Polytope of Type {4,15,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,15,2}*1920
if this polytope has a name.
Group : SmallGroup(1920,240409)
Rank : 4
Schlafli Type : {4,15,2}
Number of vertices, edges, etc : 32, 240, 120, 2
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 : {4,15,2}*960
3-fold quotients : {4,5,2}*640
6-fold quotients : {4,5,2}*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 := ( 1,249)( 2,250)( 3,251)( 4,252)( 5,253)( 6,254)( 7,255)( 8,256)
( 9,241)( 10,242)( 11,243)( 12,244)( 13,245)( 14,246)( 15,247)( 16,248)
( 17,265)( 18,266)( 19,267)( 20,268)( 21,269)( 22,270)( 23,271)( 24,272)
( 25,257)( 26,258)( 27,259)( 28,260)( 29,261)( 30,262)( 31,263)( 32,264)
( 33,281)( 34,282)( 35,283)( 36,284)( 37,285)( 38,286)( 39,287)( 40,288)
( 41,273)( 42,274)( 43,275)( 44,276)( 45,277)( 46,278)( 47,279)( 48,280)
( 49,297)( 50,298)( 51,299)( 52,300)( 53,301)( 54,302)( 55,303)( 56,304)
( 57,289)( 58,290)( 59,291)( 60,292)( 61,293)( 62,294)( 63,295)( 64,296)
( 65,313)( 66,314)( 67,315)( 68,316)( 69,317)( 70,318)( 71,319)( 72,320)
( 73,305)( 74,306)( 75,307)( 76,308)( 77,309)( 78,310)( 79,311)( 80,312)
( 81,329)( 82,330)( 83,331)( 84,332)( 85,333)( 86,334)( 87,335)( 88,336)
( 89,321)( 90,322)( 91,323)( 92,324)( 93,325)( 94,326)( 95,327)( 96,328)
( 97,345)( 98,346)( 99,347)(100,348)(101,349)(102,350)(103,351)(104,352)
(105,337)(106,338)(107,339)(108,340)(109,341)(110,342)(111,343)(112,344)
(113,361)(114,362)(115,363)(116,364)(117,365)(118,366)(119,367)(120,368)
(121,353)(122,354)(123,355)(124,356)(125,357)(126,358)(127,359)(128,360)
(129,377)(130,378)(131,379)(132,380)(133,381)(134,382)(135,383)(136,384)
(137,369)(138,370)(139,371)(140,372)(141,373)(142,374)(143,375)(144,376)
(145,393)(146,394)(147,395)(148,396)(149,397)(150,398)(151,399)(152,400)
(153,385)(154,386)(155,387)(156,388)(157,389)(158,390)(159,391)(160,392)
(161,409)(162,410)(163,411)(164,412)(165,413)(166,414)(167,415)(168,416)
(169,401)(170,402)(171,403)(172,404)(173,405)(174,406)(175,407)(176,408)
(177,425)(178,426)(179,427)(180,428)(181,429)(182,430)(183,431)(184,432)
(185,417)(186,418)(187,419)(188,420)(189,421)(190,422)(191,423)(192,424)
(193,441)(194,442)(195,443)(196,444)(197,445)(198,446)(199,447)(200,448)
(201,433)(202,434)(203,435)(204,436)(205,437)(206,438)(207,439)(208,440)
(209,457)(210,458)(211,459)(212,460)(213,461)(214,462)(215,463)(216,464)
(217,449)(218,450)(219,451)(220,452)(221,453)(222,454)(223,455)(224,456)
(225,473)(226,474)(227,475)(228,476)(229,477)(230,478)(231,479)(232,480)
(233,465)(234,466)(235,467)(236,468)(237,469)(238,470)(239,471)(240,472);;
s1 := ( 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);;
s2 := ( 1,113)( 2,125)( 3,120)( 4,124)( 5,122)( 6,118)( 7,127)( 8,115)
( 9,121)( 10,117)( 11,128)( 12,116)( 13,114)( 14,126)( 15,119)( 16,123)
( 17, 97)( 18,109)( 19,104)( 20,108)( 21,106)( 22,102)( 23,111)( 24, 99)
( 25,105)( 26,101)( 27,112)( 28,100)( 29, 98)( 30,110)( 31,103)( 32,107)
( 33, 81)( 34, 93)( 35, 88)( 36, 92)( 37, 90)( 38, 86)( 39, 95)( 40, 83)
( 41, 89)( 42, 85)( 43, 96)( 44, 84)( 45, 82)( 46, 94)( 47, 87)( 48, 91)
( 49,145)( 50,157)( 51,152)( 52,156)( 53,154)( 54,150)( 55,159)( 56,147)
( 57,153)( 58,149)( 59,160)( 60,148)( 61,146)( 62,158)( 63,151)( 64,155)
( 65,129)( 66,141)( 67,136)( 68,140)( 69,138)( 70,134)( 71,143)( 72,131)
( 73,137)( 74,133)( 75,144)( 76,132)( 77,130)( 78,142)( 79,135)( 80,139)
(161,193)(162,205)(163,200)(164,204)(165,202)(166,198)(167,207)(168,195)
(169,201)(170,197)(171,208)(172,196)(173,194)(174,206)(175,199)(176,203)
(178,189)(179,184)(180,188)(181,186)(183,191)(187,192)(209,225)(210,237)
(211,232)(212,236)(213,234)(214,230)(215,239)(216,227)(217,233)(218,229)
(219,240)(220,228)(221,226)(222,238)(223,231)(224,235)(241,353)(242,365)
(243,360)(244,364)(245,362)(246,358)(247,367)(248,355)(249,361)(250,357)
(251,368)(252,356)(253,354)(254,366)(255,359)(256,363)(257,337)(258,349)
(259,344)(260,348)(261,346)(262,342)(263,351)(264,339)(265,345)(266,341)
(267,352)(268,340)(269,338)(270,350)(271,343)(272,347)(273,321)(274,333)
(275,328)(276,332)(277,330)(278,326)(279,335)(280,323)(281,329)(282,325)
(283,336)(284,324)(285,322)(286,334)(287,327)(288,331)(289,385)(290,397)
(291,392)(292,396)(293,394)(294,390)(295,399)(296,387)(297,393)(298,389)
(299,400)(300,388)(301,386)(302,398)(303,391)(304,395)(305,369)(306,381)
(307,376)(308,380)(309,378)(310,374)(311,383)(312,371)(313,377)(314,373)
(315,384)(316,372)(317,370)(318,382)(319,375)(320,379)(401,433)(402,445)
(403,440)(404,444)(405,442)(406,438)(407,447)(408,435)(409,441)(410,437)
(411,448)(412,436)(413,434)(414,446)(415,439)(416,443)(418,429)(419,424)
(420,428)(421,426)(423,431)(427,432)(449,465)(450,477)(451,472)(452,476)
(453,474)(454,470)(455,479)(456,467)(457,473)(458,469)(459,480)(460,468)
(461,466)(462,478)(463,471)(464,475);;
s3 := (481,482);;
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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1,
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)!( 1,249)( 2,250)( 3,251)( 4,252)( 5,253)( 6,254)( 7,255)
( 8,256)( 9,241)( 10,242)( 11,243)( 12,244)( 13,245)( 14,246)( 15,247)
( 16,248)( 17,265)( 18,266)( 19,267)( 20,268)( 21,269)( 22,270)( 23,271)
( 24,272)( 25,257)( 26,258)( 27,259)( 28,260)( 29,261)( 30,262)( 31,263)
( 32,264)( 33,281)( 34,282)( 35,283)( 36,284)( 37,285)( 38,286)( 39,287)
( 40,288)( 41,273)( 42,274)( 43,275)( 44,276)( 45,277)( 46,278)( 47,279)
( 48,280)( 49,297)( 50,298)( 51,299)( 52,300)( 53,301)( 54,302)( 55,303)
( 56,304)( 57,289)( 58,290)( 59,291)( 60,292)( 61,293)( 62,294)( 63,295)
( 64,296)( 65,313)( 66,314)( 67,315)( 68,316)( 69,317)( 70,318)( 71,319)
( 72,320)( 73,305)( 74,306)( 75,307)( 76,308)( 77,309)( 78,310)( 79,311)
( 80,312)( 81,329)( 82,330)( 83,331)( 84,332)( 85,333)( 86,334)( 87,335)
( 88,336)( 89,321)( 90,322)( 91,323)( 92,324)( 93,325)( 94,326)( 95,327)
( 96,328)( 97,345)( 98,346)( 99,347)(100,348)(101,349)(102,350)(103,351)
(104,352)(105,337)(106,338)(107,339)(108,340)(109,341)(110,342)(111,343)
(112,344)(113,361)(114,362)(115,363)(116,364)(117,365)(118,366)(119,367)
(120,368)(121,353)(122,354)(123,355)(124,356)(125,357)(126,358)(127,359)
(128,360)(129,377)(130,378)(131,379)(132,380)(133,381)(134,382)(135,383)
(136,384)(137,369)(138,370)(139,371)(140,372)(141,373)(142,374)(143,375)
(144,376)(145,393)(146,394)(147,395)(148,396)(149,397)(150,398)(151,399)
(152,400)(153,385)(154,386)(155,387)(156,388)(157,389)(158,390)(159,391)
(160,392)(161,409)(162,410)(163,411)(164,412)(165,413)(166,414)(167,415)
(168,416)(169,401)(170,402)(171,403)(172,404)(173,405)(174,406)(175,407)
(176,408)(177,425)(178,426)(179,427)(180,428)(181,429)(182,430)(183,431)
(184,432)(185,417)(186,418)(187,419)(188,420)(189,421)(190,422)(191,423)
(192,424)(193,441)(194,442)(195,443)(196,444)(197,445)(198,446)(199,447)
(200,448)(201,433)(202,434)(203,435)(204,436)(205,437)(206,438)(207,439)
(208,440)(209,457)(210,458)(211,459)(212,460)(213,461)(214,462)(215,463)
(216,464)(217,449)(218,450)(219,451)(220,452)(221,453)(222,454)(223,455)
(224,456)(225,473)(226,474)(227,475)(228,476)(229,477)(230,478)(231,479)
(232,480)(233,465)(234,466)(235,467)(236,468)(237,469)(238,470)(239,471)
(240,472);
s1 := Sym(482)!( 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);
s2 := Sym(482)!( 1,113)( 2,125)( 3,120)( 4,124)( 5,122)( 6,118)( 7,127)
( 8,115)( 9,121)( 10,117)( 11,128)( 12,116)( 13,114)( 14,126)( 15,119)
( 16,123)( 17, 97)( 18,109)( 19,104)( 20,108)( 21,106)( 22,102)( 23,111)
( 24, 99)( 25,105)( 26,101)( 27,112)( 28,100)( 29, 98)( 30,110)( 31,103)
( 32,107)( 33, 81)( 34, 93)( 35, 88)( 36, 92)( 37, 90)( 38, 86)( 39, 95)
( 40, 83)( 41, 89)( 42, 85)( 43, 96)( 44, 84)( 45, 82)( 46, 94)( 47, 87)
( 48, 91)( 49,145)( 50,157)( 51,152)( 52,156)( 53,154)( 54,150)( 55,159)
( 56,147)( 57,153)( 58,149)( 59,160)( 60,148)( 61,146)( 62,158)( 63,151)
( 64,155)( 65,129)( 66,141)( 67,136)( 68,140)( 69,138)( 70,134)( 71,143)
( 72,131)( 73,137)( 74,133)( 75,144)( 76,132)( 77,130)( 78,142)( 79,135)
( 80,139)(161,193)(162,205)(163,200)(164,204)(165,202)(166,198)(167,207)
(168,195)(169,201)(170,197)(171,208)(172,196)(173,194)(174,206)(175,199)
(176,203)(178,189)(179,184)(180,188)(181,186)(183,191)(187,192)(209,225)
(210,237)(211,232)(212,236)(213,234)(214,230)(215,239)(216,227)(217,233)
(218,229)(219,240)(220,228)(221,226)(222,238)(223,231)(224,235)(241,353)
(242,365)(243,360)(244,364)(245,362)(246,358)(247,367)(248,355)(249,361)
(250,357)(251,368)(252,356)(253,354)(254,366)(255,359)(256,363)(257,337)
(258,349)(259,344)(260,348)(261,346)(262,342)(263,351)(264,339)(265,345)
(266,341)(267,352)(268,340)(269,338)(270,350)(271,343)(272,347)(273,321)
(274,333)(275,328)(276,332)(277,330)(278,326)(279,335)(280,323)(281,329)
(282,325)(283,336)(284,324)(285,322)(286,334)(287,327)(288,331)(289,385)
(290,397)(291,392)(292,396)(293,394)(294,390)(295,399)(296,387)(297,393)
(298,389)(299,400)(300,388)(301,386)(302,398)(303,391)(304,395)(305,369)
(306,381)(307,376)(308,380)(309,378)(310,374)(311,383)(312,371)(313,377)
(314,373)(315,384)(316,372)(317,370)(318,382)(319,375)(320,379)(401,433)
(402,445)(403,440)(404,444)(405,442)(406,438)(407,447)(408,435)(409,441)
(410,437)(411,448)(412,436)(413,434)(414,446)(415,439)(416,443)(418,429)
(419,424)(420,428)(421,426)(423,431)(427,432)(449,465)(450,477)(451,472)
(452,476)(453,474)(454,470)(455,479)(456,467)(457,473)(458,469)(459,480)
(460,468)(461,466)(462,478)(463,471)(464,475);
s3 := Sym(482)!(481,482);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1,
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