Polytope of Type {2,15,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,15,8}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240269)
Rank : 4
Schlafli Type : {2,15,8}
Number of vertices, edges, etc : 2, 60, 240, 32
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-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 : {2,15,4}*960
3-fold quotients : {2,5,8}*640a
6-fold quotients : {2,5,4}*320
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 5, 29)( 6, 30)( 7, 20)( 8, 19)( 9, 13)( 10, 14)( 11, 32)( 12, 31)
( 17, 25)( 18, 26)( 21, 34)( 22, 33)( 23, 24)( 27, 28)( 35,131)( 36,132)
( 37,157)( 38,158)( 39,148)( 40,147)( 41,141)( 42,142)( 43,160)( 44,159)
( 45,137)( 46,138)( 47,143)( 48,144)( 49,153)( 50,154)( 51,136)( 52,135)
( 53,162)( 54,161)( 55,152)( 56,151)( 57,145)( 58,146)( 59,156)( 60,155)
( 61,133)( 62,134)( 63,140)( 64,139)( 65,150)( 66,149)( 67, 99)( 68,100)
( 69,125)( 70,126)( 71,116)( 72,115)( 73,109)( 74,110)( 75,128)( 76,127)
( 77,105)( 78,106)( 79,111)( 80,112)( 81,121)( 82,122)( 83,104)( 84,103)
( 85,130)( 86,129)( 87,120)( 88,119)( 89,113)( 90,114)( 91,124)( 92,123)
( 93,101)( 94,102)( 95,108)( 96,107)( 97,118)( 98,117)(163,323)(164,324)
(165,349)(166,350)(167,340)(168,339)(169,333)(170,334)(171,352)(172,351)
(173,329)(174,330)(175,335)(176,336)(177,345)(178,346)(179,328)(180,327)
(181,354)(182,353)(183,344)(184,343)(185,337)(186,338)(187,348)(188,347)
(189,325)(190,326)(191,332)(192,331)(193,342)(194,341)(195,451)(196,452)
(197,477)(198,478)(199,468)(200,467)(201,461)(202,462)(203,480)(204,479)
(205,457)(206,458)(207,463)(208,464)(209,473)(210,474)(211,456)(212,455)
(213,482)(214,481)(215,472)(216,471)(217,465)(218,466)(219,476)(220,475)
(221,453)(222,454)(223,460)(224,459)(225,470)(226,469)(227,419)(228,420)
(229,445)(230,446)(231,436)(232,435)(233,429)(234,430)(235,448)(236,447)
(237,425)(238,426)(239,431)(240,432)(241,441)(242,442)(243,424)(244,423)
(245,450)(246,449)(247,440)(248,439)(249,433)(250,434)(251,444)(252,443)
(253,421)(254,422)(255,428)(256,427)(257,438)(258,437)(259,387)(260,388)
(261,413)(262,414)(263,404)(264,403)(265,397)(266,398)(267,416)(268,415)
(269,393)(270,394)(271,399)(272,400)(273,409)(274,410)(275,392)(276,391)
(277,418)(278,417)(279,408)(280,407)(281,401)(282,402)(283,412)(284,411)
(285,389)(286,390)(287,396)(288,395)(289,406)(290,405)(291,355)(292,356)
(293,381)(294,382)(295,372)(296,371)(297,365)(298,366)(299,384)(300,383)
(301,361)(302,362)(303,367)(304,368)(305,377)(306,378)(307,360)(308,359)
(309,386)(310,385)(311,376)(312,375)(313,369)(314,370)(315,380)(316,379)
(317,357)(318,358)(319,364)(320,363)(321,374)(322,373);;
s2 := ( 3,195)( 4,196)( 5,226)( 6,225)( 7,220)( 8,219)( 9,202)( 10,201)
( 11,209)( 12,210)( 13,212)( 14,211)( 15,217)( 16,218)( 17,203)( 18,204)
( 19,206)( 20,205)( 21,216)( 22,215)( 23,214)( 24,213)( 25,207)( 26,208)
( 27,200)( 28,199)( 29,222)( 30,221)( 31,223)( 32,224)( 33,198)( 34,197)
( 35,163)( 36,164)( 37,194)( 38,193)( 39,188)( 40,187)( 41,170)( 42,169)
( 43,177)( 44,178)( 45,180)( 46,179)( 47,185)( 48,186)( 49,171)( 50,172)
( 51,174)( 52,173)( 53,184)( 54,183)( 55,182)( 56,181)( 57,175)( 58,176)
( 59,168)( 60,167)( 61,190)( 62,189)( 63,191)( 64,192)( 65,166)( 66,165)
( 67,291)( 68,292)( 69,322)( 70,321)( 71,316)( 72,315)( 73,298)( 74,297)
( 75,305)( 76,306)( 77,308)( 78,307)( 79,313)( 80,314)( 81,299)( 82,300)
( 83,302)( 84,301)( 85,312)( 86,311)( 87,310)( 88,309)( 89,303)( 90,304)
( 91,296)( 92,295)( 93,318)( 94,317)( 95,319)( 96,320)( 97,294)( 98,293)
( 99,259)(100,260)(101,290)(102,289)(103,284)(104,283)(105,266)(106,265)
(107,273)(108,274)(109,276)(110,275)(111,281)(112,282)(113,267)(114,268)
(115,270)(116,269)(117,280)(118,279)(119,278)(120,277)(121,271)(122,272)
(123,264)(124,263)(125,286)(126,285)(127,287)(128,288)(129,262)(130,261)
(131,227)(132,228)(133,258)(134,257)(135,252)(136,251)(137,234)(138,233)
(139,241)(140,242)(141,244)(142,243)(143,249)(144,250)(145,235)(146,236)
(147,238)(148,237)(149,248)(150,247)(151,246)(152,245)(153,239)(154,240)
(155,232)(156,231)(157,254)(158,253)(159,255)(160,256)(161,230)(162,229)
(323,355)(324,356)(325,386)(326,385)(327,380)(328,379)(329,362)(330,361)
(331,369)(332,370)(333,372)(334,371)(335,377)(336,378)(337,363)(338,364)
(339,366)(340,365)(341,376)(342,375)(343,374)(344,373)(345,367)(346,368)
(347,360)(348,359)(349,382)(350,381)(351,383)(352,384)(353,358)(354,357)
(387,451)(388,452)(389,482)(390,481)(391,476)(392,475)(393,458)(394,457)
(395,465)(396,466)(397,468)(398,467)(399,473)(400,474)(401,459)(402,460)
(403,462)(404,461)(405,472)(406,471)(407,470)(408,469)(409,463)(410,464)
(411,456)(412,455)(413,478)(414,477)(415,479)(416,480)(417,454)(418,453)
(421,450)(422,449)(423,444)(424,443)(425,426)(427,433)(428,434)(429,436)
(430,435)(431,441)(432,442)(437,440)(438,439)(445,446);;
s3 := ( 3, 15)( 4, 16)( 5, 18)( 6, 17)( 7, 11)( 8, 12)( 9, 14)( 10, 13)
( 19, 31)( 20, 32)( 21, 34)( 22, 33)( 23, 27)( 24, 28)( 25, 30)( 26, 29)
( 35, 47)( 36, 48)( 37, 50)( 38, 49)( 39, 43)( 40, 44)( 41, 46)( 42, 45)
( 51, 63)( 52, 64)( 53, 66)( 54, 65)( 55, 59)( 56, 60)( 57, 62)( 58, 61)
( 67, 79)( 68, 80)( 69, 82)( 70, 81)( 71, 75)( 72, 76)( 73, 78)( 74, 77)
( 83, 95)( 84, 96)( 85, 98)( 86, 97)( 87, 91)( 88, 92)( 89, 94)( 90, 93)
( 99,111)(100,112)(101,114)(102,113)(103,107)(104,108)(105,110)(106,109)
(115,127)(116,128)(117,130)(118,129)(119,123)(120,124)(121,126)(122,125)
(131,143)(132,144)(133,146)(134,145)(135,139)(136,140)(137,142)(138,141)
(147,159)(148,160)(149,162)(150,161)(151,155)(152,156)(153,158)(154,157)
(163,175)(164,176)(165,178)(166,177)(167,171)(168,172)(169,174)(170,173)
(179,191)(180,192)(181,194)(182,193)(183,187)(184,188)(185,190)(186,189)
(195,207)(196,208)(197,210)(198,209)(199,203)(200,204)(201,206)(202,205)
(211,223)(212,224)(213,226)(214,225)(215,219)(216,220)(217,222)(218,221)
(227,239)(228,240)(229,242)(230,241)(231,235)(232,236)(233,238)(234,237)
(243,255)(244,256)(245,258)(246,257)(247,251)(248,252)(249,254)(250,253)
(259,271)(260,272)(261,274)(262,273)(263,267)(264,268)(265,270)(266,269)
(275,287)(276,288)(277,290)(278,289)(279,283)(280,284)(281,286)(282,285)
(291,303)(292,304)(293,306)(294,305)(295,299)(296,300)(297,302)(298,301)
(307,319)(308,320)(309,322)(310,321)(311,315)(312,316)(313,318)(314,317)
(323,335)(324,336)(325,338)(326,337)(327,331)(328,332)(329,334)(330,333)
(339,351)(340,352)(341,354)(342,353)(343,347)(344,348)(345,350)(346,349)
(355,367)(356,368)(357,370)(358,369)(359,363)(360,364)(361,366)(362,365)
(371,383)(372,384)(373,386)(374,385)(375,379)(376,380)(377,382)(378,381)
(387,399)(388,400)(389,402)(390,401)(391,395)(392,396)(393,398)(394,397)
(403,415)(404,416)(405,418)(406,417)(407,411)(408,412)(409,414)(410,413)
(419,431)(420,432)(421,434)(422,433)(423,427)(424,428)(425,430)(426,429)
(435,447)(436,448)(437,450)(438,449)(439,443)(440,444)(441,446)(442,445)
(451,463)(452,464)(453,466)(454,465)(455,459)(456,460)(457,462)(458,461)
(467,479)(468,480)(469,482)(470,481)(471,475)(472,476)(473,478)(474,477);;
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*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s3,
s2*s3*s1*s2*s1*s2*s3*s2*s1*s3*s2*s1*s2*s1*s3*s2*s3*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(482)!(1,2);
s1 := Sym(482)!( 5, 29)( 6, 30)( 7, 20)( 8, 19)( 9, 13)( 10, 14)( 11, 32)
( 12, 31)( 17, 25)( 18, 26)( 21, 34)( 22, 33)( 23, 24)( 27, 28)( 35,131)
( 36,132)( 37,157)( 38,158)( 39,148)( 40,147)( 41,141)( 42,142)( 43,160)
( 44,159)( 45,137)( 46,138)( 47,143)( 48,144)( 49,153)( 50,154)( 51,136)
( 52,135)( 53,162)( 54,161)( 55,152)( 56,151)( 57,145)( 58,146)( 59,156)
( 60,155)( 61,133)( 62,134)( 63,140)( 64,139)( 65,150)( 66,149)( 67, 99)
( 68,100)( 69,125)( 70,126)( 71,116)( 72,115)( 73,109)( 74,110)( 75,128)
( 76,127)( 77,105)( 78,106)( 79,111)( 80,112)( 81,121)( 82,122)( 83,104)
( 84,103)( 85,130)( 86,129)( 87,120)( 88,119)( 89,113)( 90,114)( 91,124)
( 92,123)( 93,101)( 94,102)( 95,108)( 96,107)( 97,118)( 98,117)(163,323)
(164,324)(165,349)(166,350)(167,340)(168,339)(169,333)(170,334)(171,352)
(172,351)(173,329)(174,330)(175,335)(176,336)(177,345)(178,346)(179,328)
(180,327)(181,354)(182,353)(183,344)(184,343)(185,337)(186,338)(187,348)
(188,347)(189,325)(190,326)(191,332)(192,331)(193,342)(194,341)(195,451)
(196,452)(197,477)(198,478)(199,468)(200,467)(201,461)(202,462)(203,480)
(204,479)(205,457)(206,458)(207,463)(208,464)(209,473)(210,474)(211,456)
(212,455)(213,482)(214,481)(215,472)(216,471)(217,465)(218,466)(219,476)
(220,475)(221,453)(222,454)(223,460)(224,459)(225,470)(226,469)(227,419)
(228,420)(229,445)(230,446)(231,436)(232,435)(233,429)(234,430)(235,448)
(236,447)(237,425)(238,426)(239,431)(240,432)(241,441)(242,442)(243,424)
(244,423)(245,450)(246,449)(247,440)(248,439)(249,433)(250,434)(251,444)
(252,443)(253,421)(254,422)(255,428)(256,427)(257,438)(258,437)(259,387)
(260,388)(261,413)(262,414)(263,404)(264,403)(265,397)(266,398)(267,416)
(268,415)(269,393)(270,394)(271,399)(272,400)(273,409)(274,410)(275,392)
(276,391)(277,418)(278,417)(279,408)(280,407)(281,401)(282,402)(283,412)
(284,411)(285,389)(286,390)(287,396)(288,395)(289,406)(290,405)(291,355)
(292,356)(293,381)(294,382)(295,372)(296,371)(297,365)(298,366)(299,384)
(300,383)(301,361)(302,362)(303,367)(304,368)(305,377)(306,378)(307,360)
(308,359)(309,386)(310,385)(311,376)(312,375)(313,369)(314,370)(315,380)
(316,379)(317,357)(318,358)(319,364)(320,363)(321,374)(322,373);
s2 := Sym(482)!( 3,195)( 4,196)( 5,226)( 6,225)( 7,220)( 8,219)( 9,202)
( 10,201)( 11,209)( 12,210)( 13,212)( 14,211)( 15,217)( 16,218)( 17,203)
( 18,204)( 19,206)( 20,205)( 21,216)( 22,215)( 23,214)( 24,213)( 25,207)
( 26,208)( 27,200)( 28,199)( 29,222)( 30,221)( 31,223)( 32,224)( 33,198)
( 34,197)( 35,163)( 36,164)( 37,194)( 38,193)( 39,188)( 40,187)( 41,170)
( 42,169)( 43,177)( 44,178)( 45,180)( 46,179)( 47,185)( 48,186)( 49,171)
( 50,172)( 51,174)( 52,173)( 53,184)( 54,183)( 55,182)( 56,181)( 57,175)
( 58,176)( 59,168)( 60,167)( 61,190)( 62,189)( 63,191)( 64,192)( 65,166)
( 66,165)( 67,291)( 68,292)( 69,322)( 70,321)( 71,316)( 72,315)( 73,298)
( 74,297)( 75,305)( 76,306)( 77,308)( 78,307)( 79,313)( 80,314)( 81,299)
( 82,300)( 83,302)( 84,301)( 85,312)( 86,311)( 87,310)( 88,309)( 89,303)
( 90,304)( 91,296)( 92,295)( 93,318)( 94,317)( 95,319)( 96,320)( 97,294)
( 98,293)( 99,259)(100,260)(101,290)(102,289)(103,284)(104,283)(105,266)
(106,265)(107,273)(108,274)(109,276)(110,275)(111,281)(112,282)(113,267)
(114,268)(115,270)(116,269)(117,280)(118,279)(119,278)(120,277)(121,271)
(122,272)(123,264)(124,263)(125,286)(126,285)(127,287)(128,288)(129,262)
(130,261)(131,227)(132,228)(133,258)(134,257)(135,252)(136,251)(137,234)
(138,233)(139,241)(140,242)(141,244)(142,243)(143,249)(144,250)(145,235)
(146,236)(147,238)(148,237)(149,248)(150,247)(151,246)(152,245)(153,239)
(154,240)(155,232)(156,231)(157,254)(158,253)(159,255)(160,256)(161,230)
(162,229)(323,355)(324,356)(325,386)(326,385)(327,380)(328,379)(329,362)
(330,361)(331,369)(332,370)(333,372)(334,371)(335,377)(336,378)(337,363)
(338,364)(339,366)(340,365)(341,376)(342,375)(343,374)(344,373)(345,367)
(346,368)(347,360)(348,359)(349,382)(350,381)(351,383)(352,384)(353,358)
(354,357)(387,451)(388,452)(389,482)(390,481)(391,476)(392,475)(393,458)
(394,457)(395,465)(396,466)(397,468)(398,467)(399,473)(400,474)(401,459)
(402,460)(403,462)(404,461)(405,472)(406,471)(407,470)(408,469)(409,463)
(410,464)(411,456)(412,455)(413,478)(414,477)(415,479)(416,480)(417,454)
(418,453)(421,450)(422,449)(423,444)(424,443)(425,426)(427,433)(428,434)
(429,436)(430,435)(431,441)(432,442)(437,440)(438,439)(445,446);
s3 := Sym(482)!( 3, 15)( 4, 16)( 5, 18)( 6, 17)( 7, 11)( 8, 12)( 9, 14)
( 10, 13)( 19, 31)( 20, 32)( 21, 34)( 22, 33)( 23, 27)( 24, 28)( 25, 30)
( 26, 29)( 35, 47)( 36, 48)( 37, 50)( 38, 49)( 39, 43)( 40, 44)( 41, 46)
( 42, 45)( 51, 63)( 52, 64)( 53, 66)( 54, 65)( 55, 59)( 56, 60)( 57, 62)
( 58, 61)( 67, 79)( 68, 80)( 69, 82)( 70, 81)( 71, 75)( 72, 76)( 73, 78)
( 74, 77)( 83, 95)( 84, 96)( 85, 98)( 86, 97)( 87, 91)( 88, 92)( 89, 94)
( 90, 93)( 99,111)(100,112)(101,114)(102,113)(103,107)(104,108)(105,110)
(106,109)(115,127)(116,128)(117,130)(118,129)(119,123)(120,124)(121,126)
(122,125)(131,143)(132,144)(133,146)(134,145)(135,139)(136,140)(137,142)
(138,141)(147,159)(148,160)(149,162)(150,161)(151,155)(152,156)(153,158)
(154,157)(163,175)(164,176)(165,178)(166,177)(167,171)(168,172)(169,174)
(170,173)(179,191)(180,192)(181,194)(182,193)(183,187)(184,188)(185,190)
(186,189)(195,207)(196,208)(197,210)(198,209)(199,203)(200,204)(201,206)
(202,205)(211,223)(212,224)(213,226)(214,225)(215,219)(216,220)(217,222)
(218,221)(227,239)(228,240)(229,242)(230,241)(231,235)(232,236)(233,238)
(234,237)(243,255)(244,256)(245,258)(246,257)(247,251)(248,252)(249,254)
(250,253)(259,271)(260,272)(261,274)(262,273)(263,267)(264,268)(265,270)
(266,269)(275,287)(276,288)(277,290)(278,289)(279,283)(280,284)(281,286)
(282,285)(291,303)(292,304)(293,306)(294,305)(295,299)(296,300)(297,302)
(298,301)(307,319)(308,320)(309,322)(310,321)(311,315)(312,316)(313,318)
(314,317)(323,335)(324,336)(325,338)(326,337)(327,331)(328,332)(329,334)
(330,333)(339,351)(340,352)(341,354)(342,353)(343,347)(344,348)(345,350)
(346,349)(355,367)(356,368)(357,370)(358,369)(359,363)(360,364)(361,366)
(362,365)(371,383)(372,384)(373,386)(374,385)(375,379)(376,380)(377,382)
(378,381)(387,399)(388,400)(389,402)(390,401)(391,395)(392,396)(393,398)
(394,397)(403,415)(404,416)(405,418)(406,417)(407,411)(408,412)(409,414)
(410,413)(419,431)(420,432)(421,434)(422,433)(423,427)(424,428)(425,430)
(426,429)(435,447)(436,448)(437,450)(438,449)(439,443)(440,444)(441,446)
(442,445)(451,463)(452,464)(453,466)(454,465)(455,459)(456,460)(457,462)
(458,461)(467,479)(468,480)(469,482)(470,481)(471,475)(472,476)(473,478)
(474,477);
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*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s3,
s2*s3*s1*s2*s1*s2*s3*s2*s1*s3*s2*s1*s2*s1*s3*s2*s3*s2*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 >;
to this polytope