Polytope of Type {30,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,4}*1920b
if this polytope has a name.
Group : SmallGroup(1920,239570)
Rank : 3
Schlafli Type : {30,4}
Number of vertices, edges, etc : 240, 480, 32
Order of s₀s₁s₂ : 120
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {30,4}*960b
   4-fold quotients : {30,4}*480
   5-fold quotients : {6,4}*384b
   8-fold quotients : {30,4}*240a, {15,4}*240, {30,4}*240b, {30,4}*240c
   10-fold quotients : {6,4}*192b
   16-fold quotients : {15,4}*120, {30,2}*120
   20-fold quotients : {6,4}*96
   24-fold quotients : {10,4}*80
   32-fold quotients : {15,2}*60
   40-fold quotients : {6,4}*48a, {3,4}*48, {6,4}*48b, {6,4}*48c
   48-fold quotients : {10,2}*40
   80-fold quotients : {3,4}*24, {6,2}*24
   96-fold quotients : {5,2}*20
   120-fold quotients : {2,4}*16
   160-fold quotients : {3,2}*12
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope