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