Polytope of Type {24,30}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope