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