Polytope of Type {2,30,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,30,4}*1920d
if this polytope has a name.
Group : SmallGroup(1920,240409)
Rank : 4
Schlafli Type : {2,30,4}
Number of vertices, edges, etc : 2, 120, 240, 16
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-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 : {2,15,4}*960
3-fold quotients : {2,10,4}*640b
6-fold quotients : {2,5,4}*320
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 13)( 5, 16)( 6, 10)( 8, 17)( 9, 12)( 11, 15)( 19, 67)( 20, 77)
( 21, 80)( 22, 74)( 23, 71)( 24, 81)( 25, 76)( 26, 70)( 27, 79)( 28, 73)
( 29, 68)( 30, 78)( 31, 75)( 32, 69)( 33, 72)( 34, 82)( 35, 51)( 36, 61)
( 37, 64)( 38, 58)( 39, 55)( 40, 65)( 41, 60)( 42, 54)( 43, 63)( 44, 57)
( 45, 52)( 46, 62)( 47, 59)( 48, 53)( 49, 56)( 50, 66)( 83,163)( 84,173)
( 85,176)( 86,170)( 87,167)( 88,177)( 89,172)( 90,166)( 91,175)( 92,169)
( 93,164)( 94,174)( 95,171)( 96,165)( 97,168)( 98,178)( 99,227)(100,237)
(101,240)(102,234)(103,231)(104,241)(105,236)(106,230)(107,239)(108,233)
(109,228)(110,238)(111,235)(112,229)(113,232)(114,242)(115,211)(116,221)
(117,224)(118,218)(119,215)(120,225)(121,220)(122,214)(123,223)(124,217)
(125,212)(126,222)(127,219)(128,213)(129,216)(130,226)(131,195)(132,205)
(133,208)(134,202)(135,199)(136,209)(137,204)(138,198)(139,207)(140,201)
(141,196)(142,206)(143,203)(144,197)(145,200)(146,210)(147,179)(148,189)
(149,192)(150,186)(151,183)(152,193)(153,188)(154,182)(155,191)(156,185)
(157,180)(158,190)(159,187)(160,181)(161,184)(162,194)(244,253)(245,256)
(246,250)(248,257)(249,252)(251,255)(259,307)(260,317)(261,320)(262,314)
(263,311)(264,321)(265,316)(266,310)(267,319)(268,313)(269,308)(270,318)
(271,315)(272,309)(273,312)(274,322)(275,291)(276,301)(277,304)(278,298)
(279,295)(280,305)(281,300)(282,294)(283,303)(284,297)(285,292)(286,302)
(287,299)(288,293)(289,296)(290,306)(323,403)(324,413)(325,416)(326,410)
(327,407)(328,417)(329,412)(330,406)(331,415)(332,409)(333,404)(334,414)
(335,411)(336,405)(337,408)(338,418)(339,467)(340,477)(341,480)(342,474)
(343,471)(344,481)(345,476)(346,470)(347,479)(348,473)(349,468)(350,478)
(351,475)(352,469)(353,472)(354,482)(355,451)(356,461)(357,464)(358,458)
(359,455)(360,465)(361,460)(362,454)(363,463)(364,457)(365,452)(366,462)
(367,459)(368,453)(369,456)(370,466)(371,435)(372,445)(373,448)(374,442)
(375,439)(376,449)(377,444)(378,438)(379,447)(380,441)(381,436)(382,446)
(383,443)(384,437)(385,440)(386,450)(387,419)(388,429)(389,432)(390,426)
(391,423)(392,433)(393,428)(394,422)(395,431)(396,425)(397,420)(398,430)
(399,427)(400,421)(401,424)(402,434);;
s2 := ( 3,339)( 4,340)( 5,342)( 6,341)( 7,344)( 8,343)( 9,345)( 10,346)
( 11,354)( 12,353)( 13,351)( 14,352)( 15,349)( 16,350)( 17,348)( 18,347)
( 19,323)( 20,324)( 21,326)( 22,325)( 23,328)( 24,327)( 25,329)( 26,330)
( 27,338)( 28,337)( 29,335)( 30,336)( 31,333)( 32,334)( 33,332)( 34,331)
( 35,387)( 36,388)( 37,390)( 38,389)( 39,392)( 40,391)( 41,393)( 42,394)
( 43,402)( 44,401)( 45,399)( 46,400)( 47,397)( 48,398)( 49,396)( 50,395)
( 51,371)( 52,372)( 53,374)( 54,373)( 55,376)( 56,375)( 57,377)( 58,378)
( 59,386)( 60,385)( 61,383)( 62,384)( 63,381)( 64,382)( 65,380)( 66,379)
( 67,355)( 68,356)( 69,358)( 70,357)( 71,360)( 72,359)( 73,361)( 74,362)
( 75,370)( 76,369)( 77,367)( 78,368)( 79,365)( 80,366)( 81,364)( 82,363)
( 83,259)( 84,260)( 85,262)( 86,261)( 87,264)( 88,263)( 89,265)( 90,266)
( 91,274)( 92,273)( 93,271)( 94,272)( 95,269)( 96,270)( 97,268)( 98,267)
( 99,243)(100,244)(101,246)(102,245)(103,248)(104,247)(105,249)(106,250)
(107,258)(108,257)(109,255)(110,256)(111,253)(112,254)(113,252)(114,251)
(115,307)(116,308)(117,310)(118,309)(119,312)(120,311)(121,313)(122,314)
(123,322)(124,321)(125,319)(126,320)(127,317)(128,318)(129,316)(130,315)
(131,291)(132,292)(133,294)(134,293)(135,296)(136,295)(137,297)(138,298)
(139,306)(140,305)(141,303)(142,304)(143,301)(144,302)(145,300)(146,299)
(147,275)(148,276)(149,278)(150,277)(151,280)(152,279)(153,281)(154,282)
(155,290)(156,289)(157,287)(158,288)(159,285)(160,286)(161,284)(162,283)
(163,419)(164,420)(165,422)(166,421)(167,424)(168,423)(169,425)(170,426)
(171,434)(172,433)(173,431)(174,432)(175,429)(176,430)(177,428)(178,427)
(179,403)(180,404)(181,406)(182,405)(183,408)(184,407)(185,409)(186,410)
(187,418)(188,417)(189,415)(190,416)(191,413)(192,414)(193,412)(194,411)
(195,467)(196,468)(197,470)(198,469)(199,472)(200,471)(201,473)(202,474)
(203,482)(204,481)(205,479)(206,480)(207,477)(208,478)(209,476)(210,475)
(211,451)(212,452)(213,454)(214,453)(215,456)(216,455)(217,457)(218,458)
(219,466)(220,465)(221,463)(222,464)(223,461)(224,462)(225,460)(226,459)
(227,435)(228,436)(229,438)(230,437)(231,440)(232,439)(233,441)(234,442)
(235,450)(236,449)(237,447)(238,448)(239,445)(240,446)(241,444)(242,443);;
s3 := ( 3,247)( 4,248)( 5,249)( 6,250)( 7,243)( 8,244)( 9,245)( 10,246)
( 11,255)( 12,256)( 13,257)( 14,258)( 15,251)( 16,252)( 17,253)( 18,254)
( 19,263)( 20,264)( 21,265)( 22,266)( 23,259)( 24,260)( 25,261)( 26,262)
( 27,271)( 28,272)( 29,273)( 30,274)( 31,267)( 32,268)( 33,269)( 34,270)
( 35,279)( 36,280)( 37,281)( 38,282)( 39,275)( 40,276)( 41,277)( 42,278)
( 43,287)( 44,288)( 45,289)( 46,290)( 47,283)( 48,284)( 49,285)( 50,286)
( 51,295)( 52,296)( 53,297)( 54,298)( 55,291)( 56,292)( 57,293)( 58,294)
( 59,303)( 60,304)( 61,305)( 62,306)( 63,299)( 64,300)( 65,301)( 66,302)
( 67,311)( 68,312)( 69,313)( 70,314)( 71,307)( 72,308)( 73,309)( 74,310)
( 75,319)( 76,320)( 77,321)( 78,322)( 79,315)( 80,316)( 81,317)( 82,318)
( 83,327)( 84,328)( 85,329)( 86,330)( 87,323)( 88,324)( 89,325)( 90,326)
( 91,335)( 92,336)( 93,337)( 94,338)( 95,331)( 96,332)( 97,333)( 98,334)
( 99,343)(100,344)(101,345)(102,346)(103,339)(104,340)(105,341)(106,342)
(107,351)(108,352)(109,353)(110,354)(111,347)(112,348)(113,349)(114,350)
(115,359)(116,360)(117,361)(118,362)(119,355)(120,356)(121,357)(122,358)
(123,367)(124,368)(125,369)(126,370)(127,363)(128,364)(129,365)(130,366)
(131,375)(132,376)(133,377)(134,378)(135,371)(136,372)(137,373)(138,374)
(139,383)(140,384)(141,385)(142,386)(143,379)(144,380)(145,381)(146,382)
(147,391)(148,392)(149,393)(150,394)(151,387)(152,388)(153,389)(154,390)
(155,399)(156,400)(157,401)(158,402)(159,395)(160,396)(161,397)(162,398)
(163,407)(164,408)(165,409)(166,410)(167,403)(168,404)(169,405)(170,406)
(171,415)(172,416)(173,417)(174,418)(175,411)(176,412)(177,413)(178,414)
(179,423)(180,424)(181,425)(182,426)(183,419)(184,420)(185,421)(186,422)
(187,431)(188,432)(189,433)(190,434)(191,427)(192,428)(193,429)(194,430)
(195,439)(196,440)(197,441)(198,442)(199,435)(200,436)(201,437)(202,438)
(203,447)(204,448)(205,449)(206,450)(207,443)(208,444)(209,445)(210,446)
(211,455)(212,456)(213,457)(214,458)(215,451)(216,452)(217,453)(218,454)
(219,463)(220,464)(221,465)(222,466)(223,459)(224,460)(225,461)(226,462)
(227,471)(228,472)(229,473)(230,474)(231,467)(232,468)(233,469)(234,470)
(235,479)(236,480)(237,481)(238,482)(239,475)(240,476)(241,477)(242,478);;
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,
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(482)!(1,2);
s1 := Sym(482)!( 4, 13)( 5, 16)( 6, 10)( 8, 17)( 9, 12)( 11, 15)( 19, 67)
( 20, 77)( 21, 80)( 22, 74)( 23, 71)( 24, 81)( 25, 76)( 26, 70)( 27, 79)
( 28, 73)( 29, 68)( 30, 78)( 31, 75)( 32, 69)( 33, 72)( 34, 82)( 35, 51)
( 36, 61)( 37, 64)( 38, 58)( 39, 55)( 40, 65)( 41, 60)( 42, 54)( 43, 63)
( 44, 57)( 45, 52)( 46, 62)( 47, 59)( 48, 53)( 49, 56)( 50, 66)( 83,163)
( 84,173)( 85,176)( 86,170)( 87,167)( 88,177)( 89,172)( 90,166)( 91,175)
( 92,169)( 93,164)( 94,174)( 95,171)( 96,165)( 97,168)( 98,178)( 99,227)
(100,237)(101,240)(102,234)(103,231)(104,241)(105,236)(106,230)(107,239)
(108,233)(109,228)(110,238)(111,235)(112,229)(113,232)(114,242)(115,211)
(116,221)(117,224)(118,218)(119,215)(120,225)(121,220)(122,214)(123,223)
(124,217)(125,212)(126,222)(127,219)(128,213)(129,216)(130,226)(131,195)
(132,205)(133,208)(134,202)(135,199)(136,209)(137,204)(138,198)(139,207)
(140,201)(141,196)(142,206)(143,203)(144,197)(145,200)(146,210)(147,179)
(148,189)(149,192)(150,186)(151,183)(152,193)(153,188)(154,182)(155,191)
(156,185)(157,180)(158,190)(159,187)(160,181)(161,184)(162,194)(244,253)
(245,256)(246,250)(248,257)(249,252)(251,255)(259,307)(260,317)(261,320)
(262,314)(263,311)(264,321)(265,316)(266,310)(267,319)(268,313)(269,308)
(270,318)(271,315)(272,309)(273,312)(274,322)(275,291)(276,301)(277,304)
(278,298)(279,295)(280,305)(281,300)(282,294)(283,303)(284,297)(285,292)
(286,302)(287,299)(288,293)(289,296)(290,306)(323,403)(324,413)(325,416)
(326,410)(327,407)(328,417)(329,412)(330,406)(331,415)(332,409)(333,404)
(334,414)(335,411)(336,405)(337,408)(338,418)(339,467)(340,477)(341,480)
(342,474)(343,471)(344,481)(345,476)(346,470)(347,479)(348,473)(349,468)
(350,478)(351,475)(352,469)(353,472)(354,482)(355,451)(356,461)(357,464)
(358,458)(359,455)(360,465)(361,460)(362,454)(363,463)(364,457)(365,452)
(366,462)(367,459)(368,453)(369,456)(370,466)(371,435)(372,445)(373,448)
(374,442)(375,439)(376,449)(377,444)(378,438)(379,447)(380,441)(381,436)
(382,446)(383,443)(384,437)(385,440)(386,450)(387,419)(388,429)(389,432)
(390,426)(391,423)(392,433)(393,428)(394,422)(395,431)(396,425)(397,420)
(398,430)(399,427)(400,421)(401,424)(402,434);
s2 := Sym(482)!( 3,339)( 4,340)( 5,342)( 6,341)( 7,344)( 8,343)( 9,345)
( 10,346)( 11,354)( 12,353)( 13,351)( 14,352)( 15,349)( 16,350)( 17,348)
( 18,347)( 19,323)( 20,324)( 21,326)( 22,325)( 23,328)( 24,327)( 25,329)
( 26,330)( 27,338)( 28,337)( 29,335)( 30,336)( 31,333)( 32,334)( 33,332)
( 34,331)( 35,387)( 36,388)( 37,390)( 38,389)( 39,392)( 40,391)( 41,393)
( 42,394)( 43,402)( 44,401)( 45,399)( 46,400)( 47,397)( 48,398)( 49,396)
( 50,395)( 51,371)( 52,372)( 53,374)( 54,373)( 55,376)( 56,375)( 57,377)
( 58,378)( 59,386)( 60,385)( 61,383)( 62,384)( 63,381)( 64,382)( 65,380)
( 66,379)( 67,355)( 68,356)( 69,358)( 70,357)( 71,360)( 72,359)( 73,361)
( 74,362)( 75,370)( 76,369)( 77,367)( 78,368)( 79,365)( 80,366)( 81,364)
( 82,363)( 83,259)( 84,260)( 85,262)( 86,261)( 87,264)( 88,263)( 89,265)
( 90,266)( 91,274)( 92,273)( 93,271)( 94,272)( 95,269)( 96,270)( 97,268)
( 98,267)( 99,243)(100,244)(101,246)(102,245)(103,248)(104,247)(105,249)
(106,250)(107,258)(108,257)(109,255)(110,256)(111,253)(112,254)(113,252)
(114,251)(115,307)(116,308)(117,310)(118,309)(119,312)(120,311)(121,313)
(122,314)(123,322)(124,321)(125,319)(126,320)(127,317)(128,318)(129,316)
(130,315)(131,291)(132,292)(133,294)(134,293)(135,296)(136,295)(137,297)
(138,298)(139,306)(140,305)(141,303)(142,304)(143,301)(144,302)(145,300)
(146,299)(147,275)(148,276)(149,278)(150,277)(151,280)(152,279)(153,281)
(154,282)(155,290)(156,289)(157,287)(158,288)(159,285)(160,286)(161,284)
(162,283)(163,419)(164,420)(165,422)(166,421)(167,424)(168,423)(169,425)
(170,426)(171,434)(172,433)(173,431)(174,432)(175,429)(176,430)(177,428)
(178,427)(179,403)(180,404)(181,406)(182,405)(183,408)(184,407)(185,409)
(186,410)(187,418)(188,417)(189,415)(190,416)(191,413)(192,414)(193,412)
(194,411)(195,467)(196,468)(197,470)(198,469)(199,472)(200,471)(201,473)
(202,474)(203,482)(204,481)(205,479)(206,480)(207,477)(208,478)(209,476)
(210,475)(211,451)(212,452)(213,454)(214,453)(215,456)(216,455)(217,457)
(218,458)(219,466)(220,465)(221,463)(222,464)(223,461)(224,462)(225,460)
(226,459)(227,435)(228,436)(229,438)(230,437)(231,440)(232,439)(233,441)
(234,442)(235,450)(236,449)(237,447)(238,448)(239,445)(240,446)(241,444)
(242,443);
s3 := Sym(482)!( 3,247)( 4,248)( 5,249)( 6,250)( 7,243)( 8,244)( 9,245)
( 10,246)( 11,255)( 12,256)( 13,257)( 14,258)( 15,251)( 16,252)( 17,253)
( 18,254)( 19,263)( 20,264)( 21,265)( 22,266)( 23,259)( 24,260)( 25,261)
( 26,262)( 27,271)( 28,272)( 29,273)( 30,274)( 31,267)( 32,268)( 33,269)
( 34,270)( 35,279)( 36,280)( 37,281)( 38,282)( 39,275)( 40,276)( 41,277)
( 42,278)( 43,287)( 44,288)( 45,289)( 46,290)( 47,283)( 48,284)( 49,285)
( 50,286)( 51,295)( 52,296)( 53,297)( 54,298)( 55,291)( 56,292)( 57,293)
( 58,294)( 59,303)( 60,304)( 61,305)( 62,306)( 63,299)( 64,300)( 65,301)
( 66,302)( 67,311)( 68,312)( 69,313)( 70,314)( 71,307)( 72,308)( 73,309)
( 74,310)( 75,319)( 76,320)( 77,321)( 78,322)( 79,315)( 80,316)( 81,317)
( 82,318)( 83,327)( 84,328)( 85,329)( 86,330)( 87,323)( 88,324)( 89,325)
( 90,326)( 91,335)( 92,336)( 93,337)( 94,338)( 95,331)( 96,332)( 97,333)
( 98,334)( 99,343)(100,344)(101,345)(102,346)(103,339)(104,340)(105,341)
(106,342)(107,351)(108,352)(109,353)(110,354)(111,347)(112,348)(113,349)
(114,350)(115,359)(116,360)(117,361)(118,362)(119,355)(120,356)(121,357)
(122,358)(123,367)(124,368)(125,369)(126,370)(127,363)(128,364)(129,365)
(130,366)(131,375)(132,376)(133,377)(134,378)(135,371)(136,372)(137,373)
(138,374)(139,383)(140,384)(141,385)(142,386)(143,379)(144,380)(145,381)
(146,382)(147,391)(148,392)(149,393)(150,394)(151,387)(152,388)(153,389)
(154,390)(155,399)(156,400)(157,401)(158,402)(159,395)(160,396)(161,397)
(162,398)(163,407)(164,408)(165,409)(166,410)(167,403)(168,404)(169,405)
(170,406)(171,415)(172,416)(173,417)(174,418)(175,411)(176,412)(177,413)
(178,414)(179,423)(180,424)(181,425)(182,426)(183,419)(184,420)(185,421)
(186,422)(187,431)(188,432)(189,433)(190,434)(191,427)(192,428)(193,429)
(194,430)(195,439)(196,440)(197,441)(198,442)(199,435)(200,436)(201,437)
(202,438)(203,447)(204,448)(205,449)(206,450)(207,443)(208,444)(209,445)
(210,446)(211,455)(212,456)(213,457)(214,458)(215,451)(216,452)(217,453)
(218,454)(219,463)(220,464)(221,465)(222,466)(223,459)(224,460)(225,461)
(226,462)(227,471)(228,472)(229,473)(230,474)(231,467)(232,468)(233,469)
(234,470)(235,479)(236,480)(237,481)(238,482)(239,475)(240,476)(241,477)
(242,478);
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, s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s3 >;
to this polytope