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