Polytope of Type {30,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,24}*1920a
if this polytope has a name.
Group : SmallGroup(1920,238882)
Rank : 3
Schlafli Type : {30,24}
Number of vertices, edges, etc : 40, 480, 32
Order of s₀s₁s₂ : 40
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {30,12}*960b
   4-fold quotients : {30,6}*480
   5-fold quotients : {6,24}*384a
   8-fold quotients : {15,6}*240
   10-fold quotients : {6,12}*192a
   12-fold quotients : {10,8}*160
   20-fold quotients : {6,6}*96
   24-fold quotients : {10,4}*80
   40-fold quotients : {3,6}*48, {6,3}*48
   48-fold quotients : {10,2}*40
   60-fold quotients : {2,8}*32
   80-fold quotients : {3,3}*24
   96-fold quotients : {5,2}*20
   120-fold quotients : {2,4}*16
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope