Polytope of Type {2,15,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,15,12}*960
if this polytope has a name.
Group : SmallGroup(960,10958)
Rank : 4
Schlafli Type : {2,15,12}
Number of vertices, edges, etc : 2, 20, 120, 16
Order of s0s1s2s3 : 40
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,15,12,2} of size 1920
Vertex Figure Of :
{2,2,15,12} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,15,6}*480
5-fold quotients : {2,3,12}*192
10-fold quotients : {2,3,6}*96
20-fold quotients : {2,3,3}*48
24-fold quotients : {2,5,2}*40
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,30,12}*1920a
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3,363)( 4,364)( 5,367)( 6,368)( 7,365)( 8,366)( 9,370)( 10,369)
( 11,395)( 12,396)( 13,399)( 14,400)( 15,397)( 16,398)( 17,402)( 18,401)
( 19,387)( 20,388)( 21,391)( 22,392)( 23,389)( 24,390)( 25,394)( 26,393)
( 27,379)( 28,380)( 29,383)( 30,384)( 31,381)( 32,382)( 33,386)( 34,385)
( 35,371)( 36,372)( 37,375)( 38,376)( 39,373)( 40,374)( 41,378)( 42,377)
( 43,443)( 44,444)( 45,447)( 46,448)( 47,445)( 48,446)( 49,450)( 50,449)
( 51,475)( 52,476)( 53,479)( 54,480)( 55,477)( 56,478)( 57,482)( 58,481)
( 59,467)( 60,468)( 61,471)( 62,472)( 63,469)( 64,470)( 65,474)( 66,473)
( 67,459)( 68,460)( 69,463)( 70,464)( 71,461)( 72,462)( 73,466)( 74,465)
( 75,451)( 76,452)( 77,455)( 78,456)( 79,453)( 80,454)( 81,458)( 82,457)
( 83,403)( 84,404)( 85,407)( 86,408)( 87,405)( 88,406)( 89,410)( 90,409)
( 91,435)( 92,436)( 93,439)( 94,440)( 95,437)( 96,438)( 97,442)( 98,441)
( 99,427)(100,428)(101,431)(102,432)(103,429)(104,430)(105,434)(106,433)
(107,419)(108,420)(109,423)(110,424)(111,421)(112,422)(113,426)(114,425)
(115,411)(116,412)(117,415)(118,416)(119,413)(120,414)(121,418)(122,417)
(123,244)(124,243)(125,248)(126,247)(127,246)(128,245)(129,249)(130,250)
(131,276)(132,275)(133,280)(134,279)(135,278)(136,277)(137,281)(138,282)
(139,268)(140,267)(141,272)(142,271)(143,270)(144,269)(145,273)(146,274)
(147,260)(148,259)(149,264)(150,263)(151,262)(152,261)(153,265)(154,266)
(155,252)(156,251)(157,256)(158,255)(159,254)(160,253)(161,257)(162,258)
(163,324)(164,323)(165,328)(166,327)(167,326)(168,325)(169,329)(170,330)
(171,356)(172,355)(173,360)(174,359)(175,358)(176,357)(177,361)(178,362)
(179,348)(180,347)(181,352)(182,351)(183,350)(184,349)(185,353)(186,354)
(187,340)(188,339)(189,344)(190,343)(191,342)(192,341)(193,345)(194,346)
(195,332)(196,331)(197,336)(198,335)(199,334)(200,333)(201,337)(202,338)
(203,284)(204,283)(205,288)(206,287)(207,286)(208,285)(209,289)(210,290)
(211,316)(212,315)(213,320)(214,319)(215,318)(216,317)(217,321)(218,322)
(219,308)(220,307)(221,312)(222,311)(223,310)(224,309)(225,313)(226,314)
(227,300)(228,299)(229,304)(230,303)(231,302)(232,301)(233,305)(234,306)
(235,292)(236,291)(237,296)(238,295)(239,294)(240,293)(241,297)(242,298);;
s2 := ( 3,411)( 4,412)( 5,414)( 6,413)( 7,417)( 8,418)( 9,415)( 10,416)
( 11,403)( 12,404)( 13,406)( 14,405)( 15,409)( 16,410)( 17,407)( 18,408)
( 19,435)( 20,436)( 21,438)( 22,437)( 23,441)( 24,442)( 25,439)( 26,440)
( 27,427)( 28,428)( 29,430)( 30,429)( 31,433)( 32,434)( 33,431)( 34,432)
( 35,419)( 36,420)( 37,422)( 38,421)( 39,425)( 40,426)( 41,423)( 42,424)
( 43,371)( 44,372)( 45,374)( 46,373)( 47,377)( 48,378)( 49,375)( 50,376)
( 51,363)( 52,364)( 53,366)( 54,365)( 55,369)( 56,370)( 57,367)( 58,368)
( 59,395)( 60,396)( 61,398)( 62,397)( 63,401)( 64,402)( 65,399)( 66,400)
( 67,387)( 68,388)( 69,390)( 70,389)( 71,393)( 72,394)( 73,391)( 74,392)
( 75,379)( 76,380)( 77,382)( 78,381)( 79,385)( 80,386)( 81,383)( 82,384)
( 83,451)( 84,452)( 85,454)( 86,453)( 87,457)( 88,458)( 89,455)( 90,456)
( 91,443)( 92,444)( 93,446)( 94,445)( 95,449)( 96,450)( 97,447)( 98,448)
( 99,475)(100,476)(101,478)(102,477)(103,481)(104,482)(105,479)(106,480)
(107,467)(108,468)(109,470)(110,469)(111,473)(112,474)(113,471)(114,472)
(115,459)(116,460)(117,462)(118,461)(119,465)(120,466)(121,463)(122,464)
(123,292)(124,291)(125,293)(126,294)(127,298)(128,297)(129,296)(130,295)
(131,284)(132,283)(133,285)(134,286)(135,290)(136,289)(137,288)(138,287)
(139,316)(140,315)(141,317)(142,318)(143,322)(144,321)(145,320)(146,319)
(147,308)(148,307)(149,309)(150,310)(151,314)(152,313)(153,312)(154,311)
(155,300)(156,299)(157,301)(158,302)(159,306)(160,305)(161,304)(162,303)
(163,252)(164,251)(165,253)(166,254)(167,258)(168,257)(169,256)(170,255)
(171,244)(172,243)(173,245)(174,246)(175,250)(176,249)(177,248)(178,247)
(179,276)(180,275)(181,277)(182,278)(183,282)(184,281)(185,280)(186,279)
(187,268)(188,267)(189,269)(190,270)(191,274)(192,273)(193,272)(194,271)
(195,260)(196,259)(197,261)(198,262)(199,266)(200,265)(201,264)(202,263)
(203,332)(204,331)(205,333)(206,334)(207,338)(208,337)(209,336)(210,335)
(211,324)(212,323)(213,325)(214,326)(215,330)(216,329)(217,328)(218,327)
(219,356)(220,355)(221,357)(222,358)(223,362)(224,361)(225,360)(226,359)
(227,348)(228,347)(229,349)(230,350)(231,354)(232,353)(233,352)(234,351)
(235,340)(236,339)(237,341)(238,342)(239,346)(240,345)(241,344)(242,343);;
s3 := ( 3,129)( 4,130)( 5,126)( 6,125)( 7,127)( 8,128)( 9,123)( 10,124)
( 11,137)( 12,138)( 13,134)( 14,133)( 15,135)( 16,136)( 17,131)( 18,132)
( 19,145)( 20,146)( 21,142)( 22,141)( 23,143)( 24,144)( 25,139)( 26,140)
( 27,153)( 28,154)( 29,150)( 30,149)( 31,151)( 32,152)( 33,147)( 34,148)
( 35,161)( 36,162)( 37,158)( 38,157)( 39,159)( 40,160)( 41,155)( 42,156)
( 43,209)( 44,210)( 45,206)( 46,205)( 47,207)( 48,208)( 49,203)( 50,204)
( 51,217)( 52,218)( 53,214)( 54,213)( 55,215)( 56,216)( 57,211)( 58,212)
( 59,225)( 60,226)( 61,222)( 62,221)( 63,223)( 64,224)( 65,219)( 66,220)
( 67,233)( 68,234)( 69,230)( 70,229)( 71,231)( 72,232)( 73,227)( 74,228)
( 75,241)( 76,242)( 77,238)( 78,237)( 79,239)( 80,240)( 81,235)( 82,236)
( 83,169)( 84,170)( 85,166)( 86,165)( 87,167)( 88,168)( 89,163)( 90,164)
( 91,177)( 92,178)( 93,174)( 94,173)( 95,175)( 96,176)( 97,171)( 98,172)
( 99,185)(100,186)(101,182)(102,181)(103,183)(104,184)(105,179)(106,180)
(107,193)(108,194)(109,190)(110,189)(111,191)(112,192)(113,187)(114,188)
(115,201)(116,202)(117,198)(118,197)(119,199)(120,200)(121,195)(122,196)
(243,369)(244,370)(245,366)(246,365)(247,367)(248,368)(249,363)(250,364)
(251,377)(252,378)(253,374)(254,373)(255,375)(256,376)(257,371)(258,372)
(259,385)(260,386)(261,382)(262,381)(263,383)(264,384)(265,379)(266,380)
(267,393)(268,394)(269,390)(270,389)(271,391)(272,392)(273,387)(274,388)
(275,401)(276,402)(277,398)(278,397)(279,399)(280,400)(281,395)(282,396)
(283,449)(284,450)(285,446)(286,445)(287,447)(288,448)(289,443)(290,444)
(291,457)(292,458)(293,454)(294,453)(295,455)(296,456)(297,451)(298,452)
(299,465)(300,466)(301,462)(302,461)(303,463)(304,464)(305,459)(306,460)
(307,473)(308,474)(309,470)(310,469)(311,471)(312,472)(313,467)(314,468)
(315,481)(316,482)(317,478)(318,477)(319,479)(320,480)(321,475)(322,476)
(323,409)(324,410)(325,406)(326,405)(327,407)(328,408)(329,403)(330,404)
(331,417)(332,418)(333,414)(334,413)(335,415)(336,416)(337,411)(338,412)
(339,425)(340,426)(341,422)(342,421)(343,423)(344,424)(345,419)(346,420)
(347,433)(348,434)(349,430)(350,429)(351,431)(352,432)(353,427)(354,428)
(355,441)(356,442)(357,438)(358,437)(359,439)(360,440)(361,435)(362,436);;
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*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s3*s1*s2*s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(482)!(1,2);
s1 := Sym(482)!( 3,363)( 4,364)( 5,367)( 6,368)( 7,365)( 8,366)( 9,370)
( 10,369)( 11,395)( 12,396)( 13,399)( 14,400)( 15,397)( 16,398)( 17,402)
( 18,401)( 19,387)( 20,388)( 21,391)( 22,392)( 23,389)( 24,390)( 25,394)
( 26,393)( 27,379)( 28,380)( 29,383)( 30,384)( 31,381)( 32,382)( 33,386)
( 34,385)( 35,371)( 36,372)( 37,375)( 38,376)( 39,373)( 40,374)( 41,378)
( 42,377)( 43,443)( 44,444)( 45,447)( 46,448)( 47,445)( 48,446)( 49,450)
( 50,449)( 51,475)( 52,476)( 53,479)( 54,480)( 55,477)( 56,478)( 57,482)
( 58,481)( 59,467)( 60,468)( 61,471)( 62,472)( 63,469)( 64,470)( 65,474)
( 66,473)( 67,459)( 68,460)( 69,463)( 70,464)( 71,461)( 72,462)( 73,466)
( 74,465)( 75,451)( 76,452)( 77,455)( 78,456)( 79,453)( 80,454)( 81,458)
( 82,457)( 83,403)( 84,404)( 85,407)( 86,408)( 87,405)( 88,406)( 89,410)
( 90,409)( 91,435)( 92,436)( 93,439)( 94,440)( 95,437)( 96,438)( 97,442)
( 98,441)( 99,427)(100,428)(101,431)(102,432)(103,429)(104,430)(105,434)
(106,433)(107,419)(108,420)(109,423)(110,424)(111,421)(112,422)(113,426)
(114,425)(115,411)(116,412)(117,415)(118,416)(119,413)(120,414)(121,418)
(122,417)(123,244)(124,243)(125,248)(126,247)(127,246)(128,245)(129,249)
(130,250)(131,276)(132,275)(133,280)(134,279)(135,278)(136,277)(137,281)
(138,282)(139,268)(140,267)(141,272)(142,271)(143,270)(144,269)(145,273)
(146,274)(147,260)(148,259)(149,264)(150,263)(151,262)(152,261)(153,265)
(154,266)(155,252)(156,251)(157,256)(158,255)(159,254)(160,253)(161,257)
(162,258)(163,324)(164,323)(165,328)(166,327)(167,326)(168,325)(169,329)
(170,330)(171,356)(172,355)(173,360)(174,359)(175,358)(176,357)(177,361)
(178,362)(179,348)(180,347)(181,352)(182,351)(183,350)(184,349)(185,353)
(186,354)(187,340)(188,339)(189,344)(190,343)(191,342)(192,341)(193,345)
(194,346)(195,332)(196,331)(197,336)(198,335)(199,334)(200,333)(201,337)
(202,338)(203,284)(204,283)(205,288)(206,287)(207,286)(208,285)(209,289)
(210,290)(211,316)(212,315)(213,320)(214,319)(215,318)(216,317)(217,321)
(218,322)(219,308)(220,307)(221,312)(222,311)(223,310)(224,309)(225,313)
(226,314)(227,300)(228,299)(229,304)(230,303)(231,302)(232,301)(233,305)
(234,306)(235,292)(236,291)(237,296)(238,295)(239,294)(240,293)(241,297)
(242,298);
s2 := Sym(482)!( 3,411)( 4,412)( 5,414)( 6,413)( 7,417)( 8,418)( 9,415)
( 10,416)( 11,403)( 12,404)( 13,406)( 14,405)( 15,409)( 16,410)( 17,407)
( 18,408)( 19,435)( 20,436)( 21,438)( 22,437)( 23,441)( 24,442)( 25,439)
( 26,440)( 27,427)( 28,428)( 29,430)( 30,429)( 31,433)( 32,434)( 33,431)
( 34,432)( 35,419)( 36,420)( 37,422)( 38,421)( 39,425)( 40,426)( 41,423)
( 42,424)( 43,371)( 44,372)( 45,374)( 46,373)( 47,377)( 48,378)( 49,375)
( 50,376)( 51,363)( 52,364)( 53,366)( 54,365)( 55,369)( 56,370)( 57,367)
( 58,368)( 59,395)( 60,396)( 61,398)( 62,397)( 63,401)( 64,402)( 65,399)
( 66,400)( 67,387)( 68,388)( 69,390)( 70,389)( 71,393)( 72,394)( 73,391)
( 74,392)( 75,379)( 76,380)( 77,382)( 78,381)( 79,385)( 80,386)( 81,383)
( 82,384)( 83,451)( 84,452)( 85,454)( 86,453)( 87,457)( 88,458)( 89,455)
( 90,456)( 91,443)( 92,444)( 93,446)( 94,445)( 95,449)( 96,450)( 97,447)
( 98,448)( 99,475)(100,476)(101,478)(102,477)(103,481)(104,482)(105,479)
(106,480)(107,467)(108,468)(109,470)(110,469)(111,473)(112,474)(113,471)
(114,472)(115,459)(116,460)(117,462)(118,461)(119,465)(120,466)(121,463)
(122,464)(123,292)(124,291)(125,293)(126,294)(127,298)(128,297)(129,296)
(130,295)(131,284)(132,283)(133,285)(134,286)(135,290)(136,289)(137,288)
(138,287)(139,316)(140,315)(141,317)(142,318)(143,322)(144,321)(145,320)
(146,319)(147,308)(148,307)(149,309)(150,310)(151,314)(152,313)(153,312)
(154,311)(155,300)(156,299)(157,301)(158,302)(159,306)(160,305)(161,304)
(162,303)(163,252)(164,251)(165,253)(166,254)(167,258)(168,257)(169,256)
(170,255)(171,244)(172,243)(173,245)(174,246)(175,250)(176,249)(177,248)
(178,247)(179,276)(180,275)(181,277)(182,278)(183,282)(184,281)(185,280)
(186,279)(187,268)(188,267)(189,269)(190,270)(191,274)(192,273)(193,272)
(194,271)(195,260)(196,259)(197,261)(198,262)(199,266)(200,265)(201,264)
(202,263)(203,332)(204,331)(205,333)(206,334)(207,338)(208,337)(209,336)
(210,335)(211,324)(212,323)(213,325)(214,326)(215,330)(216,329)(217,328)
(218,327)(219,356)(220,355)(221,357)(222,358)(223,362)(224,361)(225,360)
(226,359)(227,348)(228,347)(229,349)(230,350)(231,354)(232,353)(233,352)
(234,351)(235,340)(236,339)(237,341)(238,342)(239,346)(240,345)(241,344)
(242,343);
s3 := Sym(482)!( 3,129)( 4,130)( 5,126)( 6,125)( 7,127)( 8,128)( 9,123)
( 10,124)( 11,137)( 12,138)( 13,134)( 14,133)( 15,135)( 16,136)( 17,131)
( 18,132)( 19,145)( 20,146)( 21,142)( 22,141)( 23,143)( 24,144)( 25,139)
( 26,140)( 27,153)( 28,154)( 29,150)( 30,149)( 31,151)( 32,152)( 33,147)
( 34,148)( 35,161)( 36,162)( 37,158)( 38,157)( 39,159)( 40,160)( 41,155)
( 42,156)( 43,209)( 44,210)( 45,206)( 46,205)( 47,207)( 48,208)( 49,203)
( 50,204)( 51,217)( 52,218)( 53,214)( 54,213)( 55,215)( 56,216)( 57,211)
( 58,212)( 59,225)( 60,226)( 61,222)( 62,221)( 63,223)( 64,224)( 65,219)
( 66,220)( 67,233)( 68,234)( 69,230)( 70,229)( 71,231)( 72,232)( 73,227)
( 74,228)( 75,241)( 76,242)( 77,238)( 78,237)( 79,239)( 80,240)( 81,235)
( 82,236)( 83,169)( 84,170)( 85,166)( 86,165)( 87,167)( 88,168)( 89,163)
( 90,164)( 91,177)( 92,178)( 93,174)( 94,173)( 95,175)( 96,176)( 97,171)
( 98,172)( 99,185)(100,186)(101,182)(102,181)(103,183)(104,184)(105,179)
(106,180)(107,193)(108,194)(109,190)(110,189)(111,191)(112,192)(113,187)
(114,188)(115,201)(116,202)(117,198)(118,197)(119,199)(120,200)(121,195)
(122,196)(243,369)(244,370)(245,366)(246,365)(247,367)(248,368)(249,363)
(250,364)(251,377)(252,378)(253,374)(254,373)(255,375)(256,376)(257,371)
(258,372)(259,385)(260,386)(261,382)(262,381)(263,383)(264,384)(265,379)
(266,380)(267,393)(268,394)(269,390)(270,389)(271,391)(272,392)(273,387)
(274,388)(275,401)(276,402)(277,398)(278,397)(279,399)(280,400)(281,395)
(282,396)(283,449)(284,450)(285,446)(286,445)(287,447)(288,448)(289,443)
(290,444)(291,457)(292,458)(293,454)(294,453)(295,455)(296,456)(297,451)
(298,452)(299,465)(300,466)(301,462)(302,461)(303,463)(304,464)(305,459)
(306,460)(307,473)(308,474)(309,470)(310,469)(311,471)(312,472)(313,467)
(314,468)(315,481)(316,482)(317,478)(318,477)(319,479)(320,480)(321,475)
(322,476)(323,409)(324,410)(325,406)(326,405)(327,407)(328,408)(329,403)
(330,404)(331,417)(332,418)(333,414)(334,413)(335,415)(336,416)(337,411)
(338,412)(339,425)(340,426)(341,422)(342,421)(343,423)(344,424)(345,419)
(346,420)(347,433)(348,434)(349,430)(350,429)(351,431)(352,432)(353,427)
(354,428)(355,441)(356,442)(357,438)(358,437)(359,439)(360,440)(361,435)
(362,436);
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*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s3*s1*s2*s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s1*s2*s1*s2 >;
to this polytope