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