(133,365)(134,366)(135,368)(136,367)
(137,396)(138,395)(139,394)(140,393)(141,397)(142,398)(143,400)(144,399)
(145,388)(146,387)(147,386)(148,385)(149,389)(150,390)(151,392)(152,391)
(153,380)(154,379)(155,378)(156,377)(157,381)(158,382)(159,384)(160,383)
(161,452)(162,451)(163,450)(164,449)(165,453)(166,454)(167,456)(168,455)
(169,444)(170,443)(171,442)(172,441)(173,445)(174,446)(175,448)(176,447)
(177,476)(178,475)(179,474)(180,473)(181,477)(182,478)(183,480)(184,479)
(185,468)(186,467)(187,466)(188,465)(189,469)(190,470)(191,472)(192,471)
(193,460)(194,459)(195,458)(196,457)(197,461)(198,462)(199,464)(200,463)
(201,412)(202,411)(203,410)(204,409)(205,413)(206,414)(207,416)(208,415)
(209,404)(210,403)(211,402)(212,401)(213,405)(214,406)(215,408)(216,407)
(217,436)(218,435)(219,434)(220,433)(221,437)(222,438)(223,440)(224,439)
(225,428)(226,427)(227,426)(228,425)(229,429)(230,430)(231,432)(232,431)
(233,420)(234,419)(235,418)(236,417)(237,421)(238,422)(239,424)(240,423);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*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*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(480)!( 3, 4)( 5, 7)( 6, 8)( 11, 12)( 13, 15)( 14, 16)( 19, 20)
( 21, 23)( 22, 24)( 27, 28)( 29, 31)( 30, 32)( 35, 36)( 37, 39)( 38, 40)
( 41, 81)( 42, 82)( 43, 84)( 44, 83)( 45, 87)( 46, 88)( 47, 85)( 48, 86)
( 49, 89)( 50, 90)( 51, 92)( 52, 91)( 53, 95)( 54, 96)( 55, 93)( 56, 94)
( 57, 97)( 58, 98)( 59,100)( 60, 99)( 61,103)( 62,104)( 63,101)( 64,102)
( 65,105)( 66,106)( 67,108)( 68,107)( 69,111)( 70,112)( 71,109)( 72,110)
( 73,113)( 74,114)( 75,116)( 76,115)( 77,119)( 78,120)( 79,117)( 80,118)
(123,124)(125,127)(126,128)(131,132)(133,135)(134,136)(139,140)(141,143)
(142,144)(147,148)(149,151)(150,152)(155,156)(157,159)(158,160)(161,201)
(162,202)(163,204)(164,203)(165,207)(166,208)(167,205)(168,206)(169,209)
(170,210)(171,212)(172,211)(173,215)(174,216)(175,213)(176,214)(177,217)
(178,218)(179,220)(180,219)(181,223)(182,224)(183,221)(184,222)(185,225)
(186,226)(187,228)(188,227)(189,231)(190,232)(191,229)(192,230)(193,233)
(194,234)(195,236)(196,235)(197,239)(198,240)(199,237)(200,238)(241,242)
(245,248)(246,247)(249,250)(253,256)(254,255)(257,258)(261,264)(262,263)
(265,266)(269,272)(270,271)(273,274)(277,280)(278,279)(281,322)(282,321)
(283,323)(284,324)(285,328)(286,327)(287,326)(288,325)(289,330)(290,329)
(291,331)(292,332)(293,336)(294,335)(295,334)(296,333)(297,338)(298,337)
(299,339)(300,340)(301,344)(302,343)(303,342)(304,341)(305,346)(306,345)
(307,347)(308,348)(309,352)(310,351)(311,350)(312,349)(313,354)(314,353)
(315,355)(316,356)(317,360)(318,359)(319,358)(320,357)(361,362)(365,368)
(366,367)(369,370)(373,376)(374,375)(377,378)(381,384)(382,383)(385,386)
(389,392)(390,391)(393,394)(397,400)(398,399)(401,442)(402,441)(403,443)
(404,444)(405,448)(406,447)(407,446)(408,445)(409,450)(410,449)(411,451)
(412,452)(413,456)(414,455)(415,454)(416,453)(417,458)(418,457)(419,459)
(420,460)(421,464)(422,463)(423,462)(424,461)(425,466)(426,465)(427,467)
(428,468)(429,472)(430,471)(431,470)(432,469)(433,474)(434,473)(435,475)
(436,476)(437,480)(438,479)(439,478)(440,477);
s1 := Sym(480)!( 1, 41)( 2, 42)( 3, 47)( 4, 48)( 5, 46)( 6, 45)( 7, 43)
( 8, 44)( 9, 73)( 10, 74)( 11, 79)( 12, 80)( 13, 78)( 14, 77)( 15, 75)
( 16, 76)( 17, 65)( 18, 66)( 19, 71)( 20, 72)( 21, 70)( 22, 69)( 23, 67)
( 24, 68)( 25, 57)( 26, 58)( 27, 63)( 28, 64)( 29, 62)( 30, 61)( 31, 59)
( 32, 60)( 33, 49)( 34, 50)( 35, 55)( 36, 56)( 37, 54)( 38, 53)( 39, 51)
( 40, 52)( 83, 87)( 84, 88)( 85, 86)( 89,113)( 90,114)( 91,119)( 92,120)
( 93,118)( 94,117)( 95,115)( 96,116)( 97,105)( 98,106)( 99,111)(100,112)
(101,110)(102,109)(103,107)(104,108)(121,162)(122,161)(123,168)(124,167)
(125,165)(126,166)(127,164)(128,163)(129,194)(130,193)(131,200)(132,199)
(133,197)(134,198)(135,196)(136,195)(137,186)(138,185)(139,192)(140,191)
(141,189)(142,190)(143,188)(144,187)(145,178)(146,177)(147,184)(148,183)
(149,181)(150,182)(151,180)(152,179)(153,170)(154,169)(155,176)(156,175)
(157,173)(158,174)(159,172)(160,171)(201,202)(203,208)(204,207)(209,234)
(210,233)(211,240)(212,239)(213,237)(214,238)(215,236)(216,235)(217,226)
(218,225)(219,232)(220,231)(221,229)(222,230)(223,228)(224,227)(241,402)
(242,401)(243,408)(244,407)(245,405)(246,406)(247,404)(248,403)(249,434)
(250,433)(251,440)(252,439)(253,437)(254,438)(255,436)(256,435)(257,426)
(258,425)(259,432)(260,431)(261,429)(262,430)(263,428)(264,427)(265,418)
(266,417)(267,424)(268,423)(269,421)(270,422)(271,420)(272,419)(273,410)
(274,409)(275,416)(276,415)(277,413)(278,414)(279,412)(280,411)(281,362)
(282,361)(283,368)(284,367)(285,365)(286,366)(287,364)(288,363)(289,394)
(290,393)(291,400)(292,399)(293,397)(294,398)(295,396)(296,395)(297,386)
(298,385)(299,392)(300,391)(301,389)(302,390)(303,388)(304,387)(305,378)
(306,377)(307,384)(308,383)(309,381)(310,382)(311,380)(312,379)(313,370)
(314,369)(315,376)(316,375)(317,373)(318,374)(319,372)(320,371)(321,442)
(322,441)(323,448)(324,447)(325,445)(326,446)(327,444)(328,443)(329,474)
(330,473)(331,480)(332,479)(333,477)(334,478)(335,476)(336,475)(337,466)
(338,465)(339,472)(340,471)(341,469)(342,470)(343,468)(344,467)(345,458)
(346,457)(347,464)(348,463)(349,461)(350,462)(351,460)(352,459)(353,450)
(354,449)(355,456)(356,455)(357,453)(358,454)(359,452)(360,451);
s2 := Sym(480)!( 1,251)( 2,252)( 3,249)( 4,250)( 5,254)( 6,253)( 7,255)
( 8,256)( 9,243)( 10,244)( 11,241)( 12,242)( 13,246)( 14,245)( 15,247)
( 16,248)( 17,275)( 18,276)( 19,273)( 20,274)( 21,278)( 22,277)( 23,279)
( 24,280)( 25,267)( 26,268)( 27,265)( 28,266)( 29,270)( 30,269)( 31,271)
( 32,272)( 33,259)( 34,260)( 35,257)( 36,258)( 37,262)( 38,261)( 39,263)
( 40,264)( 41,331)( 42,332)( 43,329)( 44,330)( 45,334)( 46,333)( 47,335)
( 48,336)( 49,323)( 50,324)( 51,321)( 52,322)( 53,326)( 54,325)( 55,327)
( 56,328)( 57,355)( 58,356)( 59,353)( 60,354)( 61,358)( 62,357)( 63,359)
( 64,360)( 65,347)( 66,348)( 67,345)( 68,346)( 69,350)( 70,349)( 71,351)
( 72,352)( 73,339)( 74,340)( 75,337)( 76,338)( 77,342)( 78,341)( 79,343)
( 80,344)( 81,291)( 82,292)( 83,289)( 84,290)( 85,294)( 86,293)( 87,295)
( 88,296)( 89,283)( 90,284)( 91,281)( 92,282)( 93,286)( 94,285)( 95,287)
( 96,288)( 97,315)( 98,316)( 99,313)(100,314)(101,318)(102,317)(103,319)
(104,320)(105,307)(106,308)(107,305)(108,306)(109,310)(110,309)(111,311)
(112,312)(113,299)(114,300)(115,297)(116,298)(117,302)(118,301)(119,303)
(120,304)(121,372)(122,371)(123,370)(124,369)(125,373)(126,374)(127,376)
(128,375)(129,364)(130,363)(131,362)(132,361)(133,365)(134,366)(135,368)
(136,367)(137,396)(138,395)(139,394)(140,393)(141,397)(142,398)(143,400)
(144,399)(145,388)(146,387)(147,386)(148,385)(149,389)(150,390)(151,392)
(152,391)(153,380)(154,379)(155,378)(156,377)(157,381)(158,382)(159,384)
(160,383)(161,452)(162,451)(163,450)(164,449)(165,453)(166,454)(167,456)
(168,455)(169,444)(170,443)(171,442)(172,441)(173,445)(174,446)(175,448)
(176,447)(177,476)(178,475)(179,474)(180,473)(181,477)(182,478)(183,480)
(184,479)(185,468)(186,467)(187,466)(188,465)(189,469)(190,470)(191,472)
(192,471)(193,460)(194,459)(195,458)(196,457)(197,461)(198,462)(199,464)
(200,463)(201,412)(202,411)(203,410)(204,409)(205,413)(206,414)(207,416)
(208,415)(209,404)(210,403)(211,402)(212,401)(213,405)(214,406)(215,408)
(216,407)(217,436)(218,435)(219,434)(220,433)(221,437)(222,438)(223,440)
(224,439)(225,428)(226,427)(227,426)(228,425)(229,429)(230,430)(231,432)
(232,431)(233,420)(234,419)(235,418)(236,417)(237,421)(238,422)(239,424)
(240,423);
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*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*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 >;
References : None.
to this polytope