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