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Polytope of Type {15,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,4}*960
if this polytope has a name.
Group : SmallGroup(960,11375)
Rank : 3
Schlafli Type : {15,4}
Number of vertices, edges, etc : 120, 240, 32
Order of s0s1s2 : 30
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {15,4,2} of size 1920
Vertex Figure Of :
   {2,15,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {15,4}*480
   3-fold quotients : {5,4}*320
   6-fold quotients : {5,4}*160
   16-fold quotients : {15,2}*60
   48-fold quotients : {5,2}*20
   80-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {15,8}*1920b, {15,4}*1920a, {15,8}*1920c, {30,4}*1920c, {30,4}*1920d
Permutation Representation (GAP) :
s0 := (  2, 11)(  3, 14)(  4,  8)(  6, 15)(  7, 10)(  9, 13)( 17, 65)( 18, 75)
( 19, 78)( 20, 72)( 21, 69)( 22, 79)( 23, 74)( 24, 68)( 25, 77)( 26, 71)
( 27, 66)( 28, 76)( 29, 73)( 30, 67)( 31, 70)( 32, 80)( 33, 49)( 34, 59)
( 35, 62)( 36, 56)( 37, 53)( 38, 63)( 39, 58)( 40, 52)( 41, 61)( 42, 55)
( 43, 50)( 44, 60)( 45, 57)( 46, 51)( 47, 54)( 48, 64)( 81,161)( 82,171)
( 83,174)( 84,168)( 85,165)( 86,175)( 87,170)( 88,164)( 89,173)( 90,167)
( 91,162)( 92,172)( 93,169)( 94,163)( 95,166)( 96,176)( 97,225)( 98,235)
( 99,238)(100,232)(101,229)(102,239)(103,234)(104,228)(105,237)(106,231)
(107,226)(108,236)(109,233)(110,227)(111,230)(112,240)(113,209)(114,219)
(115,222)(116,216)(117,213)(118,223)(119,218)(120,212)(121,221)(122,215)
(123,210)(124,220)(125,217)(126,211)(127,214)(128,224)(129,193)(130,203)
(131,206)(132,200)(133,197)(134,207)(135,202)(136,196)(137,205)(138,199)
(139,194)(140,204)(141,201)(142,195)(143,198)(144,208)(145,177)(146,187)
(147,190)(148,184)(149,181)(150,191)(151,186)(152,180)(153,189)(154,183)
(155,178)(156,188)(157,185)(158,179)(159,182)(160,192)(242,251)(243,254)
(244,248)(246,255)(247,250)(249,253)(257,305)(258,315)(259,318)(260,312)
(261,309)(262,319)(263,314)(264,308)(265,317)(266,311)(267,306)(268,316)
(269,313)(270,307)(271,310)(272,320)(273,289)(274,299)(275,302)(276,296)
(277,293)(278,303)(279,298)(280,292)(281,301)(282,295)(283,290)(284,300)
(285,297)(286,291)(287,294)(288,304)(321,401)(322,411)(323,414)(324,408)
(325,405)(326,415)(327,410)(328,404)(329,413)(330,407)(331,402)(332,412)
(333,409)(334,403)(335,406)(336,416)(337,465)(338,475)(339,478)(340,472)
(341,469)(342,479)(343,474)(344,468)(345,477)(346,471)(347,466)(348,476)
(349,473)(350,467)(351,470)(352,480)(353,449)(354,459)(355,462)(356,456)
(357,453)(358,463)(359,458)(360,452)(361,461)(362,455)(363,450)(364,460)
(365,457)(366,451)(367,454)(368,464)(369,433)(370,443)(371,446)(372,440)
(373,437)(374,447)(375,442)(376,436)(377,445)(378,439)(379,434)(380,444)
(381,441)(382,435)(383,438)(384,448)(385,417)(386,427)(387,430)(388,424)
(389,421)(390,431)(391,426)(392,420)(393,429)(394,423)(395,418)(396,428)
(397,425)(398,419)(399,422)(400,432);;
s1 := (  1, 97)(  2, 98)(  3,100)(  4, 99)(  5,102)(  6,101)(  7,103)(  8,104)
(  9,112)( 10,111)( 11,109)( 12,110)( 13,107)( 14,108)( 15,106)( 16,105)
( 17, 81)( 18, 82)( 19, 84)( 20, 83)( 21, 86)( 22, 85)( 23, 87)( 24, 88)
( 25, 96)( 26, 95)( 27, 93)( 28, 94)( 29, 91)( 30, 92)( 31, 90)( 32, 89)
( 33,145)( 34,146)( 35,148)( 36,147)( 37,150)( 38,149)( 39,151)( 40,152)
( 41,160)( 42,159)( 43,157)( 44,158)( 45,155)( 46,156)( 47,154)( 48,153)
( 49,129)( 50,130)( 51,132)( 52,131)( 53,134)( 54,133)( 55,135)( 56,136)
( 57,144)( 58,143)( 59,141)( 60,142)( 61,139)( 62,140)( 63,138)( 64,137)
( 65,113)( 66,114)( 67,116)( 68,115)( 69,118)( 70,117)( 71,119)( 72,120)
( 73,128)( 74,127)( 75,125)( 76,126)( 77,123)( 78,124)( 79,122)( 80,121)
(161,177)(162,178)(163,180)(164,179)(165,182)(166,181)(167,183)(168,184)
(169,192)(170,191)(171,189)(172,190)(173,187)(174,188)(175,186)(176,185)
(193,225)(194,226)(195,228)(196,227)(197,230)(198,229)(199,231)(200,232)
(201,240)(202,239)(203,237)(204,238)(205,235)(206,236)(207,234)(208,233)
(211,212)(213,214)(217,224)(218,223)(219,221)(220,222)(241,337)(242,338)
(243,340)(244,339)(245,342)(246,341)(247,343)(248,344)(249,352)(250,351)
(251,349)(252,350)(253,347)(254,348)(255,346)(256,345)(257,321)(258,322)
(259,324)(260,323)(261,326)(262,325)(263,327)(264,328)(265,336)(266,335)
(267,333)(268,334)(269,331)(270,332)(271,330)(272,329)(273,385)(274,386)
(275,388)(276,387)(277,390)(278,389)(279,391)(280,392)(281,400)(282,399)
(283,397)(284,398)(285,395)(286,396)(287,394)(288,393)(289,369)(290,370)
(291,372)(292,371)(293,374)(294,373)(295,375)(296,376)(297,384)(298,383)
(299,381)(300,382)(301,379)(302,380)(303,378)(304,377)(305,353)(306,354)
(307,356)(308,355)(309,358)(310,357)(311,359)(312,360)(313,368)(314,367)
(315,365)(316,366)(317,363)(318,364)(319,362)(320,361)(401,417)(402,418)
(403,420)(404,419)(405,422)(406,421)(407,423)(408,424)(409,432)(410,431)
(411,429)(412,430)(413,427)(414,428)(415,426)(416,425)(433,465)(434,466)
(435,468)(436,467)(437,470)(438,469)(439,471)(440,472)(441,480)(442,479)
(443,477)(444,478)(445,475)(446,476)(447,474)(448,473)(451,452)(453,454)
(457,464)(458,463)(459,461)(460,462);;
s2 := (  1,245)(  2,246)(  3,247)(  4,248)(  5,241)(  6,242)(  7,243)(  8,244)
(  9,253)( 10,254)( 11,255)( 12,256)( 13,249)( 14,250)( 15,251)( 16,252)
( 17,261)( 18,262)( 19,263)( 20,264)( 21,257)( 22,258)( 23,259)( 24,260)
( 25,269)( 26,270)( 27,271)( 28,272)( 29,265)( 30,266)( 31,267)( 32,268)
( 33,277)( 34,278)( 35,279)( 36,280)( 37,273)( 38,274)( 39,275)( 40,276)
( 41,285)( 42,286)( 43,287)( 44,288)( 45,281)( 46,282)( 47,283)( 48,284)
( 49,293)( 50,294)( 51,295)( 52,296)( 53,289)( 54,290)( 55,291)( 56,292)
( 57,301)( 58,302)( 59,303)( 60,304)( 61,297)( 62,298)( 63,299)( 64,300)
( 65,309)( 66,310)( 67,311)( 68,312)( 69,305)( 70,306)( 71,307)( 72,308)
( 73,317)( 74,318)( 75,319)( 76,320)( 77,313)( 78,314)( 79,315)( 80,316)
( 81,325)( 82,326)( 83,327)( 84,328)( 85,321)( 86,322)( 87,323)( 88,324)
( 89,333)( 90,334)( 91,335)( 92,336)( 93,329)( 94,330)( 95,331)( 96,332)
( 97,341)( 98,342)( 99,343)(100,344)(101,337)(102,338)(103,339)(104,340)
(105,349)(106,350)(107,351)(108,352)(109,345)(110,346)(111,347)(112,348)
(113,357)(114,358)(115,359)(116,360)(117,353)(118,354)(119,355)(120,356)
(121,365)(122,366)(123,367)(124,368)(125,361)(126,362)(127,363)(128,364)
(129,373)(130,374)(131,375)(132,376)(133,369)(134,370)(135,371)(136,372)
(137,381)(138,382)(139,383)(140,384)(141,377)(142,378)(143,379)(144,380)
(145,389)(146,390)(147,391)(148,392)(149,385)(150,386)(151,387)(152,388)
(153,397)(154,398)(155,399)(156,400)(157,393)(158,394)(159,395)(160,396)
(161,405)(162,406)(163,407)(164,408)(165,401)(166,402)(167,403)(168,404)
(169,413)(170,414)(171,415)(172,416)(173,409)(174,410)(175,411)(176,412)
(177,421)(178,422)(179,423)(180,424)(181,417)(182,418)(183,419)(184,420)
(185,429)(186,430)(187,431)(188,432)(189,425)(190,426)(191,427)(192,428)
(193,437)(194,438)(195,439)(196,440)(197,433)(198,434)(199,435)(200,436)
(201,445)(202,446)(203,447)(204,448)(205,441)(206,442)(207,443)(208,444)
(209,453)(210,454)(211,455)(212,456)(213,449)(214,450)(215,451)(216,452)
(217,461)(218,462)(219,463)(220,464)(221,457)(222,458)(223,459)(224,460)
(225,469)(226,470)(227,471)(228,472)(229,465)(230,466)(231,467)(232,468)
(233,477)(234,478)(235,479)(236,480)(237,473)(238,474)(239,475)(240,476);;
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, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*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*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)!(  2, 11)(  3, 14)(  4,  8)(  6, 15)(  7, 10)(  9, 13)( 17, 65)
( 18, 75)( 19, 78)( 20, 72)( 21, 69)( 22, 79)( 23, 74)( 24, 68)( 25, 77)
( 26, 71)( 27, 66)( 28, 76)( 29, 73)( 30, 67)( 31, 70)( 32, 80)( 33, 49)
( 34, 59)( 35, 62)( 36, 56)( 37, 53)( 38, 63)( 39, 58)( 40, 52)( 41, 61)
( 42, 55)( 43, 50)( 44, 60)( 45, 57)( 46, 51)( 47, 54)( 48, 64)( 81,161)
( 82,171)( 83,174)( 84,168)( 85,165)( 86,175)( 87,170)( 88,164)( 89,173)
( 90,167)( 91,162)( 92,172)( 93,169)( 94,163)( 95,166)( 96,176)( 97,225)
( 98,235)( 99,238)(100,232)(101,229)(102,239)(103,234)(104,228)(105,237)
(106,231)(107,226)(108,236)(109,233)(110,227)(111,230)(112,240)(113,209)
(114,219)(115,222)(116,216)(117,213)(118,223)(119,218)(120,212)(121,221)
(122,215)(123,210)(124,220)(125,217)(126,211)(127,214)(128,224)(129,193)
(130,203)(131,206)(132,200)(133,197)(134,207)(135,202)(136,196)(137,205)
(138,199)(139,194)(140,204)(141,201)(142,195)(143,198)(144,208)(145,177)
(146,187)(147,190)(148,184)(149,181)(150,191)(151,186)(152,180)(153,189)
(154,183)(155,178)(156,188)(157,185)(158,179)(159,182)(160,192)(242,251)
(243,254)(244,248)(246,255)(247,250)(249,253)(257,305)(258,315)(259,318)
(260,312)(261,309)(262,319)(263,314)(264,308)(265,317)(266,311)(267,306)
(268,316)(269,313)(270,307)(271,310)(272,320)(273,289)(274,299)(275,302)
(276,296)(277,293)(278,303)(279,298)(280,292)(281,301)(282,295)(283,290)
(284,300)(285,297)(286,291)(287,294)(288,304)(321,401)(322,411)(323,414)
(324,408)(325,405)(326,415)(327,410)(328,404)(329,413)(330,407)(331,402)
(332,412)(333,409)(334,403)(335,406)(336,416)(337,465)(338,475)(339,478)
(340,472)(341,469)(342,479)(343,474)(344,468)(345,477)(346,471)(347,466)
(348,476)(349,473)(350,467)(351,470)(352,480)(353,449)(354,459)(355,462)
(356,456)(357,453)(358,463)(359,458)(360,452)(361,461)(362,455)(363,450)
(364,460)(365,457)(366,451)(367,454)(368,464)(369,433)(370,443)(371,446)
(372,440)(373,437)(374,447)(375,442)(376,436)(377,445)(378,439)(379,434)
(380,444)(381,441)(382,435)(383,438)(384,448)(385,417)(386,427)(387,430)
(388,424)(389,421)(390,431)(391,426)(392,420)(393,429)(394,423)(395,418)
(396,428)(397,425)(398,419)(399,422)(400,432);
s1 := Sym(480)!(  1, 97)(  2, 98)(  3,100)(  4, 99)(  5,102)(  6,101)(  7,103)
(  8,104)(  9,112)( 10,111)( 11,109)( 12,110)( 13,107)( 14,108)( 15,106)
( 16,105)( 17, 81)( 18, 82)( 19, 84)( 20, 83)( 21, 86)( 22, 85)( 23, 87)
( 24, 88)( 25, 96)( 26, 95)( 27, 93)( 28, 94)( 29, 91)( 30, 92)( 31, 90)
( 32, 89)( 33,145)( 34,146)( 35,148)( 36,147)( 37,150)( 38,149)( 39,151)
( 40,152)( 41,160)( 42,159)( 43,157)( 44,158)( 45,155)( 46,156)( 47,154)
( 48,153)( 49,129)( 50,130)( 51,132)( 52,131)( 53,134)( 54,133)( 55,135)
( 56,136)( 57,144)( 58,143)( 59,141)( 60,142)( 61,139)( 62,140)( 63,138)
( 64,137)( 65,113)( 66,114)( 67,116)( 68,115)( 69,118)( 70,117)( 71,119)
( 72,120)( 73,128)( 74,127)( 75,125)( 76,126)( 77,123)( 78,124)( 79,122)
( 80,121)(161,177)(162,178)(163,180)(164,179)(165,182)(166,181)(167,183)
(168,184)(169,192)(170,191)(171,189)(172,190)(173,187)(174,188)(175,186)
(176,185)(193,225)(194,226)(195,228)(196,227)(197,230)(198,229)(199,231)
(200,232)(201,240)(202,239)(203,237)(204,238)(205,235)(206,236)(207,234)
(208,233)(211,212)(213,214)(217,224)(218,223)(219,221)(220,222)(241,337)
(242,338)(243,340)(244,339)(245,342)(246,341)(247,343)(248,344)(249,352)
(250,351)(251,349)(252,350)(253,347)(254,348)(255,346)(256,345)(257,321)
(258,322)(259,324)(260,323)(261,326)(262,325)(263,327)(264,328)(265,336)
(266,335)(267,333)(268,334)(269,331)(270,332)(271,330)(272,329)(273,385)
(274,386)(275,388)(276,387)(277,390)(278,389)(279,391)(280,392)(281,400)
(282,399)(283,397)(284,398)(285,395)(286,396)(287,394)(288,393)(289,369)
(290,370)(291,372)(292,371)(293,374)(294,373)(295,375)(296,376)(297,384)
(298,383)(299,381)(300,382)(301,379)(302,380)(303,378)(304,377)(305,353)
(306,354)(307,356)(308,355)(309,358)(310,357)(311,359)(312,360)(313,368)
(314,367)(315,365)(316,366)(317,363)(318,364)(319,362)(320,361)(401,417)
(402,418)(403,420)(404,419)(405,422)(406,421)(407,423)(408,424)(409,432)
(410,431)(411,429)(412,430)(413,427)(414,428)(415,426)(416,425)(433,465)
(434,466)(435,468)(436,467)(437,470)(438,469)(439,471)(440,472)(441,480)
(442,479)(443,477)(444,478)(445,475)(446,476)(447,474)(448,473)(451,452)
(453,454)(457,464)(458,463)(459,461)(460,462);
s2 := Sym(480)!(  1,245)(  2,246)(  3,247)(  4,248)(  5,241)(  6,242)(  7,243)
(  8,244)(  9,253)( 10,254)( 11,255)( 12,256)( 13,249)( 14,250)( 15,251)
( 16,252)( 17,261)( 18,262)( 19,263)( 20,264)( 21,257)( 22,258)( 23,259)
( 24,260)( 25,269)( 26,270)( 27,271)( 28,272)( 29,265)( 30,266)( 31,267)
( 32,268)( 33,277)( 34,278)( 35,279)( 36,280)( 37,273)( 38,274)( 39,275)
( 40,276)( 41,285)( 42,286)( 43,287)( 44,288)( 45,281)( 46,282)( 47,283)
( 48,284)( 49,293)( 50,294)( 51,295)( 52,296)( 53,289)( 54,290)( 55,291)
( 56,292)( 57,301)( 58,302)( 59,303)( 60,304)( 61,297)( 62,298)( 63,299)
( 64,300)( 65,309)( 66,310)( 67,311)( 68,312)( 69,305)( 70,306)( 71,307)
( 72,308)( 73,317)( 74,318)( 75,319)( 76,320)( 77,313)( 78,314)( 79,315)
( 80,316)( 81,325)( 82,326)( 83,327)( 84,328)( 85,321)( 86,322)( 87,323)
( 88,324)( 89,333)( 90,334)( 91,335)( 92,336)( 93,329)( 94,330)( 95,331)
( 96,332)( 97,341)( 98,342)( 99,343)(100,344)(101,337)(102,338)(103,339)
(104,340)(105,349)(106,350)(107,351)(108,352)(109,345)(110,346)(111,347)
(112,348)(113,357)(114,358)(115,359)(116,360)(117,353)(118,354)(119,355)
(120,356)(121,365)(122,366)(123,367)(124,368)(125,361)(126,362)(127,363)
(128,364)(129,373)(130,374)(131,375)(132,376)(133,369)(134,370)(135,371)
(136,372)(137,381)(138,382)(139,383)(140,384)(141,377)(142,378)(143,379)
(144,380)(145,389)(146,390)(147,391)(148,392)(149,385)(150,386)(151,387)
(152,388)(153,397)(154,398)(155,399)(156,400)(157,393)(158,394)(159,395)
(160,396)(161,405)(162,406)(163,407)(164,408)(165,401)(166,402)(167,403)
(168,404)(169,413)(170,414)(171,415)(172,416)(173,409)(174,410)(175,411)
(176,412)(177,421)(178,422)(179,423)(180,424)(181,417)(182,418)(183,419)
(184,420)(185,429)(186,430)(187,431)(188,432)(189,425)(190,426)(191,427)
(192,428)(193,437)(194,438)(195,439)(196,440)(197,433)(198,434)(199,435)
(200,436)(201,445)(202,446)(203,447)(204,448)(205,441)(206,442)(207,443)
(208,444)(209,453)(210,454)(211,455)(212,456)(213,449)(214,450)(215,451)
(216,452)(217,461)(218,462)(219,463)(220,464)(221,457)(222,458)(223,459)
(224,460)(225,469)(226,470)(227,471)(228,472)(229,465)(230,466)(231,467)
(232,468)(233,477)(234,478)(235,479)(236,480)(237,473)(238,474)(239,475)
(240,476);
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, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*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*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