Polytope of Type {120,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {120,6}*1920b
if this polytope has a name.
Group : SmallGroup(1920,238657)
Rank : 3
Schlafli Type : {120,6}
Number of vertices, edges, etc : 160, 480, 8
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 12
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
   4-fold quotients : {30,6}*480
   5-fold quotients : {24,6}*384b
   8-fold quotients : {15,6}*240
   10-fold quotients : {12,6}*192a
   20-fold quotients : {6,6}*96
   24-fold quotients : {20,2}*80
   40-fold quotients : {3,6}*48, {6,3}*48
   48-fold quotients : {10,2}*40
   80-fold quotients : {3,3}*24
   96-fold quotients : {5,2}*20
   120-fold quotients : {4,2}*16
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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