Polytope of Type {2,30,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,30,8}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240302)
Rank : 4
Schlafli Type : {2,30,8}
Number of vertices, edges, etc : 2, 60, 240, 16
Order of s0s1s2s3 : 60
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
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 : {2,15,8}*960, {2,30,4}*960
4-fold quotients : {2,15,4}*480, {2,30,4}*480b, {2,30,4}*480c
5-fold quotients : {2,6,8}*384b
8-fold quotients : {2,15,4}*240, {2,30,2}*240
10-fold quotients : {2,3,8}*192, {2,6,4}*192
16-fold quotients : {2,15,2}*120
20-fold quotients : {2,3,4}*96, {2,6,4}*96b, {2,6,4}*96c
24-fold quotients : {2,10,2}*80
40-fold quotients : {2,3,4}*48, {2,6,2}*48
48-fold quotients : {2,5,2}*40
80-fold quotients : {2,3,2}*24
120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 5, 8)( 6, 7)( 9, 10)( 11, 35)( 12, 36)( 13, 40)( 14, 39)( 15, 38)
( 16, 37)( 17, 42)( 18, 41)( 19, 27)( 20, 28)( 21, 32)( 22, 31)( 23, 30)
( 24, 29)( 25, 34)( 26, 33)( 43, 83)( 44, 84)( 45, 88)( 46, 87)( 47, 86)
( 48, 85)( 49, 90)( 50, 89)( 51,115)( 52,116)( 53,120)( 54,119)( 55,118)
( 56,117)( 57,122)( 58,121)( 59,107)( 60,108)( 61,112)( 62,111)( 63,110)
( 64,109)( 65,114)( 66,113)( 67, 99)( 68,100)( 69,104)( 70,103)( 71,102)
( 72,101)( 73,106)( 74,105)( 75, 91)( 76, 92)( 77, 96)( 78, 95)( 79, 94)
( 80, 93)( 81, 98)( 82, 97)(123,124)(125,127)(126,128)(131,156)(132,155)
(133,159)(134,160)(135,157)(136,158)(137,161)(138,162)(139,148)(140,147)
(141,151)(142,152)(143,149)(144,150)(145,153)(146,154)(163,204)(164,203)
(165,207)(166,208)(167,205)(168,206)(169,209)(170,210)(171,236)(172,235)
(173,239)(174,240)(175,237)(176,238)(177,241)(178,242)(179,228)(180,227)
(181,231)(182,232)(183,229)(184,230)(185,233)(186,234)(187,220)(188,219)
(189,223)(190,224)(191,221)(192,222)(193,225)(194,226)(195,212)(196,211)
(197,215)(198,216)(199,213)(200,214)(201,217)(202,218)(245,248)(246,247)
(249,250)(251,275)(252,276)(253,280)(254,279)(255,278)(256,277)(257,282)
(258,281)(259,267)(260,268)(261,272)(262,271)(263,270)(264,269)(265,274)
(266,273)(283,323)(284,324)(285,328)(286,327)(287,326)(288,325)(289,330)
(290,329)(291,355)(292,356)(293,360)(294,359)(295,358)(296,357)(297,362)
(298,361)(299,347)(300,348)(301,352)(302,351)(303,350)(304,349)(305,354)
(306,353)(307,339)(308,340)(309,344)(310,343)(311,342)(312,341)(313,346)
(314,345)(315,331)(316,332)(317,336)(318,335)(319,334)(320,333)(321,338)
(322,337)(363,364)(365,367)(366,368)(371,396)(372,395)(373,399)(374,400)
(375,397)(376,398)(377,401)(378,402)(379,388)(380,387)(381,391)(382,392)
(383,389)(384,390)(385,393)(386,394)(403,444)(404,443)(405,447)(406,448)
(407,445)(408,446)(409,449)(410,450)(411,476)(412,475)(413,479)(414,480)
(415,477)(416,478)(417,481)(418,482)(419,468)(420,467)(421,471)(422,472)
(423,469)(424,470)(425,473)(426,474)(427,460)(428,459)(429,463)(430,464)
(431,461)(432,462)(433,465)(434,466)(435,452)(436,451)(437,455)(438,456)
(439,453)(440,454)(441,457)(442,458);;
s2 := ( 3,291)( 4,292)( 5,294)( 6,293)( 7,297)( 8,298)( 9,295)( 10,296)
( 11,283)( 12,284)( 13,286)( 14,285)( 15,289)( 16,290)( 17,287)( 18,288)
( 19,315)( 20,316)( 21,318)( 22,317)( 23,321)( 24,322)( 25,319)( 26,320)
( 27,307)( 28,308)( 29,310)( 30,309)( 31,313)( 32,314)( 33,311)( 34,312)
( 35,299)( 36,300)( 37,302)( 38,301)( 39,305)( 40,306)( 41,303)( 42,304)
( 43,251)( 44,252)( 45,254)( 46,253)( 47,257)( 48,258)( 49,255)( 50,256)
( 51,243)( 52,244)( 53,246)( 54,245)( 55,249)( 56,250)( 57,247)( 58,248)
( 59,275)( 60,276)( 61,278)( 62,277)( 63,281)( 64,282)( 65,279)( 66,280)
( 67,267)( 68,268)( 69,270)( 70,269)( 71,273)( 72,274)( 73,271)( 74,272)
( 75,259)( 76,260)( 77,262)( 78,261)( 79,265)( 80,266)( 81,263)( 82,264)
( 83,331)( 84,332)( 85,334)( 86,333)( 87,337)( 88,338)( 89,335)( 90,336)
( 91,323)( 92,324)( 93,326)( 94,325)( 95,329)( 96,330)( 97,327)( 98,328)
( 99,355)(100,356)(101,358)(102,357)(103,361)(104,362)(105,359)(106,360)
(107,347)(108,348)(109,350)(110,349)(111,353)(112,354)(113,351)(114,352)
(115,339)(116,340)(117,342)(118,341)(119,345)(120,346)(121,343)(122,344)
(123,412)(124,411)(125,413)(126,414)(127,418)(128,417)(129,416)(130,415)
(131,404)(132,403)(133,405)(134,406)(135,410)(136,409)(137,408)(138,407)
(139,436)(140,435)(141,437)(142,438)(143,442)(144,441)(145,440)(146,439)
(147,428)(148,427)(149,429)(150,430)(151,434)(152,433)(153,432)(154,431)
(155,420)(156,419)(157,421)(158,422)(159,426)(160,425)(161,424)(162,423)
(163,372)(164,371)(165,373)(166,374)(167,378)(168,377)(169,376)(170,375)
(171,364)(172,363)(173,365)(174,366)(175,370)(176,369)(177,368)(178,367)
(179,396)(180,395)(181,397)(182,398)(183,402)(184,401)(185,400)(186,399)
(187,388)(188,387)(189,389)(190,390)(191,394)(192,393)(193,392)(194,391)
(195,380)(196,379)(197,381)(198,382)(199,386)(200,385)(201,384)(202,383)
(203,452)(204,451)(205,453)(206,454)(207,458)(208,457)(209,456)(210,455)
(211,444)(212,443)(213,445)(214,446)(215,450)(216,449)(217,448)(218,447)
(219,476)(220,475)(221,477)(222,478)(223,482)(224,481)(225,480)(226,479)
(227,468)(228,467)(229,469)(230,470)(231,474)(232,473)(233,472)(234,471)
(235,460)(236,459)(237,461)(238,462)(239,466)(240,465)(241,464)(242,463);;
s3 := ( 3,129)( 4,130)( 5,127)( 6,128)( 7,126)( 8,125)( 9,124)( 10,123)
( 11,137)( 12,138)( 13,135)( 14,136)( 15,134)( 16,133)( 17,132)( 18,131)
( 19,145)( 20,146)( 21,143)( 22,144)( 23,142)( 24,141)( 25,140)( 26,139)
( 27,153)( 28,154)( 29,151)( 30,152)( 31,150)( 32,149)( 33,148)( 34,147)
( 35,161)( 36,162)( 37,159)( 38,160)( 39,158)( 40,157)( 41,156)( 42,155)
( 43,169)( 44,170)( 45,167)( 46,168)( 47,166)( 48,165)( 49,164)( 50,163)
( 51,177)( 52,178)( 53,175)( 54,176)( 55,174)( 56,173)( 57,172)( 58,171)
( 59,185)( 60,186)( 61,183)( 62,184)( 63,182)( 64,181)( 65,180)( 66,179)
( 67,193)( 68,194)( 69,191)( 70,192)( 71,190)( 72,189)( 73,188)( 74,187)
( 75,201)( 76,202)( 77,199)( 78,200)( 79,198)( 80,197)( 81,196)( 82,195)
( 83,209)( 84,210)( 85,207)( 86,208)( 87,206)( 88,205)( 89,204)( 90,203)
( 91,217)( 92,218)( 93,215)( 94,216)( 95,214)( 96,213)( 97,212)( 98,211)
( 99,225)(100,226)(101,223)(102,224)(103,222)(104,221)(105,220)(106,219)
(107,233)(108,234)(109,231)(110,232)(111,230)(112,229)(113,228)(114,227)
(115,241)(116,242)(117,239)(118,240)(119,238)(120,237)(121,236)(122,235)
(243,369)(244,370)(245,367)(246,368)(247,366)(248,365)(249,364)(250,363)
(251,377)(252,378)(253,375)(254,376)(255,374)(256,373)(257,372)(258,371)
(259,385)(260,386)(261,383)(262,384)(263,382)(264,381)(265,380)(266,379)
(267,393)(268,394)(269,391)(270,392)(271,390)(272,389)(273,388)(274,387)
(275,401)(276,402)(277,399)(278,400)(279,398)(280,397)(281,396)(282,395)
(283,409)(284,410)(285,407)(286,408)(287,406)(288,405)(289,404)(290,403)
(291,417)(292,418)(293,415)(294,416)(295,414)(296,413)(297,412)(298,411)
(299,425)(300,426)(301,423)(302,424)(303,422)(304,421)(305,420)(306,419)
(307,433)(308,434)(309,431)(310,432)(311,430)(312,429)(313,428)(314,427)
(315,441)(316,442)(317,439)(318,440)(319,438)(320,437)(321,436)(322,435)
(323,449)(324,450)(325,447)(326,448)(327,446)(328,445)(329,444)(330,443)
(331,457)(332,458)(333,455)(334,456)(335,454)(336,453)(337,452)(338,451)
(339,465)(340,466)(341,463)(342,464)(343,462)(344,461)(345,460)(346,459)
(347,473)(348,474)(349,471)(350,472)(351,470)(352,469)(353,468)(354,467)
(355,481)(356,482)(357,479)(358,480)(359,478)(360,477)(361,476)(362,475);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*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*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(482)!(1,2);
s1 := Sym(482)!( 5, 8)( 6, 7)( 9, 10)( 11, 35)( 12, 36)( 13, 40)( 14, 39)
( 15, 38)( 16, 37)( 17, 42)( 18, 41)( 19, 27)( 20, 28)( 21, 32)( 22, 31)
( 23, 30)( 24, 29)( 25, 34)( 26, 33)( 43, 83)( 44, 84)( 45, 88)( 46, 87)
( 47, 86)( 48, 85)( 49, 90)( 50, 89)( 51,115)( 52,116)( 53,120)( 54,119)
( 55,118)( 56,117)( 57,122)( 58,121)( 59,107)( 60,108)( 61,112)( 62,111)
( 63,110)( 64,109)( 65,114)( 66,113)( 67, 99)( 68,100)( 69,104)( 70,103)
( 71,102)( 72,101)( 73,106)( 74,105)( 75, 91)( 76, 92)( 77, 96)( 78, 95)
( 79, 94)( 80, 93)( 81, 98)( 82, 97)(123,124)(125,127)(126,128)(131,156)
(132,155)(133,159)(134,160)(135,157)(136,158)(137,161)(138,162)(139,148)
(140,147)(141,151)(142,152)(143,149)(144,150)(145,153)(146,154)(163,204)
(164,203)(165,207)(166,208)(167,205)(168,206)(169,209)(170,210)(171,236)
(172,235)(173,239)(174,240)(175,237)(176,238)(177,241)(178,242)(179,228)
(180,227)(181,231)(182,232)(183,229)(184,230)(185,233)(186,234)(187,220)
(188,219)(189,223)(190,224)(191,221)(192,222)(193,225)(194,226)(195,212)
(196,211)(197,215)(198,216)(199,213)(200,214)(201,217)(202,218)(245,248)
(246,247)(249,250)(251,275)(252,276)(253,280)(254,279)(255,278)(256,277)
(257,282)(258,281)(259,267)(260,268)(261,272)(262,271)(263,270)(264,269)
(265,274)(266,273)(283,323)(284,324)(285,328)(286,327)(287,326)(288,325)
(289,330)(290,329)(291,355)(292,356)(293,360)(294,359)(295,358)(296,357)
(297,362)(298,361)(299,347)(300,348)(301,352)(302,351)(303,350)(304,349)
(305,354)(306,353)(307,339)(308,340)(309,344)(310,343)(311,342)(312,341)
(313,346)(314,345)(315,331)(316,332)(317,336)(318,335)(319,334)(320,333)
(321,338)(322,337)(363,364)(365,367)(366,368)(371,396)(372,395)(373,399)
(374,400)(375,397)(376,398)(377,401)(378,402)(379,388)(380,387)(381,391)
(382,392)(383,389)(384,390)(385,393)(386,394)(403,444)(404,443)(405,447)
(406,448)(407,445)(408,446)(409,449)(410,450)(411,476)(412,475)(413,479)
(414,480)(415,477)(416,478)(417,481)(418,482)(419,468)(420,467)(421,471)
(422,472)(423,469)(424,470)(425,473)(426,474)(427,460)(428,459)(429,463)
(430,464)(431,461)(432,462)(433,465)(434,466)(435,452)(436,451)(437,455)
(438,456)(439,453)(440,454)(441,457)(442,458);
s2 := Sym(482)!( 3,291)( 4,292)( 5,294)( 6,293)( 7,297)( 8,298)( 9,295)
( 10,296)( 11,283)( 12,284)( 13,286)( 14,285)( 15,289)( 16,290)( 17,287)
( 18,288)( 19,315)( 20,316)( 21,318)( 22,317)( 23,321)( 24,322)( 25,319)
( 26,320)( 27,307)( 28,308)( 29,310)( 30,309)( 31,313)( 32,314)( 33,311)
( 34,312)( 35,299)( 36,300)( 37,302)( 38,301)( 39,305)( 40,306)( 41,303)
( 42,304)( 43,251)( 44,252)( 45,254)( 46,253)( 47,257)( 48,258)( 49,255)
( 50,256)( 51,243)( 52,244)( 53,246)( 54,245)( 55,249)( 56,250)( 57,247)
( 58,248)( 59,275)( 60,276)( 61,278)( 62,277)( 63,281)( 64,282)( 65,279)
( 66,280)( 67,267)( 68,268)( 69,270)( 70,269)( 71,273)( 72,274)( 73,271)
( 74,272)( 75,259)( 76,260)( 77,262)( 78,261)( 79,265)( 80,266)( 81,263)
( 82,264)( 83,331)( 84,332)( 85,334)( 86,333)( 87,337)( 88,338)( 89,335)
( 90,336)( 91,323)( 92,324)( 93,326)( 94,325)( 95,329)( 96,330)( 97,327)
( 98,328)( 99,355)(100,356)(101,358)(102,357)(103,361)(104,362)(105,359)
(106,360)(107,347)(108,348)(109,350)(110,349)(111,353)(112,354)(113,351)
(114,352)(115,339)(116,340)(117,342)(118,341)(119,345)(120,346)(121,343)
(122,344)(123,412)(124,411)(125,413)(126,414)(127,418)(128,417)(129,416)
(130,415)(131,404)(132,403)(133,405)(134,406)(135,410)(136,409)(137,408)
(138,407)(139,436)(140,435)(141,437)(142,438)(143,442)(144,441)(145,440)
(146,439)(147,428)(148,427)(149,429)(150,430)(151,434)(152,433)(153,432)
(154,431)(155,420)(156,419)(157,421)(158,422)(159,426)(160,425)(161,424)
(162,423)(163,372)(164,371)(165,373)(166,374)(167,378)(168,377)(169,376)
(170,375)(171,364)(172,363)(173,365)(174,366)(175,370)(176,369)(177,368)
(178,367)(179,396)(180,395)(181,397)(182,398)(183,402)(184,401)(185,400)
(186,399)(187,388)(188,387)(189,389)(190,390)(191,394)(192,393)(193,392)
(194,391)(195,380)(196,379)(197,381)(198,382)(199,386)(200,385)(201,384)
(202,383)(203,452)(204,451)(205,453)(206,454)(207,458)(208,457)(209,456)
(210,455)(211,444)(212,443)(213,445)(214,446)(215,450)(216,449)(217,448)
(218,447)(219,476)(220,475)(221,477)(222,478)(223,482)(224,481)(225,480)
(226,479)(227,468)(228,467)(229,469)(230,470)(231,474)(232,473)(233,472)
(234,471)(235,460)(236,459)(237,461)(238,462)(239,466)(240,465)(241,464)
(242,463);
s3 := Sym(482)!( 3,129)( 4,130)( 5,127)( 6,128)( 7,126)( 8,125)( 9,124)
( 10,123)( 11,137)( 12,138)( 13,135)( 14,136)( 15,134)( 16,133)( 17,132)
( 18,131)( 19,145)( 20,146)( 21,143)( 22,144)( 23,142)( 24,141)( 25,140)
( 26,139)( 27,153)( 28,154)( 29,151)( 30,152)( 31,150)( 32,149)( 33,148)
( 34,147)( 35,161)( 36,162)( 37,159)( 38,160)( 39,158)( 40,157)( 41,156)
( 42,155)( 43,169)( 44,170)( 45,167)( 46,168)( 47,166)( 48,165)( 49,164)
( 50,163)( 51,177)( 52,178)( 53,175)( 54,176)( 55,174)( 56,173)( 57,172)
( 58,171)( 59,185)( 60,186)( 61,183)( 62,184)( 63,182)( 64,181)( 65,180)
( 66,179)( 67,193)( 68,194)( 69,191)( 70,192)( 71,190)( 72,189)( 73,188)
( 74,187)( 75,201)( 76,202)( 77,199)( 78,200)( 79,198)( 80,197)( 81,196)
( 82,195)( 83,209)( 84,210)( 85,207)( 86,208)( 87,206)( 88,205)( 89,204)
( 90,203)( 91,217)( 92,218)( 93,215)( 94,216)( 95,214)( 96,213)( 97,212)
( 98,211)( 99,225)(100,226)(101,223)(102,224)(103,222)(104,221)(105,220)
(106,219)(107,233)(108,234)(109,231)(110,232)(111,230)(112,229)(113,228)
(114,227)(115,241)(116,242)(117,239)(118,240)(119,238)(120,237)(121,236)
(122,235)(243,369)(244,370)(245,367)(246,368)(247,366)(248,365)(249,364)
(250,363)(251,377)(252,378)(253,375)(254,376)(255,374)(256,373)(257,372)
(258,371)(259,385)(260,386)(261,383)(262,384)(263,382)(264,381)(265,380)
(266,379)(267,393)(268,394)(269,391)(270,392)(271,390)(272,389)(273,388)
(274,387)(275,401)(276,402)(277,399)(278,400)(279,398)(280,397)(281,396)
(282,395)(283,409)(284,410)(285,407)(286,408)(287,406)(288,405)(289,404)
(290,403)(291,417)(292,418)(293,415)(294,416)(295,414)(296,413)(297,412)
(298,411)(299,425)(300,426)(301,423)(302,424)(303,422)(304,421)(305,420)
(306,419)(307,433)(308,434)(309,431)(310,432)(311,430)(312,429)(313,428)
(314,427)(315,441)(316,442)(317,439)(318,440)(319,438)(320,437)(321,436)
(322,435)(323,449)(324,450)(325,447)(326,448)(327,446)(328,445)(329,444)
(330,443)(331,457)(332,458)(333,455)(334,456)(335,454)(336,453)(337,452)
(338,451)(339,465)(340,466)(341,463)(342,464)(343,462)(344,461)(345,460)
(346,459)(347,473)(348,474)(349,471)(350,472)(351,470)(352,469)(353,468)
(354,467)(355,481)(356,482)(357,479)(358,480)(359,478)(360,477)(361,476)
(362,475);
poly := sub<Sym(482)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*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*s1*s2 >;
to this polytope