Polytope of Type {4,30}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,30}*1920b
if this polytope has a name.
Group : SmallGroup(1920,239570)
Rank : 3
Schlafli Type : {4,30}
Number of vertices, edges, etc : 32, 480, 240
Order of s0s1s2 : 120
Order of s0s1s2s1 : 8
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 : {4,30}*960b
4-fold quotients : {4,30}*480
5-fold quotients : {4,6}*384b
8-fold quotients : {4,30}*240a, {4,15}*240, {4,30}*240b, {4,30}*240c
10-fold quotients : {4,6}*192b
16-fold quotients : {4,15}*120, {2,30}*120
20-fold quotients : {4,6}*96
24-fold quotients : {4,10}*80
32-fold quotients : {2,15}*60
40-fold quotients : {4,6}*48a, {4,3}*48, {4,6}*48b, {4,6}*48c
48-fold quotients : {2,10}*40
80-fold quotients : {4,3}*24, {2,6}*24
96-fold quotients : {2,5}*20
120-fold quotients : {4,2}*16
160-fold quotients : {2,3}*12
240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,245)( 2,246)( 3,248)( 4,247)( 5,242)( 6,241)( 7,243)( 8,244)
( 9,253)( 10,254)( 11,256)( 12,255)( 13,250)( 14,249)( 15,251)( 16,252)
( 17,261)( 18,262)( 19,264)( 20,263)( 21,258)( 22,257)( 23,259)( 24,260)
( 25,269)( 26,270)( 27,272)( 28,271)( 29,266)( 30,265)( 31,267)( 32,268)
( 33,277)( 34,278)( 35,280)( 36,279)( 37,274)( 38,273)( 39,275)( 40,276)
( 41,285)( 42,286)( 43,288)( 44,287)( 45,282)( 46,281)( 47,283)( 48,284)
( 49,293)( 50,294)( 51,296)( 52,295)( 53,290)( 54,289)( 55,291)( 56,292)
( 57,301)( 58,302)( 59,304)( 60,303)( 61,298)( 62,297)( 63,299)( 64,300)
( 65,309)( 66,310)( 67,312)( 68,311)( 69,306)( 70,305)( 71,307)( 72,308)
( 73,317)( 74,318)( 75,320)( 76,319)( 77,314)( 78,313)( 79,315)( 80,316)
( 81,325)( 82,326)( 83,328)( 84,327)( 85,322)( 86,321)( 87,323)( 88,324)
( 89,333)( 90,334)( 91,336)( 92,335)( 93,330)( 94,329)( 95,331)( 96,332)
( 97,341)( 98,342)( 99,344)(100,343)(101,338)(102,337)(103,339)(104,340)
(105,349)(106,350)(107,352)(108,351)(109,346)(110,345)(111,347)(112,348)
(113,357)(114,358)(115,360)(116,359)(117,354)(118,353)(119,355)(120,356)
(121,366)(122,365)(123,367)(124,368)(125,361)(126,362)(127,364)(128,363)
(129,374)(130,373)(131,375)(132,376)(133,369)(134,370)(135,372)(136,371)
(137,382)(138,381)(139,383)(140,384)(141,377)(142,378)(143,380)(144,379)
(145,390)(146,389)(147,391)(148,392)(149,385)(150,386)(151,388)(152,387)
(153,398)(154,397)(155,399)(156,400)(157,393)(158,394)(159,396)(160,395)
(161,406)(162,405)(163,407)(164,408)(165,401)(166,402)(167,404)(168,403)
(169,414)(170,413)(171,415)(172,416)(173,409)(174,410)(175,412)(176,411)
(177,422)(178,421)(179,423)(180,424)(181,417)(182,418)(183,420)(184,419)
(185,430)(186,429)(187,431)(188,432)(189,425)(190,426)(191,428)(192,427)
(193,438)(194,437)(195,439)(196,440)(197,433)(198,434)(199,436)(200,435)
(201,446)(202,445)(203,447)(204,448)(205,441)(206,442)(207,444)(208,443)
(209,454)(210,453)(211,455)(212,456)(213,449)(214,450)(215,452)(216,451)
(217,462)(218,461)(219,463)(220,464)(221,457)(222,458)(223,460)(224,459)
(225,470)(226,469)(227,471)(228,472)(229,465)(230,466)(231,468)(232,467)
(233,478)(234,477)(235,479)(236,480)(237,473)(238,474)(239,476)(240,475);;
s1 := ( 3, 4)( 5, 7)( 6, 8)( 9, 33)( 10, 34)( 11, 36)( 12, 35)( 13, 39)
( 14, 40)( 15, 37)( 16, 38)( 17, 25)( 18, 26)( 19, 28)( 20, 27)( 21, 31)
( 22, 32)( 23, 29)( 24, 30)( 41, 81)( 42, 82)( 43, 84)( 44, 83)( 45, 87)
( 46, 88)( 47, 85)( 48, 86)( 49,113)( 50,114)( 51,116)( 52,115)( 53,119)
( 54,120)( 55,117)( 56,118)( 57,105)( 58,106)( 59,108)( 60,107)( 61,111)
( 62,112)( 63,109)( 64,110)( 65, 97)( 66, 98)( 67,100)( 68, 99)( 69,103)
( 70,104)( 71,101)( 72,102)( 73, 89)( 74, 90)( 75, 92)( 76, 91)( 77, 95)
( 78, 96)( 79, 93)( 80, 94)(121,122)(125,128)(126,127)(129,154)(130,153)
(131,155)(132,156)(133,160)(134,159)(135,158)(136,157)(137,146)(138,145)
(139,147)(140,148)(141,152)(142,151)(143,150)(144,149)(161,202)(162,201)
(163,203)(164,204)(165,208)(166,207)(167,206)(168,205)(169,234)(170,233)
(171,235)(172,236)(173,240)(174,239)(175,238)(176,237)(177,226)(178,225)
(179,227)(180,228)(181,232)(182,231)(183,230)(184,229)(185,218)(186,217)
(187,219)(188,220)(189,224)(190,223)(191,222)(192,221)(193,210)(194,209)
(195,211)(196,212)(197,216)(198,215)(199,214)(200,213)(241,362)(242,361)
(243,363)(244,364)(245,368)(246,367)(247,366)(248,365)(249,394)(250,393)
(251,395)(252,396)(253,400)(254,399)(255,398)(256,397)(257,386)(258,385)
(259,387)(260,388)(261,392)(262,391)(263,390)(264,389)(265,378)(266,377)
(267,379)(268,380)(269,384)(270,383)(271,382)(272,381)(273,370)(274,369)
(275,371)(276,372)(277,376)(278,375)(279,374)(280,373)(281,442)(282,441)
(283,443)(284,444)(285,448)(286,447)(287,446)(288,445)(289,474)(290,473)
(291,475)(292,476)(293,480)(294,479)(295,478)(296,477)(297,466)(298,465)
(299,467)(300,468)(301,472)(302,471)(303,470)(304,469)(305,458)(306,457)
(307,459)(308,460)(309,464)(310,463)(311,462)(312,461)(313,450)(314,449)
(315,451)(316,452)(317,456)(318,455)(319,454)(320,453)(321,402)(322,401)
(323,403)(324,404)(325,408)(326,407)(327,406)(328,405)(329,434)(330,433)
(331,435)(332,436)(333,440)(334,439)(335,438)(336,437)(337,426)(338,425)
(339,427)(340,428)(341,432)(342,431)(343,430)(344,429)(345,418)(346,417)
(347,419)(348,420)(349,424)(350,423)(351,422)(352,421)(353,410)(354,409)
(355,411)(356,412)(357,416)(358,415)(359,414)(360,413);;
s2 := ( 1, 49)( 2, 50)( 3, 55)( 4, 56)( 5, 54)( 6, 53)( 7, 51)( 8, 52)
( 9, 41)( 10, 42)( 11, 47)( 12, 48)( 13, 46)( 14, 45)( 15, 43)( 16, 44)
( 17, 73)( 18, 74)( 19, 79)( 20, 80)( 21, 78)( 22, 77)( 23, 75)( 24, 76)
( 25, 65)( 26, 66)( 27, 71)( 28, 72)( 29, 70)( 30, 69)( 31, 67)( 32, 68)
( 33, 57)( 34, 58)( 35, 63)( 36, 64)( 37, 62)( 38, 61)( 39, 59)( 40, 60)
( 81, 89)( 82, 90)( 83, 95)( 84, 96)( 85, 94)( 86, 93)( 87, 91)( 88, 92)
( 97,113)( 98,114)( 99,119)(100,120)(101,118)(102,117)(103,115)(104,116)
(107,111)(108,112)(109,110)(121,169)(122,170)(123,175)(124,176)(125,174)
(126,173)(127,171)(128,172)(129,161)(130,162)(131,167)(132,168)(133,166)
(134,165)(135,163)(136,164)(137,193)(138,194)(139,199)(140,200)(141,198)
(142,197)(143,195)(144,196)(145,185)(146,186)(147,191)(148,192)(149,190)
(150,189)(151,187)(152,188)(153,177)(154,178)(155,183)(156,184)(157,182)
(158,181)(159,179)(160,180)(201,209)(202,210)(203,215)(204,216)(205,214)
(206,213)(207,211)(208,212)(217,233)(218,234)(219,239)(220,240)(221,238)
(222,237)(223,235)(224,236)(227,231)(228,232)(229,230)(241,290)(242,289)
(243,296)(244,295)(245,293)(246,294)(247,292)(248,291)(249,282)(250,281)
(251,288)(252,287)(253,285)(254,286)(255,284)(256,283)(257,314)(258,313)
(259,320)(260,319)(261,317)(262,318)(263,316)(264,315)(265,306)(266,305)
(267,312)(268,311)(269,309)(270,310)(271,308)(272,307)(273,298)(274,297)
(275,304)(276,303)(277,301)(278,302)(279,300)(280,299)(321,330)(322,329)
(323,336)(324,335)(325,333)(326,334)(327,332)(328,331)(337,354)(338,353)
(339,360)(340,359)(341,357)(342,358)(343,356)(344,355)(345,346)(347,352)
(348,351)(361,410)(362,409)(363,416)(364,415)(365,413)(366,414)(367,412)
(368,411)(369,402)(370,401)(371,408)(372,407)(373,405)(374,406)(375,404)
(376,403)(377,434)(378,433)(379,440)(380,439)(381,437)(382,438)(383,436)
(384,435)(385,426)(386,425)(387,432)(388,431)(389,429)(390,430)(391,428)
(392,427)(393,418)(394,417)(395,424)(396,423)(397,421)(398,422)(399,420)
(400,419)(441,450)(442,449)(443,456)(444,455)(445,453)(446,454)(447,452)
(448,451)(457,474)(458,473)(459,480)(460,479)(461,477)(462,478)(463,476)
(464,475)(465,466)(467,472)(468,471);;
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,
s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s0*s1*s2*s1*s0*s1,
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)!( 1,245)( 2,246)( 3,248)( 4,247)( 5,242)( 6,241)( 7,243)
( 8,244)( 9,253)( 10,254)( 11,256)( 12,255)( 13,250)( 14,249)( 15,251)
( 16,252)( 17,261)( 18,262)( 19,264)( 20,263)( 21,258)( 22,257)( 23,259)
( 24,260)( 25,269)( 26,270)( 27,272)( 28,271)( 29,266)( 30,265)( 31,267)
( 32,268)( 33,277)( 34,278)( 35,280)( 36,279)( 37,274)( 38,273)( 39,275)
( 40,276)( 41,285)( 42,286)( 43,288)( 44,287)( 45,282)( 46,281)( 47,283)
( 48,284)( 49,293)( 50,294)( 51,296)( 52,295)( 53,290)( 54,289)( 55,291)
( 56,292)( 57,301)( 58,302)( 59,304)( 60,303)( 61,298)( 62,297)( 63,299)
( 64,300)( 65,309)( 66,310)( 67,312)( 68,311)( 69,306)( 70,305)( 71,307)
( 72,308)( 73,317)( 74,318)( 75,320)( 76,319)( 77,314)( 78,313)( 79,315)
( 80,316)( 81,325)( 82,326)( 83,328)( 84,327)( 85,322)( 86,321)( 87,323)
( 88,324)( 89,333)( 90,334)( 91,336)( 92,335)( 93,330)( 94,329)( 95,331)
( 96,332)( 97,341)( 98,342)( 99,344)(100,343)(101,338)(102,337)(103,339)
(104,340)(105,349)(106,350)(107,352)(108,351)(109,346)(110,345)(111,347)
(112,348)(113,357)(114,358)(115,360)(116,359)(117,354)(118,353)(119,355)
(120,356)(121,366)(122,365)(123,367)(124,368)(125,361)(126,362)(127,364)
(128,363)(129,374)(130,373)(131,375)(132,376)(133,369)(134,370)(135,372)
(136,371)(137,382)(138,381)(139,383)(140,384)(141,377)(142,378)(143,380)
(144,379)(145,390)(146,389)(147,391)(148,392)(149,385)(150,386)(151,388)
(152,387)(153,398)(154,397)(155,399)(156,400)(157,393)(158,394)(159,396)
(160,395)(161,406)(162,405)(163,407)(164,408)(165,401)(166,402)(167,404)
(168,403)(169,414)(170,413)(171,415)(172,416)(173,409)(174,410)(175,412)
(176,411)(177,422)(178,421)(179,423)(180,424)(181,417)(182,418)(183,420)
(184,419)(185,430)(186,429)(187,431)(188,432)(189,425)(190,426)(191,428)
(192,427)(193,438)(194,437)(195,439)(196,440)(197,433)(198,434)(199,436)
(200,435)(201,446)(202,445)(203,447)(204,448)(205,441)(206,442)(207,444)
(208,443)(209,454)(210,453)(211,455)(212,456)(213,449)(214,450)(215,452)
(216,451)(217,462)(218,461)(219,463)(220,464)(221,457)(222,458)(223,460)
(224,459)(225,470)(226,469)(227,471)(228,472)(229,465)(230,466)(231,468)
(232,467)(233,478)(234,477)(235,479)(236,480)(237,473)(238,474)(239,476)
(240,475);
s1 := Sym(480)!( 3, 4)( 5, 7)( 6, 8)( 9, 33)( 10, 34)( 11, 36)( 12, 35)
( 13, 39)( 14, 40)( 15, 37)( 16, 38)( 17, 25)( 18, 26)( 19, 28)( 20, 27)
( 21, 31)( 22, 32)( 23, 29)( 24, 30)( 41, 81)( 42, 82)( 43, 84)( 44, 83)
( 45, 87)( 46, 88)( 47, 85)( 48, 86)( 49,113)( 50,114)( 51,116)( 52,115)
( 53,119)( 54,120)( 55,117)( 56,118)( 57,105)( 58,106)( 59,108)( 60,107)
( 61,111)( 62,112)( 63,109)( 64,110)( 65, 97)( 66, 98)( 67,100)( 68, 99)
( 69,103)( 70,104)( 71,101)( 72,102)( 73, 89)( 74, 90)( 75, 92)( 76, 91)
( 77, 95)( 78, 96)( 79, 93)( 80, 94)(121,122)(125,128)(126,127)(129,154)
(130,153)(131,155)(132,156)(133,160)(134,159)(135,158)(136,157)(137,146)
(138,145)(139,147)(140,148)(141,152)(142,151)(143,150)(144,149)(161,202)
(162,201)(163,203)(164,204)(165,208)(166,207)(167,206)(168,205)(169,234)
(170,233)(171,235)(172,236)(173,240)(174,239)(175,238)(176,237)(177,226)
(178,225)(179,227)(180,228)(181,232)(182,231)(183,230)(184,229)(185,218)
(186,217)(187,219)(188,220)(189,224)(190,223)(191,222)(192,221)(193,210)
(194,209)(195,211)(196,212)(197,216)(198,215)(199,214)(200,213)(241,362)
(242,361)(243,363)(244,364)(245,368)(246,367)(247,366)(248,365)(249,394)
(250,393)(251,395)(252,396)(253,400)(254,399)(255,398)(256,397)(257,386)
(258,385)(259,387)(260,388)(261,392)(262,391)(263,390)(264,389)(265,378)
(266,377)(267,379)(268,380)(269,384)(270,383)(271,382)(272,381)(273,370)
(274,369)(275,371)(276,372)(277,376)(278,375)(279,374)(280,373)(281,442)
(282,441)(283,443)(284,444)(285,448)(286,447)(287,446)(288,445)(289,474)
(290,473)(291,475)(292,476)(293,480)(294,479)(295,478)(296,477)(297,466)
(298,465)(299,467)(300,468)(301,472)(302,471)(303,470)(304,469)(305,458)
(306,457)(307,459)(308,460)(309,464)(310,463)(311,462)(312,461)(313,450)
(314,449)(315,451)(316,452)(317,456)(318,455)(319,454)(320,453)(321,402)
(322,401)(323,403)(324,404)(325,408)(326,407)(327,406)(328,405)(329,434)
(330,433)(331,435)(332,436)(333,440)(334,439)(335,438)(336,437)(337,426)
(338,425)(339,427)(340,428)(341,432)(342,431)(343,430)(344,429)(345,418)
(346,417)(347,419)(348,420)(349,424)(350,423)(351,422)(352,421)(353,410)
(354,409)(355,411)(356,412)(357,416)(358,415)(359,414)(360,413);
s2 := Sym(480)!( 1, 49)( 2, 50)( 3, 55)( 4, 56)( 5, 54)( 6, 53)( 7, 51)
( 8, 52)( 9, 41)( 10, 42)( 11, 47)( 12, 48)( 13, 46)( 14, 45)( 15, 43)
( 16, 44)( 17, 73)( 18, 74)( 19, 79)( 20, 80)( 21, 78)( 22, 77)( 23, 75)
( 24, 76)( 25, 65)( 26, 66)( 27, 71)( 28, 72)( 29, 70)( 30, 69)( 31, 67)
( 32, 68)( 33, 57)( 34, 58)( 35, 63)( 36, 64)( 37, 62)( 38, 61)( 39, 59)
( 40, 60)( 81, 89)( 82, 90)( 83, 95)( 84, 96)( 85, 94)( 86, 93)( 87, 91)
( 88, 92)( 97,113)( 98,114)( 99,119)(100,120)(101,118)(102,117)(103,115)
(104,116)(107,111)(108,112)(109,110)(121,169)(122,170)(123,175)(124,176)
(125,174)(126,173)(127,171)(128,172)(129,161)(130,162)(131,167)(132,168)
(133,166)(134,165)(135,163)(136,164)(137,193)(138,194)(139,199)(140,200)
(141,198)(142,197)(143,195)(144,196)(145,185)(146,186)(147,191)(148,192)
(149,190)(150,189)(151,187)(152,188)(153,177)(154,178)(155,183)(156,184)
(157,182)(158,181)(159,179)(160,180)(201,209)(202,210)(203,215)(204,216)
(205,214)(206,213)(207,211)(208,212)(217,233)(218,234)(219,239)(220,240)
(221,238)(222,237)(223,235)(224,236)(227,231)(228,232)(229,230)(241,290)
(242,289)(243,296)(244,295)(245,293)(246,294)(247,292)(248,291)(249,282)
(250,281)(251,288)(252,287)(253,285)(254,286)(255,284)(256,283)(257,314)
(258,313)(259,320)(260,319)(261,317)(262,318)(263,316)(264,315)(265,306)
(266,305)(267,312)(268,311)(269,309)(270,310)(271,308)(272,307)(273,298)
(274,297)(275,304)(276,303)(277,301)(278,302)(279,300)(280,299)(321,330)
(322,329)(323,336)(324,335)(325,333)(326,334)(327,332)(328,331)(337,354)
(338,353)(339,360)(340,359)(341,357)(342,358)(343,356)(344,355)(345,346)
(347,352)(348,351)(361,410)(362,409)(363,416)(364,415)(365,413)(366,414)
(367,412)(368,411)(369,402)(370,401)(371,408)(372,407)(373,405)(374,406)
(375,404)(376,403)(377,434)(378,433)(379,440)(380,439)(381,437)(382,438)
(383,436)(384,435)(385,426)(386,425)(387,432)(388,431)(389,429)(390,430)
(391,428)(392,427)(393,418)(394,417)(395,424)(396,423)(397,421)(398,422)
(399,420)(400,419)(441,450)(442,449)(443,456)(444,455)(445,453)(446,454)
(447,452)(448,451)(457,474)(458,473)(459,480)(460,479)(461,477)(462,478)
(463,476)(464,475)(465,466)(467,472)(468,471);
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,
s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s0*s1*s2*s1*s0*s1,
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