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