Polytope of Type {8,15}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,15}*960c
if this polytope has a name.
Group : SmallGroup(960,10999)
Rank : 3
Schlafli Type : {8,15}
Number of vertices, edges, etc : 32, 240, 60
Order of s0s1s2 : 30
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{8,15,2} of size 1920
Vertex Figure Of :
{2,8,15} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,15}*480
3-fold quotients : {8,5}*320a
6-fold quotients : {4,5}*160
Covers (Minimal Covers in Boldface) :
2-fold covers : {8,15}*1920b, {8,30}*1920h, {8,30}*1920j
Permutation Representation (GAP) :
s0 := ( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 14)( 6, 13)( 7, 16)( 8, 15)
( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 30)( 22, 29)( 23, 32)( 24, 31)
( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 46)( 38, 45)( 39, 48)( 40, 47)
( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 62)( 54, 61)( 55, 64)( 56, 63)
( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 78)( 70, 77)( 71, 80)( 72, 79)
( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 94)( 86, 93)( 87, 96)( 88, 95)
( 97,105)( 98,106)( 99,107)(100,108)(101,110)(102,109)(103,112)(104,111)
(113,121)(114,122)(115,123)(116,124)(117,126)(118,125)(119,128)(120,127)
(129,137)(130,138)(131,139)(132,140)(133,142)(134,141)(135,144)(136,143)
(145,153)(146,154)(147,155)(148,156)(149,158)(150,157)(151,160)(152,159)
(161,169)(162,170)(163,171)(164,172)(165,174)(166,173)(167,176)(168,175)
(177,185)(178,186)(179,187)(180,188)(181,190)(182,189)(183,192)(184,191)
(193,201)(194,202)(195,203)(196,204)(197,206)(198,205)(199,208)(200,207)
(209,217)(210,218)(211,219)(212,220)(213,222)(214,221)(215,224)(216,223)
(225,233)(226,234)(227,235)(228,236)(229,238)(230,237)(231,240)(232,239)
(241,249)(242,250)(243,251)(244,252)(245,254)(246,253)(247,256)(248,255)
(257,265)(258,266)(259,267)(260,268)(261,270)(262,269)(263,272)(264,271)
(273,281)(274,282)(275,283)(276,284)(277,286)(278,285)(279,288)(280,287)
(289,297)(290,298)(291,299)(292,300)(293,302)(294,301)(295,304)(296,303)
(305,313)(306,314)(307,315)(308,316)(309,318)(310,317)(311,320)(312,319)
(321,329)(322,330)(323,331)(324,332)(325,334)(326,333)(327,336)(328,335)
(337,345)(338,346)(339,347)(340,348)(341,350)(342,349)(343,352)(344,351)
(353,361)(354,362)(355,363)(356,364)(357,366)(358,365)(359,368)(360,367)
(369,377)(370,378)(371,379)(372,380)(373,382)(374,381)(375,384)(376,383)
(385,393)(386,394)(387,395)(388,396)(389,398)(390,397)(391,400)(392,399)
(401,409)(402,410)(403,411)(404,412)(405,414)(406,413)(407,416)(408,415)
(417,425)(418,426)(419,427)(420,428)(421,430)(422,429)(423,432)(424,431)
(433,441)(434,442)(435,443)(436,444)(437,446)(438,445)(439,448)(440,447)
(449,457)(450,458)(451,459)(452,460)(453,462)(454,461)(455,464)(456,463)
(465,473)(466,474)(467,475)(468,476)(469,478)(470,477)(471,480)(472,479);;
s1 := ( 3, 27)( 4, 28)( 5, 18)( 6, 17)( 7, 11)( 8, 12)( 9, 30)( 10, 29)
( 15, 23)( 16, 24)( 19, 32)( 20, 31)( 21, 22)( 25, 26)( 33,129)( 34,130)
( 35,155)( 36,156)( 37,146)( 38,145)( 39,139)( 40,140)( 41,158)( 42,157)
( 43,135)( 44,136)( 45,141)( 46,142)( 47,151)( 48,152)( 49,134)( 50,133)
( 51,160)( 52,159)( 53,150)( 54,149)( 55,143)( 56,144)( 57,154)( 58,153)
( 59,131)( 60,132)( 61,138)( 62,137)( 63,148)( 64,147)( 65, 97)( 66, 98)
( 67,123)( 68,124)( 69,114)( 70,113)( 71,107)( 72,108)( 73,126)( 74,125)
( 75,103)( 76,104)( 77,109)( 78,110)( 79,119)( 80,120)( 81,102)( 82,101)
( 83,128)( 84,127)( 85,118)( 86,117)( 87,111)( 88,112)( 89,122)( 90,121)
( 91, 99)( 92,100)( 93,106)( 94,105)( 95,116)( 96,115)(161,321)(162,322)
(163,347)(164,348)(165,338)(166,337)(167,331)(168,332)(169,350)(170,349)
(171,327)(172,328)(173,333)(174,334)(175,343)(176,344)(177,326)(178,325)
(179,352)(180,351)(181,342)(182,341)(183,335)(184,336)(185,346)(186,345)
(187,323)(188,324)(189,330)(190,329)(191,340)(192,339)(193,449)(194,450)
(195,475)(196,476)(197,466)(198,465)(199,459)(200,460)(201,478)(202,477)
(203,455)(204,456)(205,461)(206,462)(207,471)(208,472)(209,454)(210,453)
(211,480)(212,479)(213,470)(214,469)(215,463)(216,464)(217,474)(218,473)
(219,451)(220,452)(221,458)(222,457)(223,468)(224,467)(225,417)(226,418)
(227,443)(228,444)(229,434)(230,433)(231,427)(232,428)(233,446)(234,445)
(235,423)(236,424)(237,429)(238,430)(239,439)(240,440)(241,422)(242,421)
(243,448)(244,447)(245,438)(246,437)(247,431)(248,432)(249,442)(250,441)
(251,419)(252,420)(253,426)(254,425)(255,436)(256,435)(257,385)(258,386)
(259,411)(260,412)(261,402)(262,401)(263,395)(264,396)(265,414)(266,413)
(267,391)(268,392)(269,397)(270,398)(271,407)(272,408)(273,390)(274,389)
(275,416)(276,415)(277,406)(278,405)(279,399)(280,400)(281,410)(282,409)
(283,387)(284,388)(285,394)(286,393)(287,404)(288,403)(289,353)(290,354)
(291,379)(292,380)(293,370)(294,369)(295,363)(296,364)(297,382)(298,381)
(299,359)(300,360)(301,365)(302,366)(303,375)(304,376)(305,358)(306,357)
(307,384)(308,383)(309,374)(310,373)(311,367)(312,368)(313,378)(314,377)
(315,355)(316,356)(317,362)(318,361)(319,372)(320,371);;
s2 := ( 1,299)( 2,300)( 3,297)( 4,298)( 5,301)( 6,302)( 7,304)( 8,303)
( 9,291)( 10,292)( 11,289)( 12,290)( 13,293)( 14,294)( 15,296)( 16,295)
( 17,308)( 18,307)( 19,306)( 20,305)( 21,310)( 22,309)( 23,311)( 24,312)
( 25,316)( 26,315)( 27,314)( 28,313)( 29,318)( 30,317)( 31,319)( 32,320)
( 33,267)( 34,268)( 35,265)( 36,266)( 37,269)( 38,270)( 39,272)( 40,271)
( 41,259)( 42,260)( 43,257)( 44,258)( 45,261)( 46,262)( 47,264)( 48,263)
( 49,276)( 50,275)( 51,274)( 52,273)( 53,278)( 54,277)( 55,279)( 56,280)
( 57,284)( 58,283)( 59,282)( 60,281)( 61,286)( 62,285)( 63,287)( 64,288)
( 65,235)( 66,236)( 67,233)( 68,234)( 69,237)( 70,238)( 71,240)( 72,239)
( 73,227)( 74,228)( 75,225)( 76,226)( 77,229)( 78,230)( 79,232)( 80,231)
( 81,244)( 82,243)( 83,242)( 84,241)( 85,246)( 86,245)( 87,247)( 88,248)
( 89,252)( 90,251)( 91,250)( 92,249)( 93,254)( 94,253)( 95,255)( 96,256)
( 97,203)( 98,204)( 99,201)(100,202)(101,205)(102,206)(103,208)(104,207)
(105,195)(106,196)(107,193)(108,194)(109,197)(110,198)(111,200)(112,199)
(113,212)(114,211)(115,210)(116,209)(117,214)(118,213)(119,215)(120,216)
(121,220)(122,219)(123,218)(124,217)(125,222)(126,221)(127,223)(128,224)
(129,171)(130,172)(131,169)(132,170)(133,173)(134,174)(135,176)(136,175)
(137,163)(138,164)(139,161)(140,162)(141,165)(142,166)(143,168)(144,167)
(145,180)(146,179)(147,178)(148,177)(149,182)(150,181)(151,183)(152,184)
(153,188)(154,187)(155,186)(156,185)(157,190)(158,189)(159,191)(160,192)
(321,459)(322,460)(323,457)(324,458)(325,461)(326,462)(327,464)(328,463)
(329,451)(330,452)(331,449)(332,450)(333,453)(334,454)(335,456)(336,455)
(337,468)(338,467)(339,466)(340,465)(341,470)(342,469)(343,471)(344,472)
(345,476)(346,475)(347,474)(348,473)(349,478)(350,477)(351,479)(352,480)
(353,427)(354,428)(355,425)(356,426)(357,429)(358,430)(359,432)(360,431)
(361,419)(362,420)(363,417)(364,418)(365,421)(366,422)(367,424)(368,423)
(369,436)(370,435)(371,434)(372,433)(373,438)(374,437)(375,439)(376,440)
(377,444)(378,443)(379,442)(380,441)(381,446)(382,445)(383,447)(384,448)
(385,395)(386,396)(387,393)(388,394)(389,397)(390,398)(391,400)(392,399)
(401,404)(402,403)(405,406)(409,412)(410,411)(413,414);;
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0,
s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0,
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(480)!( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 14)( 6, 13)( 7, 16)
( 8, 15)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 30)( 22, 29)( 23, 32)
( 24, 31)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 46)( 38, 45)( 39, 48)
( 40, 47)( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 62)( 54, 61)( 55, 64)
( 56, 63)( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 78)( 70, 77)( 71, 80)
( 72, 79)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 94)( 86, 93)( 87, 96)
( 88, 95)( 97,105)( 98,106)( 99,107)(100,108)(101,110)(102,109)(103,112)
(104,111)(113,121)(114,122)(115,123)(116,124)(117,126)(118,125)(119,128)
(120,127)(129,137)(130,138)(131,139)(132,140)(133,142)(134,141)(135,144)
(136,143)(145,153)(146,154)(147,155)(148,156)(149,158)(150,157)(151,160)
(152,159)(161,169)(162,170)(163,171)(164,172)(165,174)(166,173)(167,176)
(168,175)(177,185)(178,186)(179,187)(180,188)(181,190)(182,189)(183,192)
(184,191)(193,201)(194,202)(195,203)(196,204)(197,206)(198,205)(199,208)
(200,207)(209,217)(210,218)(211,219)(212,220)(213,222)(214,221)(215,224)
(216,223)(225,233)(226,234)(227,235)(228,236)(229,238)(230,237)(231,240)
(232,239)(241,249)(242,250)(243,251)(244,252)(245,254)(246,253)(247,256)
(248,255)(257,265)(258,266)(259,267)(260,268)(261,270)(262,269)(263,272)
(264,271)(273,281)(274,282)(275,283)(276,284)(277,286)(278,285)(279,288)
(280,287)(289,297)(290,298)(291,299)(292,300)(293,302)(294,301)(295,304)
(296,303)(305,313)(306,314)(307,315)(308,316)(309,318)(310,317)(311,320)
(312,319)(321,329)(322,330)(323,331)(324,332)(325,334)(326,333)(327,336)
(328,335)(337,345)(338,346)(339,347)(340,348)(341,350)(342,349)(343,352)
(344,351)(353,361)(354,362)(355,363)(356,364)(357,366)(358,365)(359,368)
(360,367)(369,377)(370,378)(371,379)(372,380)(373,382)(374,381)(375,384)
(376,383)(385,393)(386,394)(387,395)(388,396)(389,398)(390,397)(391,400)
(392,399)(401,409)(402,410)(403,411)(404,412)(405,414)(406,413)(407,416)
(408,415)(417,425)(418,426)(419,427)(420,428)(421,430)(422,429)(423,432)
(424,431)(433,441)(434,442)(435,443)(436,444)(437,446)(438,445)(439,448)
(440,447)(449,457)(450,458)(451,459)(452,460)(453,462)(454,461)(455,464)
(456,463)(465,473)(466,474)(467,475)(468,476)(469,478)(470,477)(471,480)
(472,479);
s1 := Sym(480)!( 3, 27)( 4, 28)( 5, 18)( 6, 17)( 7, 11)( 8, 12)( 9, 30)
( 10, 29)( 15, 23)( 16, 24)( 19, 32)( 20, 31)( 21, 22)( 25, 26)( 33,129)
( 34,130)( 35,155)( 36,156)( 37,146)( 38,145)( 39,139)( 40,140)( 41,158)
( 42,157)( 43,135)( 44,136)( 45,141)( 46,142)( 47,151)( 48,152)( 49,134)
( 50,133)( 51,160)( 52,159)( 53,150)( 54,149)( 55,143)( 56,144)( 57,154)
( 58,153)( 59,131)( 60,132)( 61,138)( 62,137)( 63,148)( 64,147)( 65, 97)
( 66, 98)( 67,123)( 68,124)( 69,114)( 70,113)( 71,107)( 72,108)( 73,126)
( 74,125)( 75,103)( 76,104)( 77,109)( 78,110)( 79,119)( 80,120)( 81,102)
( 82,101)( 83,128)( 84,127)( 85,118)( 86,117)( 87,111)( 88,112)( 89,122)
( 90,121)( 91, 99)( 92,100)( 93,106)( 94,105)( 95,116)( 96,115)(161,321)
(162,322)(163,347)(164,348)(165,338)(166,337)(167,331)(168,332)(169,350)
(170,349)(171,327)(172,328)(173,333)(174,334)(175,343)(176,344)(177,326)
(178,325)(179,352)(180,351)(181,342)(182,341)(183,335)(184,336)(185,346)
(186,345)(187,323)(188,324)(189,330)(190,329)(191,340)(192,339)(193,449)
(194,450)(195,475)(196,476)(197,466)(198,465)(199,459)(200,460)(201,478)
(202,477)(203,455)(204,456)(205,461)(206,462)(207,471)(208,472)(209,454)
(210,453)(211,480)(212,479)(213,470)(214,469)(215,463)(216,464)(217,474)
(218,473)(219,451)(220,452)(221,458)(222,457)(223,468)(224,467)(225,417)
(226,418)(227,443)(228,444)(229,434)(230,433)(231,427)(232,428)(233,446)
(234,445)(235,423)(236,424)(237,429)(238,430)(239,439)(240,440)(241,422)
(242,421)(243,448)(244,447)(245,438)(246,437)(247,431)(248,432)(249,442)
(250,441)(251,419)(252,420)(253,426)(254,425)(255,436)(256,435)(257,385)
(258,386)(259,411)(260,412)(261,402)(262,401)(263,395)(264,396)(265,414)
(266,413)(267,391)(268,392)(269,397)(270,398)(271,407)(272,408)(273,390)
(274,389)(275,416)(276,415)(277,406)(278,405)(279,399)(280,400)(281,410)
(282,409)(283,387)(284,388)(285,394)(286,393)(287,404)(288,403)(289,353)
(290,354)(291,379)(292,380)(293,370)(294,369)(295,363)(296,364)(297,382)
(298,381)(299,359)(300,360)(301,365)(302,366)(303,375)(304,376)(305,358)
(306,357)(307,384)(308,383)(309,374)(310,373)(311,367)(312,368)(313,378)
(314,377)(315,355)(316,356)(317,362)(318,361)(319,372)(320,371);
s2 := Sym(480)!( 1,299)( 2,300)( 3,297)( 4,298)( 5,301)( 6,302)( 7,304)
( 8,303)( 9,291)( 10,292)( 11,289)( 12,290)( 13,293)( 14,294)( 15,296)
( 16,295)( 17,308)( 18,307)( 19,306)( 20,305)( 21,310)( 22,309)( 23,311)
( 24,312)( 25,316)( 26,315)( 27,314)( 28,313)( 29,318)( 30,317)( 31,319)
( 32,320)( 33,267)( 34,268)( 35,265)( 36,266)( 37,269)( 38,270)( 39,272)
( 40,271)( 41,259)( 42,260)( 43,257)( 44,258)( 45,261)( 46,262)( 47,264)
( 48,263)( 49,276)( 50,275)( 51,274)( 52,273)( 53,278)( 54,277)( 55,279)
( 56,280)( 57,284)( 58,283)( 59,282)( 60,281)( 61,286)( 62,285)( 63,287)
( 64,288)( 65,235)( 66,236)( 67,233)( 68,234)( 69,237)( 70,238)( 71,240)
( 72,239)( 73,227)( 74,228)( 75,225)( 76,226)( 77,229)( 78,230)( 79,232)
( 80,231)( 81,244)( 82,243)( 83,242)( 84,241)( 85,246)( 86,245)( 87,247)
( 88,248)( 89,252)( 90,251)( 91,250)( 92,249)( 93,254)( 94,253)( 95,255)
( 96,256)( 97,203)( 98,204)( 99,201)(100,202)(101,205)(102,206)(103,208)
(104,207)(105,195)(106,196)(107,193)(108,194)(109,197)(110,198)(111,200)
(112,199)(113,212)(114,211)(115,210)(116,209)(117,214)(118,213)(119,215)
(120,216)(121,220)(122,219)(123,218)(124,217)(125,222)(126,221)(127,223)
(128,224)(129,171)(130,172)(131,169)(132,170)(133,173)(134,174)(135,176)
(136,175)(137,163)(138,164)(139,161)(140,162)(141,165)(142,166)(143,168)
(144,167)(145,180)(146,179)(147,178)(148,177)(149,182)(150,181)(151,183)
(152,184)(153,188)(154,187)(155,186)(156,185)(157,190)(158,189)(159,191)
(160,192)(321,459)(322,460)(323,457)(324,458)(325,461)(326,462)(327,464)
(328,463)(329,451)(330,452)(331,449)(332,450)(333,453)(334,454)(335,456)
(336,455)(337,468)(338,467)(339,466)(340,465)(341,470)(342,469)(343,471)
(344,472)(345,476)(346,475)(347,474)(348,473)(349,478)(350,477)(351,479)
(352,480)(353,427)(354,428)(355,425)(356,426)(357,429)(358,430)(359,432)
(360,431)(361,419)(362,420)(363,417)(364,418)(365,421)(366,422)(367,424)
(368,423)(369,436)(370,435)(371,434)(372,433)(373,438)(374,437)(375,439)
(376,440)(377,444)(378,443)(379,442)(380,441)(381,446)(382,445)(383,447)
(384,448)(385,395)(386,396)(387,393)(388,394)(389,397)(390,398)(391,400)
(392,399)(401,404)(402,403)(405,406)(409,412)(410,411)(413,414);
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0,
s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0,
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 >;
References : None.
to this polytope