Polytope of Type {2,2,15,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,15,12}*1920
if this polytope has a name.
Group : SmallGroup(1920,240162)
Rank : 5
Schlafli Type : {2,2,15,12}
Number of vertices, edges, etc : 2, 2, 20, 120, 16
Order of s0s1s2s3s4 : 40
Order of s0s1s2s3s4s3s2s1 : 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 : {2,2,15,6}*960
5-fold quotients : {2,2,3,12}*384
10-fold quotients : {2,2,3,6}*192
20-fold quotients : {2,2,3,3}*96
24-fold quotients : {2,2,5,2}*80
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 5,365)( 6,366)( 7,369)( 8,370)( 9,367)( 10,368)( 11,372)( 12,371)
( 13,397)( 14,398)( 15,401)( 16,402)( 17,399)( 18,400)( 19,404)( 20,403)
( 21,389)( 22,390)( 23,393)( 24,394)( 25,391)( 26,392)( 27,396)( 28,395)
( 29,381)( 30,382)( 31,385)( 32,386)( 33,383)( 34,384)( 35,388)( 36,387)
( 37,373)( 38,374)( 39,377)( 40,378)( 41,375)( 42,376)( 43,380)( 44,379)
( 45,445)( 46,446)( 47,449)( 48,450)( 49,447)( 50,448)( 51,452)( 52,451)
( 53,477)( 54,478)( 55,481)( 56,482)( 57,479)( 58,480)( 59,484)( 60,483)
( 61,469)( 62,470)( 63,473)( 64,474)( 65,471)( 66,472)( 67,476)( 68,475)
( 69,461)( 70,462)( 71,465)( 72,466)( 73,463)( 74,464)( 75,468)( 76,467)
( 77,453)( 78,454)( 79,457)( 80,458)( 81,455)( 82,456)( 83,460)( 84,459)
( 85,405)( 86,406)( 87,409)( 88,410)( 89,407)( 90,408)( 91,412)( 92,411)
( 93,437)( 94,438)( 95,441)( 96,442)( 97,439)( 98,440)( 99,444)(100,443)
(101,429)(102,430)(103,433)(104,434)(105,431)(106,432)(107,436)(108,435)
(109,421)(110,422)(111,425)(112,426)(113,423)(114,424)(115,428)(116,427)
(117,413)(118,414)(119,417)(120,418)(121,415)(122,416)(123,420)(124,419)
(125,246)(126,245)(127,250)(128,249)(129,248)(130,247)(131,251)(132,252)
(133,278)(134,277)(135,282)(136,281)(137,280)(138,279)(139,283)(140,284)
(141,270)(142,269)(143,274)(144,273)(145,272)(146,271)(147,275)(148,276)
(149,262)(150,261)(151,266)(152,265)(153,264)(154,263)(155,267)(156,268)
(157,254)(158,253)(159,258)(160,257)(161,256)(162,255)(163,259)(164,260)
(165,326)(166,325)(167,330)(168,329)(169,328)(170,327)(171,331)(172,332)
(173,358)(174,357)(175,362)(176,361)(177,360)(178,359)(179,363)(180,364)
(181,350)(182,349)(183,354)(184,353)(185,352)(186,351)(187,355)(188,356)
(189,342)(190,341)(191,346)(192,345)(193,344)(194,343)(195,347)(196,348)
(197,334)(198,333)(199,338)(200,337)(201,336)(202,335)(203,339)(204,340)
(205,286)(206,285)(207,290)(208,289)(209,288)(210,287)(211,291)(212,292)
(213,318)(214,317)(215,322)(216,321)(217,320)(218,319)(219,323)(220,324)
(221,310)(222,309)(223,314)(224,313)(225,312)(226,311)(227,315)(228,316)
(229,302)(230,301)(231,306)(232,305)(233,304)(234,303)(235,307)(236,308)
(237,294)(238,293)(239,298)(240,297)(241,296)(242,295)(243,299)(244,300);;
s3 := ( 5,413)( 6,414)( 7,416)( 8,415)( 9,419)( 10,420)( 11,417)( 12,418)
( 13,405)( 14,406)( 15,408)( 16,407)( 17,411)( 18,412)( 19,409)( 20,410)
( 21,437)( 22,438)( 23,440)( 24,439)( 25,443)( 26,444)( 27,441)( 28,442)
( 29,429)( 30,430)( 31,432)( 32,431)( 33,435)( 34,436)( 35,433)( 36,434)
( 37,421)( 38,422)( 39,424)( 40,423)( 41,427)( 42,428)( 43,425)( 44,426)
( 45,373)( 46,374)( 47,376)( 48,375)( 49,379)( 50,380)( 51,377)( 52,378)
( 53,365)( 54,366)( 55,368)( 56,367)( 57,371)( 58,372)( 59,369)( 60,370)
( 61,397)( 62,398)( 63,400)( 64,399)( 65,403)( 66,404)( 67,401)( 68,402)
( 69,389)( 70,390)( 71,392)( 72,391)( 73,395)( 74,396)( 75,393)( 76,394)
( 77,381)( 78,382)( 79,384)( 80,383)( 81,387)( 82,388)( 83,385)( 84,386)
( 85,453)( 86,454)( 87,456)( 88,455)( 89,459)( 90,460)( 91,457)( 92,458)
( 93,445)( 94,446)( 95,448)( 96,447)( 97,451)( 98,452)( 99,449)(100,450)
(101,477)(102,478)(103,480)(104,479)(105,483)(106,484)(107,481)(108,482)
(109,469)(110,470)(111,472)(112,471)(113,475)(114,476)(115,473)(116,474)
(117,461)(118,462)(119,464)(120,463)(121,467)(122,468)(123,465)(124,466)
(125,294)(126,293)(127,295)(128,296)(129,300)(130,299)(131,298)(132,297)
(133,286)(134,285)(135,287)(136,288)(137,292)(138,291)(139,290)(140,289)
(141,318)(142,317)(143,319)(144,320)(145,324)(146,323)(147,322)(148,321)
(149,310)(150,309)(151,311)(152,312)(153,316)(154,315)(155,314)(156,313)
(157,302)(158,301)(159,303)(160,304)(161,308)(162,307)(163,306)(164,305)
(165,254)(166,253)(167,255)(168,256)(169,260)(170,259)(171,258)(172,257)
(173,246)(174,245)(175,247)(176,248)(177,252)(178,251)(179,250)(180,249)
(181,278)(182,277)(183,279)(184,280)(185,284)(186,283)(187,282)(188,281)
(189,270)(190,269)(191,271)(192,272)(193,276)(194,275)(195,274)(196,273)
(197,262)(198,261)(199,263)(200,264)(201,268)(202,267)(203,266)(204,265)
(205,334)(206,333)(207,335)(208,336)(209,340)(210,339)(211,338)(212,337)
(213,326)(214,325)(215,327)(216,328)(217,332)(218,331)(219,330)(220,329)
(221,358)(222,357)(223,359)(224,360)(225,364)(226,363)(227,362)(228,361)
(229,350)(230,349)(231,351)(232,352)(233,356)(234,355)(235,354)(236,353)
(237,342)(238,341)(239,343)(240,344)(241,348)(242,347)(243,346)(244,345);;
s4 := ( 5,131)( 6,132)( 7,128)( 8,127)( 9,129)( 10,130)( 11,125)( 12,126)
( 13,139)( 14,140)( 15,136)( 16,135)( 17,137)( 18,138)( 19,133)( 20,134)
( 21,147)( 22,148)( 23,144)( 24,143)( 25,145)( 26,146)( 27,141)( 28,142)
( 29,155)( 30,156)( 31,152)( 32,151)( 33,153)( 34,154)( 35,149)( 36,150)
( 37,163)( 38,164)( 39,160)( 40,159)( 41,161)( 42,162)( 43,157)( 44,158)
( 45,211)( 46,212)( 47,208)( 48,207)( 49,209)( 50,210)( 51,205)( 52,206)
( 53,219)( 54,220)( 55,216)( 56,215)( 57,217)( 58,218)( 59,213)( 60,214)
( 61,227)( 62,228)( 63,224)( 64,223)( 65,225)( 66,226)( 67,221)( 68,222)
( 69,235)( 70,236)( 71,232)( 72,231)( 73,233)( 74,234)( 75,229)( 76,230)
( 77,243)( 78,244)( 79,240)( 80,239)( 81,241)( 82,242)( 83,237)( 84,238)
( 85,171)( 86,172)( 87,168)( 88,167)( 89,169)( 90,170)( 91,165)( 92,166)
( 93,179)( 94,180)( 95,176)( 96,175)( 97,177)( 98,178)( 99,173)(100,174)
(101,187)(102,188)(103,184)(104,183)(105,185)(106,186)(107,181)(108,182)
(109,195)(110,196)(111,192)(112,191)(113,193)(114,194)(115,189)(116,190)
(117,203)(118,204)(119,200)(120,199)(121,201)(122,202)(123,197)(124,198)
(245,371)(246,372)(247,368)(248,367)(249,369)(250,370)(251,365)(252,366)
(253,379)(254,380)(255,376)(256,375)(257,377)(258,378)(259,373)(260,374)
(261,387)(262,388)(263,384)(264,383)(265,385)(266,386)(267,381)(268,382)
(269,395)(270,396)(271,392)(272,391)(273,393)(274,394)(275,389)(276,390)
(277,403)(278,404)(279,400)(280,399)(281,401)(282,402)(283,397)(284,398)
(285,451)(286,452)(287,448)(288,447)(289,449)(290,450)(291,445)(292,446)
(293,459)(294,460)(295,456)(296,455)(297,457)(298,458)(299,453)(300,454)
(301,467)(302,468)(303,464)(304,463)(305,465)(306,466)(307,461)(308,462)
(309,475)(310,476)(311,472)(312,471)(313,473)(314,474)(315,469)(316,470)
(317,483)(318,484)(319,480)(320,479)(321,481)(322,482)(323,477)(324,478)
(325,411)(326,412)(327,408)(328,407)(329,409)(330,410)(331,405)(332,406)
(333,419)(334,420)(335,416)(336,415)(337,417)(338,418)(339,413)(340,414)
(341,427)(342,428)(343,424)(344,423)(345,425)(346,426)(347,421)(348,422)
(349,435)(350,436)(351,432)(352,431)(353,433)(354,434)(355,429)(356,430)
(357,443)(358,444)(359,440)(360,439)(361,441)(362,442)(363,437)(364,438);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3,
s4*s2*s3*s4*s2*s3*s4*s3*s4*s3*s4*s2*s3*s4*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(484)!(1,2);
s1 := Sym(484)!(3,4);
s2 := Sym(484)!( 5,365)( 6,366)( 7,369)( 8,370)( 9,367)( 10,368)( 11,372)
( 12,371)( 13,397)( 14,398)( 15,401)( 16,402)( 17,399)( 18,400)( 19,404)
( 20,403)( 21,389)( 22,390)( 23,393)( 24,394)( 25,391)( 26,392)( 27,396)
( 28,395)( 29,381)( 30,382)( 31,385)( 32,386)( 33,383)( 34,384)( 35,388)
( 36,387)( 37,373)( 38,374)( 39,377)( 40,378)( 41,375)( 42,376)( 43,380)
( 44,379)( 45,445)( 46,446)( 47,449)( 48,450)( 49,447)( 50,448)( 51,452)
( 52,451)( 53,477)( 54,478)( 55,481)( 56,482)( 57,479)( 58,480)( 59,484)
( 60,483)( 61,469)( 62,470)( 63,473)( 64,474)( 65,471)( 66,472)( 67,476)
( 68,475)( 69,461)( 70,462)( 71,465)( 72,466)( 73,463)( 74,464)( 75,468)
( 76,467)( 77,453)( 78,454)( 79,457)( 80,458)( 81,455)( 82,456)( 83,460)
( 84,459)( 85,405)( 86,406)( 87,409)( 88,410)( 89,407)( 90,408)( 91,412)
( 92,411)( 93,437)( 94,438)( 95,441)( 96,442)( 97,439)( 98,440)( 99,444)
(100,443)(101,429)(102,430)(103,433)(104,434)(105,431)(106,432)(107,436)
(108,435)(109,421)(110,422)(111,425)(112,426)(113,423)(114,424)(115,428)
(116,427)(117,413)(118,414)(119,417)(120,418)(121,415)(122,416)(123,420)
(124,419)(125,246)(126,245)(127,250)(128,249)(129,248)(130,247)(131,251)
(132,252)(133,278)(134,277)(135,282)(136,281)(137,280)(138,279)(139,283)
(140,284)(141,270)(142,269)(143,274)(144,273)(145,272)(146,271)(147,275)
(148,276)(149,262)(150,261)(151,266)(152,265)(153,264)(154,263)(155,267)
(156,268)(157,254)(158,253)(159,258)(160,257)(161,256)(162,255)(163,259)
(164,260)(165,326)(166,325)(167,330)(168,329)(169,328)(170,327)(171,331)
(172,332)(173,358)(174,357)(175,362)(176,361)(177,360)(178,359)(179,363)
(180,364)(181,350)(182,349)(183,354)(184,353)(185,352)(186,351)(187,355)
(188,356)(189,342)(190,341)(191,346)(192,345)(193,344)(194,343)(195,347)
(196,348)(197,334)(198,333)(199,338)(200,337)(201,336)(202,335)(203,339)
(204,340)(205,286)(206,285)(207,290)(208,289)(209,288)(210,287)(211,291)
(212,292)(213,318)(214,317)(215,322)(216,321)(217,320)(218,319)(219,323)
(220,324)(221,310)(222,309)(223,314)(224,313)(225,312)(226,311)(227,315)
(228,316)(229,302)(230,301)(231,306)(232,305)(233,304)(234,303)(235,307)
(236,308)(237,294)(238,293)(239,298)(240,297)(241,296)(242,295)(243,299)
(244,300);
s3 := Sym(484)!( 5,413)( 6,414)( 7,416)( 8,415)( 9,419)( 10,420)( 11,417)
( 12,418)( 13,405)( 14,406)( 15,408)( 16,407)( 17,411)( 18,412)( 19,409)
( 20,410)( 21,437)( 22,438)( 23,440)( 24,439)( 25,443)( 26,444)( 27,441)
( 28,442)( 29,429)( 30,430)( 31,432)( 32,431)( 33,435)( 34,436)( 35,433)
( 36,434)( 37,421)( 38,422)( 39,424)( 40,423)( 41,427)( 42,428)( 43,425)
( 44,426)( 45,373)( 46,374)( 47,376)( 48,375)( 49,379)( 50,380)( 51,377)
( 52,378)( 53,365)( 54,366)( 55,368)( 56,367)( 57,371)( 58,372)( 59,369)
( 60,370)( 61,397)( 62,398)( 63,400)( 64,399)( 65,403)( 66,404)( 67,401)
( 68,402)( 69,389)( 70,390)( 71,392)( 72,391)( 73,395)( 74,396)( 75,393)
( 76,394)( 77,381)( 78,382)( 79,384)( 80,383)( 81,387)( 82,388)( 83,385)
( 84,386)( 85,453)( 86,454)( 87,456)( 88,455)( 89,459)( 90,460)( 91,457)
( 92,458)( 93,445)( 94,446)( 95,448)( 96,447)( 97,451)( 98,452)( 99,449)
(100,450)(101,477)(102,478)(103,480)(104,479)(105,483)(106,484)(107,481)
(108,482)(109,469)(110,470)(111,472)(112,471)(113,475)(114,476)(115,473)
(116,474)(117,461)(118,462)(119,464)(120,463)(121,467)(122,468)(123,465)
(124,466)(125,294)(126,293)(127,295)(128,296)(129,300)(130,299)(131,298)
(132,297)(133,286)(134,285)(135,287)(136,288)(137,292)(138,291)(139,290)
(140,289)(141,318)(142,317)(143,319)(144,320)(145,324)(146,323)(147,322)
(148,321)(149,310)(150,309)(151,311)(152,312)(153,316)(154,315)(155,314)
(156,313)(157,302)(158,301)(159,303)(160,304)(161,308)(162,307)(163,306)
(164,305)(165,254)(166,253)(167,255)(168,256)(169,260)(170,259)(171,258)
(172,257)(173,246)(174,245)(175,247)(176,248)(177,252)(178,251)(179,250)
(180,249)(181,278)(182,277)(183,279)(184,280)(185,284)(186,283)(187,282)
(188,281)(189,270)(190,269)(191,271)(192,272)(193,276)(194,275)(195,274)
(196,273)(197,262)(198,261)(199,263)(200,264)(201,268)(202,267)(203,266)
(204,265)(205,334)(206,333)(207,335)(208,336)(209,340)(210,339)(211,338)
(212,337)(213,326)(214,325)(215,327)(216,328)(217,332)(218,331)(219,330)
(220,329)(221,358)(222,357)(223,359)(224,360)(225,364)(226,363)(227,362)
(228,361)(229,350)(230,349)(231,351)(232,352)(233,356)(234,355)(235,354)
(236,353)(237,342)(238,341)(239,343)(240,344)(241,348)(242,347)(243,346)
(244,345);
s4 := Sym(484)!( 5,131)( 6,132)( 7,128)( 8,127)( 9,129)( 10,130)( 11,125)
( 12,126)( 13,139)( 14,140)( 15,136)( 16,135)( 17,137)( 18,138)( 19,133)
( 20,134)( 21,147)( 22,148)( 23,144)( 24,143)( 25,145)( 26,146)( 27,141)
( 28,142)( 29,155)( 30,156)( 31,152)( 32,151)( 33,153)( 34,154)( 35,149)
( 36,150)( 37,163)( 38,164)( 39,160)( 40,159)( 41,161)( 42,162)( 43,157)
( 44,158)( 45,211)( 46,212)( 47,208)( 48,207)( 49,209)( 50,210)( 51,205)
( 52,206)( 53,219)( 54,220)( 55,216)( 56,215)( 57,217)( 58,218)( 59,213)
( 60,214)( 61,227)( 62,228)( 63,224)( 64,223)( 65,225)( 66,226)( 67,221)
( 68,222)( 69,235)( 70,236)( 71,232)( 72,231)( 73,233)( 74,234)( 75,229)
( 76,230)( 77,243)( 78,244)( 79,240)( 80,239)( 81,241)( 82,242)( 83,237)
( 84,238)( 85,171)( 86,172)( 87,168)( 88,167)( 89,169)( 90,170)( 91,165)
( 92,166)( 93,179)( 94,180)( 95,176)( 96,175)( 97,177)( 98,178)( 99,173)
(100,174)(101,187)(102,188)(103,184)(104,183)(105,185)(106,186)(107,181)
(108,182)(109,195)(110,196)(111,192)(112,191)(113,193)(114,194)(115,189)
(116,190)(117,203)(118,204)(119,200)(120,199)(121,201)(122,202)(123,197)
(124,198)(245,371)(246,372)(247,368)(248,367)(249,369)(250,370)(251,365)
(252,366)(253,379)(254,380)(255,376)(256,375)(257,377)(258,378)(259,373)
(260,374)(261,387)(262,388)(263,384)(264,383)(265,385)(266,386)(267,381)
(268,382)(269,395)(270,396)(271,392)(272,391)(273,393)(274,394)(275,389)
(276,390)(277,403)(278,404)(279,400)(280,399)(281,401)(282,402)(283,397)
(284,398)(285,451)(286,452)(287,448)(288,447)(289,449)(290,450)(291,445)
(292,446)(293,459)(294,460)(295,456)(296,455)(297,457)(298,458)(299,453)
(300,454)(301,467)(302,468)(303,464)(304,463)(305,465)(306,466)(307,461)
(308,462)(309,475)(310,476)(311,472)(312,471)(313,473)(314,474)(315,469)
(316,470)(317,483)(318,484)(319,480)(320,479)(321,481)(322,482)(323,477)
(324,478)(325,411)(326,412)(327,408)(328,407)(329,409)(330,410)(331,405)
(332,406)(333,419)(334,420)(335,416)(336,415)(337,417)(338,418)(339,413)
(340,414)(341,427)(342,428)(343,424)(344,423)(345,425)(346,426)(347,421)
(348,422)(349,435)(350,436)(351,432)(352,431)(353,433)(354,434)(355,429)
(356,430)(357,443)(358,444)(359,440)(360,439)(361,441)(362,442)(363,437)
(364,438);
poly := sub<Sym(484)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3,
s4*s2*s3*s4*s2*s3*s4*s3*s4*s3*s4*s2*s3*s4*s2*s3*s2*s3 >;
to this polytope