Polytope of Type {2,4,15}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,15}*1920
if this polytope has a name.
Group : SmallGroup(1920,240409)
Rank : 4
Schlafli Type : {2,4,15}
Number of vertices, edges, etc : 2, 32, 240, 120
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
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 : {2,4,15}*960
3-fold quotients : {2,4,5}*640
6-fold quotients : {2,4,5}*320
16-fold quotients : {2,2,15}*120
48-fold quotients : {2,2,5}*40
80-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3,251)( 4,252)( 5,253)( 6,254)( 7,255)( 8,256)( 9,257)( 10,258)
( 11,243)( 12,244)( 13,245)( 14,246)( 15,247)( 16,248)( 17,249)( 18,250)
( 19,267)( 20,268)( 21,269)( 22,270)( 23,271)( 24,272)( 25,273)( 26,274)
( 27,259)( 28,260)( 29,261)( 30,262)( 31,263)( 32,264)( 33,265)( 34,266)
( 35,283)( 36,284)( 37,285)( 38,286)( 39,287)( 40,288)( 41,289)( 42,290)
( 43,275)( 44,276)( 45,277)( 46,278)( 47,279)( 48,280)( 49,281)( 50,282)
( 51,299)( 52,300)( 53,301)( 54,302)( 55,303)( 56,304)( 57,305)( 58,306)
( 59,291)( 60,292)( 61,293)( 62,294)( 63,295)( 64,296)( 65,297)( 66,298)
( 67,315)( 68,316)( 69,317)( 70,318)( 71,319)( 72,320)( 73,321)( 74,322)
( 75,307)( 76,308)( 77,309)( 78,310)( 79,311)( 80,312)( 81,313)( 82,314)
( 83,331)( 84,332)( 85,333)( 86,334)( 87,335)( 88,336)( 89,337)( 90,338)
( 91,323)( 92,324)( 93,325)( 94,326)( 95,327)( 96,328)( 97,329)( 98,330)
( 99,347)(100,348)(101,349)(102,350)(103,351)(104,352)(105,353)(106,354)
(107,339)(108,340)(109,341)(110,342)(111,343)(112,344)(113,345)(114,346)
(115,363)(116,364)(117,365)(118,366)(119,367)(120,368)(121,369)(122,370)
(123,355)(124,356)(125,357)(126,358)(127,359)(128,360)(129,361)(130,362)
(131,379)(132,380)(133,381)(134,382)(135,383)(136,384)(137,385)(138,386)
(139,371)(140,372)(141,373)(142,374)(143,375)(144,376)(145,377)(146,378)
(147,395)(148,396)(149,397)(150,398)(151,399)(152,400)(153,401)(154,402)
(155,387)(156,388)(157,389)(158,390)(159,391)(160,392)(161,393)(162,394)
(163,411)(164,412)(165,413)(166,414)(167,415)(168,416)(169,417)(170,418)
(171,403)(172,404)(173,405)(174,406)(175,407)(176,408)(177,409)(178,410)
(179,427)(180,428)(181,429)(182,430)(183,431)(184,432)(185,433)(186,434)
(187,419)(188,420)(189,421)(190,422)(191,423)(192,424)(193,425)(194,426)
(195,443)(196,444)(197,445)(198,446)(199,447)(200,448)(201,449)(202,450)
(203,435)(204,436)(205,437)(206,438)(207,439)(208,440)(209,441)(210,442)
(211,459)(212,460)(213,461)(214,462)(215,463)(216,464)(217,465)(218,466)
(219,451)(220,452)(221,453)(222,454)(223,455)(224,456)(225,457)(226,458)
(227,475)(228,476)(229,477)(230,478)(231,479)(232,480)(233,481)(234,482)
(235,467)(236,468)(237,469)(238,470)(239,471)(240,472)(241,473)(242,474);;
s2 := ( 4, 13)( 5, 16)( 6, 10)( 8, 17)( 9, 12)( 11, 15)( 19, 67)( 20, 77)
( 21, 80)( 22, 74)( 23, 71)( 24, 81)( 25, 76)( 26, 70)( 27, 79)( 28, 73)
( 29, 68)( 30, 78)( 31, 75)( 32, 69)( 33, 72)( 34, 82)( 35, 51)( 36, 61)
( 37, 64)( 38, 58)( 39, 55)( 40, 65)( 41, 60)( 42, 54)( 43, 63)( 44, 57)
( 45, 52)( 46, 62)( 47, 59)( 48, 53)( 49, 56)( 50, 66)( 83,163)( 84,173)
( 85,176)( 86,170)( 87,167)( 88,177)( 89,172)( 90,166)( 91,175)( 92,169)
( 93,164)( 94,174)( 95,171)( 96,165)( 97,168)( 98,178)( 99,227)(100,237)
(101,240)(102,234)(103,231)(104,241)(105,236)(106,230)(107,239)(108,233)
(109,228)(110,238)(111,235)(112,229)(113,232)(114,242)(115,211)(116,221)
(117,224)(118,218)(119,215)(120,225)(121,220)(122,214)(123,223)(124,217)
(125,212)(126,222)(127,219)(128,213)(129,216)(130,226)(131,195)(132,205)
(133,208)(134,202)(135,199)(136,209)(137,204)(138,198)(139,207)(140,201)
(141,196)(142,206)(143,203)(144,197)(145,200)(146,210)(147,179)(148,189)
(149,192)(150,186)(151,183)(152,193)(153,188)(154,182)(155,191)(156,185)
(157,180)(158,190)(159,187)(160,181)(161,184)(162,194)(244,253)(245,256)
(246,250)(248,257)(249,252)(251,255)(259,307)(260,317)(261,320)(262,314)
(263,311)(264,321)(265,316)(266,310)(267,319)(268,313)(269,308)(270,318)
(271,315)(272,309)(273,312)(274,322)(275,291)(276,301)(277,304)(278,298)
(279,295)(280,305)(281,300)(282,294)(283,303)(284,297)(285,292)(286,302)
(287,299)(288,293)(289,296)(290,306)(323,403)(324,413)(325,416)(326,410)
(327,407)(328,417)(329,412)(330,406)(331,415)(332,409)(333,404)(334,414)
(335,411)(336,405)(337,408)(338,418)(339,467)(340,477)(341,480)(342,474)
(343,471)(344,481)(345,476)(346,470)(347,479)(348,473)(349,468)(350,478)
(351,475)(352,469)(353,472)(354,482)(355,451)(356,461)(357,464)(358,458)
(359,455)(360,465)(361,460)(362,454)(363,463)(364,457)(365,452)(366,462)
(367,459)(368,453)(369,456)(370,466)(371,435)(372,445)(373,448)(374,442)
(375,439)(376,449)(377,444)(378,438)(379,447)(380,441)(381,436)(382,446)
(383,443)(384,437)(385,440)(386,450)(387,419)(388,429)(389,432)(390,426)
(391,423)(392,433)(393,428)(394,422)(395,431)(396,425)(397,420)(398,430)
(399,427)(400,421)(401,424)(402,434);;
s3 := ( 3,115)( 4,127)( 5,122)( 6,126)( 7,124)( 8,120)( 9,129)( 10,117)
( 11,123)( 12,119)( 13,130)( 14,118)( 15,116)( 16,128)( 17,121)( 18,125)
( 19, 99)( 20,111)( 21,106)( 22,110)( 23,108)( 24,104)( 25,113)( 26,101)
( 27,107)( 28,103)( 29,114)( 30,102)( 31,100)( 32,112)( 33,105)( 34,109)
( 35, 83)( 36, 95)( 37, 90)( 38, 94)( 39, 92)( 40, 88)( 41, 97)( 42, 85)
( 43, 91)( 44, 87)( 45, 98)( 46, 86)( 47, 84)( 48, 96)( 49, 89)( 50, 93)
( 51,147)( 52,159)( 53,154)( 54,158)( 55,156)( 56,152)( 57,161)( 58,149)
( 59,155)( 60,151)( 61,162)( 62,150)( 63,148)( 64,160)( 65,153)( 66,157)
( 67,131)( 68,143)( 69,138)( 70,142)( 71,140)( 72,136)( 73,145)( 74,133)
( 75,139)( 76,135)( 77,146)( 78,134)( 79,132)( 80,144)( 81,137)( 82,141)
(163,195)(164,207)(165,202)(166,206)(167,204)(168,200)(169,209)(170,197)
(171,203)(172,199)(173,210)(174,198)(175,196)(176,208)(177,201)(178,205)
(180,191)(181,186)(182,190)(183,188)(185,193)(189,194)(211,227)(212,239)
(213,234)(214,238)(215,236)(216,232)(217,241)(218,229)(219,235)(220,231)
(221,242)(222,230)(223,228)(224,240)(225,233)(226,237)(243,355)(244,367)
(245,362)(246,366)(247,364)(248,360)(249,369)(250,357)(251,363)(252,359)
(253,370)(254,358)(255,356)(256,368)(257,361)(258,365)(259,339)(260,351)
(261,346)(262,350)(263,348)(264,344)(265,353)(266,341)(267,347)(268,343)
(269,354)(270,342)(271,340)(272,352)(273,345)(274,349)(275,323)(276,335)
(277,330)(278,334)(279,332)(280,328)(281,337)(282,325)(283,331)(284,327)
(285,338)(286,326)(287,324)(288,336)(289,329)(290,333)(291,387)(292,399)
(293,394)(294,398)(295,396)(296,392)(297,401)(298,389)(299,395)(300,391)
(301,402)(302,390)(303,388)(304,400)(305,393)(306,397)(307,371)(308,383)
(309,378)(310,382)(311,380)(312,376)(313,385)(314,373)(315,379)(316,375)
(317,386)(318,374)(319,372)(320,384)(321,377)(322,381)(403,435)(404,447)
(405,442)(406,446)(407,444)(408,440)(409,449)(410,437)(411,443)(412,439)
(413,450)(414,438)(415,436)(416,448)(417,441)(418,445)(420,431)(421,426)
(422,430)(423,428)(425,433)(429,434)(451,467)(452,479)(453,474)(454,478)
(455,476)(456,472)(457,481)(458,469)(459,475)(460,471)(461,482)(462,470)
(463,468)(464,480)(465,473)(466,477);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(482)!(1,2);
s1 := Sym(482)!( 3,251)( 4,252)( 5,253)( 6,254)( 7,255)( 8,256)( 9,257)
( 10,258)( 11,243)( 12,244)( 13,245)( 14,246)( 15,247)( 16,248)( 17,249)
( 18,250)( 19,267)( 20,268)( 21,269)( 22,270)( 23,271)( 24,272)( 25,273)
( 26,274)( 27,259)( 28,260)( 29,261)( 30,262)( 31,263)( 32,264)( 33,265)
( 34,266)( 35,283)( 36,284)( 37,285)( 38,286)( 39,287)( 40,288)( 41,289)
( 42,290)( 43,275)( 44,276)( 45,277)( 46,278)( 47,279)( 48,280)( 49,281)
( 50,282)( 51,299)( 52,300)( 53,301)( 54,302)( 55,303)( 56,304)( 57,305)
( 58,306)( 59,291)( 60,292)( 61,293)( 62,294)( 63,295)( 64,296)( 65,297)
( 66,298)( 67,315)( 68,316)( 69,317)( 70,318)( 71,319)( 72,320)( 73,321)
( 74,322)( 75,307)( 76,308)( 77,309)( 78,310)( 79,311)( 80,312)( 81,313)
( 82,314)( 83,331)( 84,332)( 85,333)( 86,334)( 87,335)( 88,336)( 89,337)
( 90,338)( 91,323)( 92,324)( 93,325)( 94,326)( 95,327)( 96,328)( 97,329)
( 98,330)( 99,347)(100,348)(101,349)(102,350)(103,351)(104,352)(105,353)
(106,354)(107,339)(108,340)(109,341)(110,342)(111,343)(112,344)(113,345)
(114,346)(115,363)(116,364)(117,365)(118,366)(119,367)(120,368)(121,369)
(122,370)(123,355)(124,356)(125,357)(126,358)(127,359)(128,360)(129,361)
(130,362)(131,379)(132,380)(133,381)(134,382)(135,383)(136,384)(137,385)
(138,386)(139,371)(140,372)(141,373)(142,374)(143,375)(144,376)(145,377)
(146,378)(147,395)(148,396)(149,397)(150,398)(151,399)(152,400)(153,401)
(154,402)(155,387)(156,388)(157,389)(158,390)(159,391)(160,392)(161,393)
(162,394)(163,411)(164,412)(165,413)(166,414)(167,415)(168,416)(169,417)
(170,418)(171,403)(172,404)(173,405)(174,406)(175,407)(176,408)(177,409)
(178,410)(179,427)(180,428)(181,429)(182,430)(183,431)(184,432)(185,433)
(186,434)(187,419)(188,420)(189,421)(190,422)(191,423)(192,424)(193,425)
(194,426)(195,443)(196,444)(197,445)(198,446)(199,447)(200,448)(201,449)
(202,450)(203,435)(204,436)(205,437)(206,438)(207,439)(208,440)(209,441)
(210,442)(211,459)(212,460)(213,461)(214,462)(215,463)(216,464)(217,465)
(218,466)(219,451)(220,452)(221,453)(222,454)(223,455)(224,456)(225,457)
(226,458)(227,475)(228,476)(229,477)(230,478)(231,479)(232,480)(233,481)
(234,482)(235,467)(236,468)(237,469)(238,470)(239,471)(240,472)(241,473)
(242,474);
s2 := Sym(482)!( 4, 13)( 5, 16)( 6, 10)( 8, 17)( 9, 12)( 11, 15)( 19, 67)
( 20, 77)( 21, 80)( 22, 74)( 23, 71)( 24, 81)( 25, 76)( 26, 70)( 27, 79)
( 28, 73)( 29, 68)( 30, 78)( 31, 75)( 32, 69)( 33, 72)( 34, 82)( 35, 51)
( 36, 61)( 37, 64)( 38, 58)( 39, 55)( 40, 65)( 41, 60)( 42, 54)( 43, 63)
( 44, 57)( 45, 52)( 46, 62)( 47, 59)( 48, 53)( 49, 56)( 50, 66)( 83,163)
( 84,173)( 85,176)( 86,170)( 87,167)( 88,177)( 89,172)( 90,166)( 91,175)
( 92,169)( 93,164)( 94,174)( 95,171)( 96,165)( 97,168)( 98,178)( 99,227)
(100,237)(101,240)(102,234)(103,231)(104,241)(105,236)(106,230)(107,239)
(108,233)(109,228)(110,238)(111,235)(112,229)(113,232)(114,242)(115,211)
(116,221)(117,224)(118,218)(119,215)(120,225)(121,220)(122,214)(123,223)
(124,217)(125,212)(126,222)(127,219)(128,213)(129,216)(130,226)(131,195)
(132,205)(133,208)(134,202)(135,199)(136,209)(137,204)(138,198)(139,207)
(140,201)(141,196)(142,206)(143,203)(144,197)(145,200)(146,210)(147,179)
(148,189)(149,192)(150,186)(151,183)(152,193)(153,188)(154,182)(155,191)
(156,185)(157,180)(158,190)(159,187)(160,181)(161,184)(162,194)(244,253)
(245,256)(246,250)(248,257)(249,252)(251,255)(259,307)(260,317)(261,320)
(262,314)(263,311)(264,321)(265,316)(266,310)(267,319)(268,313)(269,308)
(270,318)(271,315)(272,309)(273,312)(274,322)(275,291)(276,301)(277,304)
(278,298)(279,295)(280,305)(281,300)(282,294)(283,303)(284,297)(285,292)
(286,302)(287,299)(288,293)(289,296)(290,306)(323,403)(324,413)(325,416)
(326,410)(327,407)(328,417)(329,412)(330,406)(331,415)(332,409)(333,404)
(334,414)(335,411)(336,405)(337,408)(338,418)(339,467)(340,477)(341,480)
(342,474)(343,471)(344,481)(345,476)(346,470)(347,479)(348,473)(349,468)
(350,478)(351,475)(352,469)(353,472)(354,482)(355,451)(356,461)(357,464)
(358,458)(359,455)(360,465)(361,460)(362,454)(363,463)(364,457)(365,452)
(366,462)(367,459)(368,453)(369,456)(370,466)(371,435)(372,445)(373,448)
(374,442)(375,439)(376,449)(377,444)(378,438)(379,447)(380,441)(381,436)
(382,446)(383,443)(384,437)(385,440)(386,450)(387,419)(388,429)(389,432)
(390,426)(391,423)(392,433)(393,428)(394,422)(395,431)(396,425)(397,420)
(398,430)(399,427)(400,421)(401,424)(402,434);
s3 := Sym(482)!( 3,115)( 4,127)( 5,122)( 6,126)( 7,124)( 8,120)( 9,129)
( 10,117)( 11,123)( 12,119)( 13,130)( 14,118)( 15,116)( 16,128)( 17,121)
( 18,125)( 19, 99)( 20,111)( 21,106)( 22,110)( 23,108)( 24,104)( 25,113)
( 26,101)( 27,107)( 28,103)( 29,114)( 30,102)( 31,100)( 32,112)( 33,105)
( 34,109)( 35, 83)( 36, 95)( 37, 90)( 38, 94)( 39, 92)( 40, 88)( 41, 97)
( 42, 85)( 43, 91)( 44, 87)( 45, 98)( 46, 86)( 47, 84)( 48, 96)( 49, 89)
( 50, 93)( 51,147)( 52,159)( 53,154)( 54,158)( 55,156)( 56,152)( 57,161)
( 58,149)( 59,155)( 60,151)( 61,162)( 62,150)( 63,148)( 64,160)( 65,153)
( 66,157)( 67,131)( 68,143)( 69,138)( 70,142)( 71,140)( 72,136)( 73,145)
( 74,133)( 75,139)( 76,135)( 77,146)( 78,134)( 79,132)( 80,144)( 81,137)
( 82,141)(163,195)(164,207)(165,202)(166,206)(167,204)(168,200)(169,209)
(170,197)(171,203)(172,199)(173,210)(174,198)(175,196)(176,208)(177,201)
(178,205)(180,191)(181,186)(182,190)(183,188)(185,193)(189,194)(211,227)
(212,239)(213,234)(214,238)(215,236)(216,232)(217,241)(218,229)(219,235)
(220,231)(221,242)(222,230)(223,228)(224,240)(225,233)(226,237)(243,355)
(244,367)(245,362)(246,366)(247,364)(248,360)(249,369)(250,357)(251,363)
(252,359)(253,370)(254,358)(255,356)(256,368)(257,361)(258,365)(259,339)
(260,351)(261,346)(262,350)(263,348)(264,344)(265,353)(266,341)(267,347)
(268,343)(269,354)(270,342)(271,340)(272,352)(273,345)(274,349)(275,323)
(276,335)(277,330)(278,334)(279,332)(280,328)(281,337)(282,325)(283,331)
(284,327)(285,338)(286,326)(287,324)(288,336)(289,329)(290,333)(291,387)
(292,399)(293,394)(294,398)(295,396)(296,392)(297,401)(298,389)(299,395)
(300,391)(301,402)(302,390)(303,388)(304,400)(305,393)(306,397)(307,371)
(308,383)(309,378)(310,382)(311,380)(312,376)(313,385)(314,373)(315,379)
(316,375)(317,386)(318,374)(319,372)(320,384)(321,377)(322,381)(403,435)
(404,447)(405,442)(406,446)(407,444)(408,440)(409,449)(410,437)(411,443)
(412,439)(413,450)(414,438)(415,436)(416,448)(417,441)(418,445)(420,431)
(421,426)(422,430)(423,428)(425,433)(429,434)(451,467)(452,479)(453,474)
(454,478)(455,476)(456,472)(457,481)(458,469)(459,475)(460,471)(461,482)
(462,470)(463,468)(464,480)(465,473)(466,477);
poly := sub<Sym(482)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope