Polytope of Type {2,30,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,30,4}*1920c
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}*640a
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, 7)( 4, 8)( 5, 9)( 6, 10)( 11, 15)( 12, 16)( 13, 17)( 14, 18)
( 19, 23)( 20, 24)( 21, 25)( 22, 26)( 27, 31)( 28, 32)( 29, 33)( 30, 34)
( 35, 39)( 36, 40)( 37, 41)( 38, 42)( 43, 47)( 44, 48)( 45, 49)( 46, 50)
( 51, 55)( 52, 56)( 53, 57)( 54, 58)( 59, 63)( 60, 64)( 61, 65)( 62, 66)
( 67, 71)( 68, 72)( 69, 73)( 70, 74)( 75, 79)( 76, 80)( 77, 81)( 78, 82)
( 83, 87)( 84, 88)( 85, 89)( 86, 90)( 91, 95)( 92, 96)( 93, 97)( 94, 98)
( 99,103)(100,104)(101,105)(102,106)(107,111)(108,112)(109,113)(110,114)
(115,119)(116,120)(117,121)(118,122)(123,127)(124,128)(125,129)(126,130)
(131,135)(132,136)(133,137)(134,138)(139,143)(140,144)(141,145)(142,146)
(147,151)(148,152)(149,153)(150,154)(155,159)(156,160)(157,161)(158,162)
(163,167)(164,168)(165,169)(166,170)(171,175)(172,176)(173,177)(174,178)
(179,183)(180,184)(181,185)(182,186)(187,191)(188,192)(189,193)(190,194)
(195,199)(196,200)(197,201)(198,202)(203,207)(204,208)(205,209)(206,210)
(211,215)(212,216)(213,217)(214,218)(219,223)(220,224)(221,225)(222,226)
(227,231)(228,232)(229,233)(230,234)(235,239)(236,240)(237,241)(238,242)
(243,247)(244,248)(245,249)(246,250)(251,255)(252,256)(253,257)(254,258)
(259,263)(260,264)(261,265)(262,266)(267,271)(268,272)(269,273)(270,274)
(275,279)(276,280)(277,281)(278,282)(283,287)(284,288)(285,289)(286,290)
(291,295)(292,296)(293,297)(294,298)(299,303)(300,304)(301,305)(302,306)
(307,311)(308,312)(309,313)(310,314)(315,319)(316,320)(317,321)(318,322)
(323,327)(324,328)(325,329)(326,330)(331,335)(332,336)(333,337)(334,338)
(339,343)(340,344)(341,345)(342,346)(347,351)(348,352)(349,353)(350,354)
(355,359)(356,360)(357,361)(358,362)(363,367)(364,368)(365,369)(366,370)
(371,375)(372,376)(373,377)(374,378)(379,383)(380,384)(381,385)(382,386)
(387,391)(388,392)(389,393)(390,394)(395,399)(396,400)(397,401)(398,402)
(403,407)(404,408)(405,409)(406,410)(411,415)(412,416)(413,417)(414,418)
(419,423)(420,424)(421,425)(422,426)(427,431)(428,432)(429,433)(430,434)
(435,439)(436,440)(437,441)(438,442)(443,447)(444,448)(445,449)(446,450)
(451,455)(452,456)(453,457)(454,458)(459,463)(460,464)(461,465)(462,466)
(467,471)(468,472)(469,473)(470,474)(475,479)(476,480)(477,481)(478,482);;
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*s1*s2*s1*s3*s2*s3*s2*s1*s2*s3*s1*s2*s3*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*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*s1*s2*s1*s2 ];;
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, 7)( 4, 8)( 5, 9)( 6, 10)( 11, 15)( 12, 16)( 13, 17)
( 14, 18)( 19, 23)( 20, 24)( 21, 25)( 22, 26)( 27, 31)( 28, 32)( 29, 33)
( 30, 34)( 35, 39)( 36, 40)( 37, 41)( 38, 42)( 43, 47)( 44, 48)( 45, 49)
( 46, 50)( 51, 55)( 52, 56)( 53, 57)( 54, 58)( 59, 63)( 60, 64)( 61, 65)
( 62, 66)( 67, 71)( 68, 72)( 69, 73)( 70, 74)( 75, 79)( 76, 80)( 77, 81)
( 78, 82)( 83, 87)( 84, 88)( 85, 89)( 86, 90)( 91, 95)( 92, 96)( 93, 97)
( 94, 98)( 99,103)(100,104)(101,105)(102,106)(107,111)(108,112)(109,113)
(110,114)(115,119)(116,120)(117,121)(118,122)(123,127)(124,128)(125,129)
(126,130)(131,135)(132,136)(133,137)(134,138)(139,143)(140,144)(141,145)
(142,146)(147,151)(148,152)(149,153)(150,154)(155,159)(156,160)(157,161)
(158,162)(163,167)(164,168)(165,169)(166,170)(171,175)(172,176)(173,177)
(174,178)(179,183)(180,184)(181,185)(182,186)(187,191)(188,192)(189,193)
(190,194)(195,199)(196,200)(197,201)(198,202)(203,207)(204,208)(205,209)
(206,210)(211,215)(212,216)(213,217)(214,218)(219,223)(220,224)(221,225)
(222,226)(227,231)(228,232)(229,233)(230,234)(235,239)(236,240)(237,241)
(238,242)(243,247)(244,248)(245,249)(246,250)(251,255)(252,256)(253,257)
(254,258)(259,263)(260,264)(261,265)(262,266)(267,271)(268,272)(269,273)
(270,274)(275,279)(276,280)(277,281)(278,282)(283,287)(284,288)(285,289)
(286,290)(291,295)(292,296)(293,297)(294,298)(299,303)(300,304)(301,305)
(302,306)(307,311)(308,312)(309,313)(310,314)(315,319)(316,320)(317,321)
(318,322)(323,327)(324,328)(325,329)(326,330)(331,335)(332,336)(333,337)
(334,338)(339,343)(340,344)(341,345)(342,346)(347,351)(348,352)(349,353)
(350,354)(355,359)(356,360)(357,361)(358,362)(363,367)(364,368)(365,369)
(366,370)(371,375)(372,376)(373,377)(374,378)(379,383)(380,384)(381,385)
(382,386)(387,391)(388,392)(389,393)(390,394)(395,399)(396,400)(397,401)
(398,402)(403,407)(404,408)(405,409)(406,410)(411,415)(412,416)(413,417)
(414,418)(419,423)(420,424)(421,425)(422,426)(427,431)(428,432)(429,433)
(430,434)(435,439)(436,440)(437,441)(438,442)(443,447)(444,448)(445,449)
(446,450)(451,455)(452,456)(453,457)(454,458)(459,463)(460,464)(461,465)
(462,466)(467,471)(468,472)(469,473)(470,474)(475,479)(476,480)(477,481)
(478,482);
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*s1*s2*s1*s3*s2*s3*s2*s1*s2*s3*s1*s2*s3*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*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*s1*s2*s1*s2 >;
to this polytope