Polytope of Type {4,30}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,30}*960c
if this polytope has a name.
Group : SmallGroup(960,11375)
Rank : 3
Schlafli Type : {4,30}
Number of vertices, edges, etc : 16, 240, 120
Order of s0s1s2 : 30
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,30,2} of size 1920
Vertex Figure Of :
{2,4,30} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,15}*480
3-fold quotients : {4,10}*320a
6-fold quotients : {4,5}*160
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,60}*1920f, {4,60}*1920g, {8,30}*1920h, {8,30}*1920i, {4,30}*1920d
Permutation Representation (GAP) :
s0 := ( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)( 8, 16)
( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)
( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)
( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)
( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)
( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)
( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)
(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)
(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)
(145,153)(146,154)(147,155)(148,156)(149,157)(150,158)(151,159)(152,160)
(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)
(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)
(193,201)(194,202)(195,203)(196,204)(197,205)(198,206)(199,207)(200,208)
(209,217)(210,218)(211,219)(212,220)(213,221)(214,222)(215,223)(216,224)
(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)(232,240)
(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)(248,256)
(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)(264,272)
(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)(280,288)
(289,297)(290,298)(291,299)(292,300)(293,301)(294,302)(295,303)(296,304)
(305,313)(306,314)(307,315)(308,316)(309,317)(310,318)(311,319)(312,320)
(321,329)(322,330)(323,331)(324,332)(325,333)(326,334)(327,335)(328,336)
(337,345)(338,346)(339,347)(340,348)(341,349)(342,350)(343,351)(344,352)
(353,361)(354,362)(355,363)(356,364)(357,365)(358,366)(359,367)(360,368)
(369,377)(370,378)(371,379)(372,380)(373,381)(374,382)(375,383)(376,384)
(385,393)(386,394)(387,395)(388,396)(389,397)(390,398)(391,399)(392,400)
(401,409)(402,410)(403,411)(404,412)(405,413)(406,414)(407,415)(408,416)
(417,425)(418,426)(419,427)(420,428)(421,429)(422,430)(423,431)(424,432)
(433,441)(434,442)(435,443)(436,444)(437,445)(438,446)(439,447)(440,448)
(449,457)(450,458)(451,459)(452,460)(453,461)(454,462)(455,463)(456,464)
(465,473)(466,474)(467,475)(468,476)(469,477)(470,478)(471,479)(472,480);;
s1 := ( 2, 11)( 3, 14)( 4, 8)( 6, 15)( 7, 10)( 9, 13)( 17, 65)( 18, 75)
( 19, 78)( 20, 72)( 21, 69)( 22, 79)( 23, 74)( 24, 68)( 25, 77)( 26, 71)
( 27, 66)( 28, 76)( 29, 73)( 30, 67)( 31, 70)( 32, 80)( 33, 49)( 34, 59)
( 35, 62)( 36, 56)( 37, 53)( 38, 63)( 39, 58)( 40, 52)( 41, 61)( 42, 55)
( 43, 50)( 44, 60)( 45, 57)( 46, 51)( 47, 54)( 48, 64)( 81,161)( 82,171)
( 83,174)( 84,168)( 85,165)( 86,175)( 87,170)( 88,164)( 89,173)( 90,167)
( 91,162)( 92,172)( 93,169)( 94,163)( 95,166)( 96,176)( 97,225)( 98,235)
( 99,238)(100,232)(101,229)(102,239)(103,234)(104,228)(105,237)(106,231)
(107,226)(108,236)(109,233)(110,227)(111,230)(112,240)(113,209)(114,219)
(115,222)(116,216)(117,213)(118,223)(119,218)(120,212)(121,221)(122,215)
(123,210)(124,220)(125,217)(126,211)(127,214)(128,224)(129,193)(130,203)
(131,206)(132,200)(133,197)(134,207)(135,202)(136,196)(137,205)(138,199)
(139,194)(140,204)(141,201)(142,195)(143,198)(144,208)(145,177)(146,187)
(147,190)(148,184)(149,181)(150,191)(151,186)(152,180)(153,189)(154,183)
(155,178)(156,188)(157,185)(158,179)(159,182)(160,192)(242,251)(243,254)
(244,248)(246,255)(247,250)(249,253)(257,305)(258,315)(259,318)(260,312)
(261,309)(262,319)(263,314)(264,308)(265,317)(266,311)(267,306)(268,316)
(269,313)(270,307)(271,310)(272,320)(273,289)(274,299)(275,302)(276,296)
(277,293)(278,303)(279,298)(280,292)(281,301)(282,295)(283,290)(284,300)
(285,297)(286,291)(287,294)(288,304)(321,401)(322,411)(323,414)(324,408)
(325,405)(326,415)(327,410)(328,404)(329,413)(330,407)(331,402)(332,412)
(333,409)(334,403)(335,406)(336,416)(337,465)(338,475)(339,478)(340,472)
(341,469)(342,479)(343,474)(344,468)(345,477)(346,471)(347,466)(348,476)
(349,473)(350,467)(351,470)(352,480)(353,449)(354,459)(355,462)(356,456)
(357,453)(358,463)(359,458)(360,452)(361,461)(362,455)(363,450)(364,460)
(365,457)(366,451)(367,454)(368,464)(369,433)(370,443)(371,446)(372,440)
(373,437)(374,447)(375,442)(376,436)(377,445)(378,439)(379,434)(380,444)
(381,441)(382,435)(383,438)(384,448)(385,417)(386,427)(387,430)(388,424)
(389,421)(390,431)(391,426)(392,420)(393,429)(394,423)(395,418)(396,428)
(397,425)(398,419)(399,422)(400,432);;
s2 := ( 1,353)( 2,365)( 3,360)( 4,364)( 5,362)( 6,358)( 7,367)( 8,355)
( 9,361)( 10,357)( 11,368)( 12,356)( 13,354)( 14,366)( 15,359)( 16,363)
( 17,337)( 18,349)( 19,344)( 20,348)( 21,346)( 22,342)( 23,351)( 24,339)
( 25,345)( 26,341)( 27,352)( 28,340)( 29,338)( 30,350)( 31,343)( 32,347)
( 33,321)( 34,333)( 35,328)( 36,332)( 37,330)( 38,326)( 39,335)( 40,323)
( 41,329)( 42,325)( 43,336)( 44,324)( 45,322)( 46,334)( 47,327)( 48,331)
( 49,385)( 50,397)( 51,392)( 52,396)( 53,394)( 54,390)( 55,399)( 56,387)
( 57,393)( 58,389)( 59,400)( 60,388)( 61,386)( 62,398)( 63,391)( 64,395)
( 65,369)( 66,381)( 67,376)( 68,380)( 69,378)( 70,374)( 71,383)( 72,371)
( 73,377)( 74,373)( 75,384)( 76,372)( 77,370)( 78,382)( 79,375)( 80,379)
( 81,273)( 82,285)( 83,280)( 84,284)( 85,282)( 86,278)( 87,287)( 88,275)
( 89,281)( 90,277)( 91,288)( 92,276)( 93,274)( 94,286)( 95,279)( 96,283)
( 97,257)( 98,269)( 99,264)(100,268)(101,266)(102,262)(103,271)(104,259)
(105,265)(106,261)(107,272)(108,260)(109,258)(110,270)(111,263)(112,267)
(113,241)(114,253)(115,248)(116,252)(117,250)(118,246)(119,255)(120,243)
(121,249)(122,245)(123,256)(124,244)(125,242)(126,254)(127,247)(128,251)
(129,305)(130,317)(131,312)(132,316)(133,314)(134,310)(135,319)(136,307)
(137,313)(138,309)(139,320)(140,308)(141,306)(142,318)(143,311)(144,315)
(145,289)(146,301)(147,296)(148,300)(149,298)(150,294)(151,303)(152,291)
(153,297)(154,293)(155,304)(156,292)(157,290)(158,302)(159,295)(160,299)
(161,433)(162,445)(163,440)(164,444)(165,442)(166,438)(167,447)(168,435)
(169,441)(170,437)(171,448)(172,436)(173,434)(174,446)(175,439)(176,443)
(177,417)(178,429)(179,424)(180,428)(181,426)(182,422)(183,431)(184,419)
(185,425)(186,421)(187,432)(188,420)(189,418)(190,430)(191,423)(192,427)
(193,401)(194,413)(195,408)(196,412)(197,410)(198,406)(199,415)(200,403)
(201,409)(202,405)(203,416)(204,404)(205,402)(206,414)(207,407)(208,411)
(209,465)(210,477)(211,472)(212,476)(213,474)(214,470)(215,479)(216,467)
(217,473)(218,469)(219,480)(220,468)(221,466)(222,478)(223,471)(224,475)
(225,449)(226,461)(227,456)(228,460)(229,458)(230,454)(231,463)(232,451)
(233,457)(234,453)(235,464)(236,452)(237,450)(238,462)(239,455)(240,459);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s0*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*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(480)!( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)
( 8, 16)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)
( 24, 32)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)
( 40, 48)( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)
( 56, 64)( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)
( 72, 80)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)
( 88, 96)( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)
(104,112)(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)
(120,128)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)
(136,144)(145,153)(146,154)(147,155)(148,156)(149,157)(150,158)(151,159)
(152,160)(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)
(168,176)(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)
(184,192)(193,201)(194,202)(195,203)(196,204)(197,205)(198,206)(199,207)
(200,208)(209,217)(210,218)(211,219)(212,220)(213,221)(214,222)(215,223)
(216,224)(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)
(232,240)(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)
(248,256)(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)
(264,272)(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)
(280,288)(289,297)(290,298)(291,299)(292,300)(293,301)(294,302)(295,303)
(296,304)(305,313)(306,314)(307,315)(308,316)(309,317)(310,318)(311,319)
(312,320)(321,329)(322,330)(323,331)(324,332)(325,333)(326,334)(327,335)
(328,336)(337,345)(338,346)(339,347)(340,348)(341,349)(342,350)(343,351)
(344,352)(353,361)(354,362)(355,363)(356,364)(357,365)(358,366)(359,367)
(360,368)(369,377)(370,378)(371,379)(372,380)(373,381)(374,382)(375,383)
(376,384)(385,393)(386,394)(387,395)(388,396)(389,397)(390,398)(391,399)
(392,400)(401,409)(402,410)(403,411)(404,412)(405,413)(406,414)(407,415)
(408,416)(417,425)(418,426)(419,427)(420,428)(421,429)(422,430)(423,431)
(424,432)(433,441)(434,442)(435,443)(436,444)(437,445)(438,446)(439,447)
(440,448)(449,457)(450,458)(451,459)(452,460)(453,461)(454,462)(455,463)
(456,464)(465,473)(466,474)(467,475)(468,476)(469,477)(470,478)(471,479)
(472,480);
s1 := Sym(480)!( 2, 11)( 3, 14)( 4, 8)( 6, 15)( 7, 10)( 9, 13)( 17, 65)
( 18, 75)( 19, 78)( 20, 72)( 21, 69)( 22, 79)( 23, 74)( 24, 68)( 25, 77)
( 26, 71)( 27, 66)( 28, 76)( 29, 73)( 30, 67)( 31, 70)( 32, 80)( 33, 49)
( 34, 59)( 35, 62)( 36, 56)( 37, 53)( 38, 63)( 39, 58)( 40, 52)( 41, 61)
( 42, 55)( 43, 50)( 44, 60)( 45, 57)( 46, 51)( 47, 54)( 48, 64)( 81,161)
( 82,171)( 83,174)( 84,168)( 85,165)( 86,175)( 87,170)( 88,164)( 89,173)
( 90,167)( 91,162)( 92,172)( 93,169)( 94,163)( 95,166)( 96,176)( 97,225)
( 98,235)( 99,238)(100,232)(101,229)(102,239)(103,234)(104,228)(105,237)
(106,231)(107,226)(108,236)(109,233)(110,227)(111,230)(112,240)(113,209)
(114,219)(115,222)(116,216)(117,213)(118,223)(119,218)(120,212)(121,221)
(122,215)(123,210)(124,220)(125,217)(126,211)(127,214)(128,224)(129,193)
(130,203)(131,206)(132,200)(133,197)(134,207)(135,202)(136,196)(137,205)
(138,199)(139,194)(140,204)(141,201)(142,195)(143,198)(144,208)(145,177)
(146,187)(147,190)(148,184)(149,181)(150,191)(151,186)(152,180)(153,189)
(154,183)(155,178)(156,188)(157,185)(158,179)(159,182)(160,192)(242,251)
(243,254)(244,248)(246,255)(247,250)(249,253)(257,305)(258,315)(259,318)
(260,312)(261,309)(262,319)(263,314)(264,308)(265,317)(266,311)(267,306)
(268,316)(269,313)(270,307)(271,310)(272,320)(273,289)(274,299)(275,302)
(276,296)(277,293)(278,303)(279,298)(280,292)(281,301)(282,295)(283,290)
(284,300)(285,297)(286,291)(287,294)(288,304)(321,401)(322,411)(323,414)
(324,408)(325,405)(326,415)(327,410)(328,404)(329,413)(330,407)(331,402)
(332,412)(333,409)(334,403)(335,406)(336,416)(337,465)(338,475)(339,478)
(340,472)(341,469)(342,479)(343,474)(344,468)(345,477)(346,471)(347,466)
(348,476)(349,473)(350,467)(351,470)(352,480)(353,449)(354,459)(355,462)
(356,456)(357,453)(358,463)(359,458)(360,452)(361,461)(362,455)(363,450)
(364,460)(365,457)(366,451)(367,454)(368,464)(369,433)(370,443)(371,446)
(372,440)(373,437)(374,447)(375,442)(376,436)(377,445)(378,439)(379,434)
(380,444)(381,441)(382,435)(383,438)(384,448)(385,417)(386,427)(387,430)
(388,424)(389,421)(390,431)(391,426)(392,420)(393,429)(394,423)(395,418)
(396,428)(397,425)(398,419)(399,422)(400,432);
s2 := Sym(480)!( 1,353)( 2,365)( 3,360)( 4,364)( 5,362)( 6,358)( 7,367)
( 8,355)( 9,361)( 10,357)( 11,368)( 12,356)( 13,354)( 14,366)( 15,359)
( 16,363)( 17,337)( 18,349)( 19,344)( 20,348)( 21,346)( 22,342)( 23,351)
( 24,339)( 25,345)( 26,341)( 27,352)( 28,340)( 29,338)( 30,350)( 31,343)
( 32,347)( 33,321)( 34,333)( 35,328)( 36,332)( 37,330)( 38,326)( 39,335)
( 40,323)( 41,329)( 42,325)( 43,336)( 44,324)( 45,322)( 46,334)( 47,327)
( 48,331)( 49,385)( 50,397)( 51,392)( 52,396)( 53,394)( 54,390)( 55,399)
( 56,387)( 57,393)( 58,389)( 59,400)( 60,388)( 61,386)( 62,398)( 63,391)
( 64,395)( 65,369)( 66,381)( 67,376)( 68,380)( 69,378)( 70,374)( 71,383)
( 72,371)( 73,377)( 74,373)( 75,384)( 76,372)( 77,370)( 78,382)( 79,375)
( 80,379)( 81,273)( 82,285)( 83,280)( 84,284)( 85,282)( 86,278)( 87,287)
( 88,275)( 89,281)( 90,277)( 91,288)( 92,276)( 93,274)( 94,286)( 95,279)
( 96,283)( 97,257)( 98,269)( 99,264)(100,268)(101,266)(102,262)(103,271)
(104,259)(105,265)(106,261)(107,272)(108,260)(109,258)(110,270)(111,263)
(112,267)(113,241)(114,253)(115,248)(116,252)(117,250)(118,246)(119,255)
(120,243)(121,249)(122,245)(123,256)(124,244)(125,242)(126,254)(127,247)
(128,251)(129,305)(130,317)(131,312)(132,316)(133,314)(134,310)(135,319)
(136,307)(137,313)(138,309)(139,320)(140,308)(141,306)(142,318)(143,311)
(144,315)(145,289)(146,301)(147,296)(148,300)(149,298)(150,294)(151,303)
(152,291)(153,297)(154,293)(155,304)(156,292)(157,290)(158,302)(159,295)
(160,299)(161,433)(162,445)(163,440)(164,444)(165,442)(166,438)(167,447)
(168,435)(169,441)(170,437)(171,448)(172,436)(173,434)(174,446)(175,439)
(176,443)(177,417)(178,429)(179,424)(180,428)(181,426)(182,422)(183,431)
(184,419)(185,425)(186,421)(187,432)(188,420)(189,418)(190,430)(191,423)
(192,427)(193,401)(194,413)(195,408)(196,412)(197,410)(198,406)(199,415)
(200,403)(201,409)(202,405)(203,416)(204,404)(205,402)(206,414)(207,407)
(208,411)(209,465)(210,477)(211,472)(212,476)(213,474)(214,470)(215,479)
(216,467)(217,473)(218,469)(219,480)(220,468)(221,466)(222,478)(223,471)
(224,475)(225,449)(226,461)(227,456)(228,460)(229,458)(230,454)(231,463)
(232,451)(233,457)(234,453)(235,464)(236,452)(237,450)(238,462)(239,455)
(240,459);
poly := sub<Sym(480)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s0*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*s1*s2*s1*s2 >;
References : None.
to this polytope