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