Polytope of Type {30,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,4}*960c
if this polytope has a name.
Group : SmallGroup(960,11375)
Rank : 3
Schlafli Type : {30,4}
Number of vertices, edges, etc : 120, 240, 16
Order of s₀s₁s₂ : 30
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {30,4,2} of size 1920
Vertex Figure Of :
   {2,30,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {15,4}*480
   3-fold quotients : {10,4}*320a
   6-fold quotients : {5,4}*160
Covers (Minimal Covers in Boldface) :
   2-fold covers : {60,4}*1920f, {60,4}*1920g, {30,8}*1920h, {30,8}*1920i, {30,4}*1920d
Permutation Representation (GAP) :

s0 := (  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);;
s1 := (  1,337)(  2,338)(  3,340)(  4,339)(  5,342)(  6,341)(  7,343)(  8,344)
(  9,352)( 10,351)( 11,349)( 12,350)( 13,347)( 14,348)( 15,346)( 16,345)
( 17,321)( 18,322)( 19,324)( 20,323)( 21,326)( 22,325)( 23,327)( 24,328)
( 25,336)( 26,335)( 27,333)( 28,334)( 29,331)( 30,332)( 31,330)( 32,329)
( 33,385)( 34,386)( 35,388)( 36,387)( 37,390)( 38,389)( 39,391)( 40,392)
( 41,400)( 42,399)( 43,397)( 44,398)( 45,395)( 46,396)( 47,394)( 48,393)
( 49,369)( 50,370)( 51,372)( 52,371)( 53,374)( 54,373)( 55,375)( 56,376)
( 57,384)( 58,383)( 59,381)( 60,382)( 61,379)( 62,380)( 63,378)( 64,377)
( 65,353)( 66,354)( 67,356)( 68,355)( 69,358)( 70,357)( 71,359)( 72,360)
( 73,368)( 74,367)( 75,365)( 76,366)( 77,363)( 78,364)( 79,362)( 80,361)
( 81,257)( 82,258)( 83,260)( 84,259)( 85,262)( 86,261)( 87,263)( 88,264)
( 89,272)( 90,271)( 91,269)( 92,270)( 93,267)( 94,268)( 95,266)( 96,265)
( 97,241)( 98,242)( 99,244)(100,243)(101,246)(102,245)(103,247)(104,248)
(105,256)(106,255)(107,253)(108,254)(109,251)(110,252)(111,250)(112,249)
(113,305)(114,306)(115,308)(116,307)(117,310)(118,309)(119,311)(120,312)
(121,320)(122,319)(123,317)(124,318)(125,315)(126,316)(127,314)(128,313)
(129,289)(130,290)(131,292)(132,291)(133,294)(134,293)(135,295)(136,296)
(137,304)(138,303)(139,301)(140,302)(141,299)(142,300)(143,298)(144,297)
(145,273)(146,274)(147,276)(148,275)(149,278)(150,277)(151,279)(152,280)
(153,288)(154,287)(155,285)(156,286)(157,283)(158,284)(159,282)(160,281)
(161,417)(162,418)(163,420)(164,419)(165,422)(166,421)(167,423)(168,424)
(169,432)(170,431)(171,429)(172,430)(173,427)(174,428)(175,426)(176,425)
(177,401)(178,402)(179,404)(180,403)(181,406)(182,405)(183,407)(184,408)
(185,416)(186,415)(187,413)(188,414)(189,411)(190,412)(191,410)(192,409)
(193,465)(194,466)(195,468)(196,467)(197,470)(198,469)(199,471)(200,472)
(201,480)(202,479)(203,477)(204,478)(205,475)(206,476)(207,474)(208,473)
(209,449)(210,450)(211,452)(212,451)(213,454)(214,453)(215,455)(216,456)
(217,464)(218,463)(219,461)(220,462)(221,459)(222,460)(223,458)(224,457)
(225,433)(226,434)(227,436)(228,435)(229,438)(230,437)(231,439)(232,440)
(233,448)(234,447)(235,445)(236,446)(237,443)(238,444)(239,442)(240,441);;
s2 := (  1,  5)(  2,  6)(  3,  7)(  4,  8)(  9, 13)( 10, 14)( 11, 15)( 12, 16)
( 17, 21)( 18, 22)( 19, 23)( 20, 24)( 25, 29)( 26, 30)( 27, 31)( 28, 32)
( 33, 37)( 34, 38)( 35, 39)( 36, 40)( 41, 45)( 42, 46)( 43, 47)( 44, 48)
( 49, 53)( 50, 54)( 51, 55)( 52, 56)( 57, 61)( 58, 62)( 59, 63)( 60, 64)
( 65, 69)( 66, 70)( 67, 71)( 68, 72)( 73, 77)( 74, 78)( 75, 79)( 76, 80)
( 81, 85)( 82, 86)( 83, 87)( 84, 88)( 89, 93)( 90, 94)( 91, 95)( 92, 96)
( 97,101)( 98,102)( 99,103)(100,104)(105,109)(106,110)(107,111)(108,112)
(113,117)(114,118)(115,119)(116,120)(121,125)(122,126)(123,127)(124,128)
(129,133)(130,134)(131,135)(132,136)(137,141)(138,142)(139,143)(140,144)
(145,149)(146,150)(147,151)(148,152)(153,157)(154,158)(155,159)(156,160)
(161,165)(162,166)(163,167)(164,168)(169,173)(170,174)(171,175)(172,176)
(177,181)(178,182)(179,183)(180,184)(185,189)(186,190)(187,191)(188,192)
(193,197)(194,198)(195,199)(196,200)(201,205)(202,206)(203,207)(204,208)
(209,213)(210,214)(211,215)(212,216)(217,221)(218,222)(219,223)(220,224)
(225,229)(226,230)(227,231)(228,232)(233,237)(234,238)(235,239)(236,240)
(241,245)(242,246)(243,247)(244,248)(249,253)(250,254)(251,255)(252,256)
(257,261)(258,262)(259,263)(260,264)(265,269)(266,270)(267,271)(268,272)
(273,277)(274,278)(275,279)(276,280)(281,285)(282,286)(283,287)(284,288)
(289,293)(290,294)(291,295)(292,296)(297,301)(298,302)(299,303)(300,304)
(305,309)(306,310)(307,311)(308,312)(313,317)(314,318)(315,319)(316,320)
(321,325)(322,326)(323,327)(324,328)(329,333)(330,334)(331,335)(332,336)
(337,341)(338,342)(339,343)(340,344)(345,349)(346,350)(347,351)(348,352)
(353,357)(354,358)(355,359)(356,360)(361,365)(362,366)(363,367)(364,368)
(369,373)(370,374)(371,375)(372,376)(377,381)(378,382)(379,383)(380,384)
(385,389)(386,390)(387,391)(388,392)(393,397)(394,398)(395,399)(396,400)
(401,405)(402,406)(403,407)(404,408)(409,413)(410,414)(411,415)(412,416)
(417,421)(418,422)(419,423)(420,424)(425,429)(426,430)(427,431)(428,432)
(433,437)(434,438)(435,439)(436,440)(441,445)(442,446)(443,447)(444,448)
(449,453)(450,454)(451,455)(452,456)(457,461)(458,462)(459,463)(460,464)
(465,469)(466,470)(467,471)(468,472)(473,477)(474,478)(475,479)(476,480);;
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := 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);
s1 := Sym(480)!(  1,337)(  2,338)(  3,340)(  4,339)(  5,342)(  6,341)(  7,343)
(  8,344)(  9,352)( 10,351)( 11,349)( 12,350)( 13,347)( 14,348)( 15,346)
( 16,345)( 17,321)( 18,322)( 19,324)( 20,323)( 21,326)( 22,325)( 23,327)
( 24,328)( 25,336)( 26,335)( 27,333)( 28,334)( 29,331)( 30,332)( 31,330)
( 32,329)( 33,385)( 34,386)( 35,388)( 36,387)( 37,390)( 38,389)( 39,391)
( 40,392)( 41,400)( 42,399)( 43,397)( 44,398)( 45,395)( 46,396)( 47,394)
( 48,393)( 49,369)( 50,370)( 51,372)( 52,371)( 53,374)( 54,373)( 55,375)
( 56,376)( 57,384)( 58,383)( 59,381)( 60,382)( 61,379)( 62,380)( 63,378)
( 64,377)( 65,353)( 66,354)( 67,356)( 68,355)( 69,358)( 70,357)( 71,359)
( 72,360)( 73,368)( 74,367)( 75,365)( 76,366)( 77,363)( 78,364)( 79,362)
( 80,361)( 81,257)( 82,258)( 83,260)( 84,259)( 85,262)( 86,261)( 87,263)
( 88,264)( 89,272)( 90,271)( 91,269)( 92,270)( 93,267)( 94,268)( 95,266)
( 96,265)( 97,241)( 98,242)( 99,244)(100,243)(101,246)(102,245)(103,247)
(104,248)(105,256)(106,255)(107,253)(108,254)(109,251)(110,252)(111,250)
(112,249)(113,305)(114,306)(115,308)(116,307)(117,310)(118,309)(119,311)
(120,312)(121,320)(122,319)(123,317)(124,318)(125,315)(126,316)(127,314)
(128,313)(129,289)(130,290)(131,292)(132,291)(133,294)(134,293)(135,295)
(136,296)(137,304)(138,303)(139,301)(140,302)(141,299)(142,300)(143,298)
(144,297)(145,273)(146,274)(147,276)(148,275)(149,278)(150,277)(151,279)
(152,280)(153,288)(154,287)(155,285)(156,286)(157,283)(158,284)(159,282)
(160,281)(161,417)(162,418)(163,420)(164,419)(165,422)(166,421)(167,423)
(168,424)(169,432)(170,431)(171,429)(172,430)(173,427)(174,428)(175,426)
(176,425)(177,401)(178,402)(179,404)(180,403)(181,406)(182,405)(183,407)
(184,408)(185,416)(186,415)(187,413)(188,414)(189,411)(190,412)(191,410)
(192,409)(193,465)(194,466)(195,468)(196,467)(197,470)(198,469)(199,471)
(200,472)(201,480)(202,479)(203,477)(204,478)(205,475)(206,476)(207,474)
(208,473)(209,449)(210,450)(211,452)(212,451)(213,454)(214,453)(215,455)
(216,456)(217,464)(218,463)(219,461)(220,462)(221,459)(222,460)(223,458)
(224,457)(225,433)(226,434)(227,436)(228,435)(229,438)(230,437)(231,439)
(232,440)(233,448)(234,447)(235,445)(236,446)(237,443)(238,444)(239,442)
(240,441);
s2 := Sym(480)!(  1,  5)(  2,  6)(  3,  7)(  4,  8)(  9, 13)( 10, 14)( 11, 15)
( 12, 16)( 17, 21)( 18, 22)( 19, 23)( 20, 24)( 25, 29)( 26, 30)( 27, 31)
( 28, 32)( 33, 37)( 34, 38)( 35, 39)( 36, 40)( 41, 45)( 42, 46)( 43, 47)
( 44, 48)( 49, 53)( 50, 54)( 51, 55)( 52, 56)( 57, 61)( 58, 62)( 59, 63)
( 60, 64)( 65, 69)( 66, 70)( 67, 71)( 68, 72)( 73, 77)( 74, 78)( 75, 79)
( 76, 80)( 81, 85)( 82, 86)( 83, 87)( 84, 88)( 89, 93)( 90, 94)( 91, 95)
( 92, 96)( 97,101)( 98,102)( 99,103)(100,104)(105,109)(106,110)(107,111)
(108,112)(113,117)(114,118)(115,119)(116,120)(121,125)(122,126)(123,127)
(124,128)(129,133)(130,134)(131,135)(132,136)(137,141)(138,142)(139,143)
(140,144)(145,149)(146,150)(147,151)(148,152)(153,157)(154,158)(155,159)
(156,160)(161,165)(162,166)(163,167)(164,168)(169,173)(170,174)(171,175)
(172,176)(177,181)(178,182)(179,183)(180,184)(185,189)(186,190)(187,191)
(188,192)(193,197)(194,198)(195,199)(196,200)(201,205)(202,206)(203,207)
(204,208)(209,213)(210,214)(211,215)(212,216)(217,221)(218,222)(219,223)
(220,224)(225,229)(226,230)(227,231)(228,232)(233,237)(234,238)(235,239)
(236,240)(241,245)(242,246)(243,247)(244,248)(249,253)(250,254)(251,255)
(252,256)(257,261)(258,262)(259,263)(260,264)(265,269)(266,270)(267,271)
(268,272)(273,277)(274,278)(275,279)(276,280)(281,285)(282,286)(283,287)
(284,288)(289,293)(290,294)(291,295)(292,296)(297,301)(298,302)(299,303)
(300,304)(305,309)(306,310)(307,311)(308,312)(313,317)(314,318)(315,319)
(316,320)(321,325)(322,326)(323,327)(324,328)(329,333)(330,334)(331,335)
(332,336)(337,341)(338,342)(339,343)(340,344)(345,349)(346,350)(347,351)
(348,352)(353,357)(354,358)(355,359)(356,360)(361,365)(362,366)(363,367)
(364,368)(369,373)(370,374)(371,375)(372,376)(377,381)(378,382)(379,383)
(380,384)(385,389)(386,390)(387,391)(388,392)(393,397)(394,398)(395,399)
(396,400)(401,405)(402,406)(403,407)(404,408)(409,413)(410,414)(411,415)
(412,416)(417,421)(418,422)(419,423)(420,424)(425,429)(426,430)(427,431)
(428,432)(433,437)(434,438)(435,439)(436,440)(441,445)(442,446)(443,447)
(444,448)(449,453)(450,454)(451,455)(452,456)(457,461)(458,462)(459,463)
(460,464)(465,469)(466,470)(467,471)(468,472)(473,477)(474,478)(475,479)
(476,480);
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope