Polytope of Type {15,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,10}*1920
if this polytope has a name.
Group : SmallGroup(1920,240046)
Rank : 3
Schlafli Type : {15,10}
Number of vertices, edges, etc : 96, 480, 64
Order of s0s1s2 : 24
Order of s0s1s2s1 : 10
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {15,10}*960
3-fold quotients : {5,10}*640
6-fold quotients : {5,5}*320, {5,10}*320a, {5,10}*320b
12-fold quotients : {5,5}*160
160-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 5, 8)( 6, 7)( 9, 11)( 10, 12)( 13, 14)( 15, 16)( 17, 32)( 18, 31)
( 19, 30)( 20, 29)( 21, 26)( 22, 25)( 23, 28)( 24, 27)( 33,129)( 34,130)
( 35,131)( 36,132)( 37,136)( 38,135)( 39,134)( 40,133)( 41,139)( 42,140)
( 43,137)( 44,138)( 45,142)( 46,141)( 47,144)( 48,143)( 49,160)( 50,159)
( 51,158)( 52,157)( 53,154)( 54,153)( 55,156)( 56,155)( 57,150)( 58,149)
( 59,152)( 60,151)( 61,148)( 62,147)( 63,146)( 64,145)( 65, 97)( 66, 98)
( 67, 99)( 68,100)( 69,104)( 70,103)( 71,102)( 72,101)( 73,107)( 74,108)
( 75,105)( 76,106)( 77,110)( 78,109)( 79,112)( 80,111)( 81,128)( 82,127)
( 83,126)( 84,125)( 85,122)( 86,121)( 87,124)( 88,123)( 89,118)( 90,117)
( 91,120)( 92,119)( 93,116)( 94,115)( 95,114)( 96,113)(161,321)(162,322)
(163,323)(164,324)(165,328)(166,327)(167,326)(168,325)(169,331)(170,332)
(171,329)(172,330)(173,334)(174,333)(175,336)(176,335)(177,352)(178,351)
(179,350)(180,349)(181,346)(182,345)(183,348)(184,347)(185,342)(186,341)
(187,344)(188,343)(189,340)(190,339)(191,338)(192,337)(193,449)(194,450)
(195,451)(196,452)(197,456)(198,455)(199,454)(200,453)(201,459)(202,460)
(203,457)(204,458)(205,462)(206,461)(207,464)(208,463)(209,480)(210,479)
(211,478)(212,477)(213,474)(214,473)(215,476)(216,475)(217,470)(218,469)
(219,472)(220,471)(221,468)(222,467)(223,466)(224,465)(225,417)(226,418)
(227,419)(228,420)(229,424)(230,423)(231,422)(232,421)(233,427)(234,428)
(235,425)(236,426)(237,430)(238,429)(239,432)(240,431)(241,448)(242,447)
(243,446)(244,445)(245,442)(246,441)(247,444)(248,443)(249,438)(250,437)
(251,440)(252,439)(253,436)(254,435)(255,434)(256,433)(257,385)(258,386)
(259,387)(260,388)(261,392)(262,391)(263,390)(264,389)(265,395)(266,396)
(267,393)(268,394)(269,398)(270,397)(271,400)(272,399)(273,416)(274,415)
(275,414)(276,413)(277,410)(278,409)(279,412)(280,411)(281,406)(282,405)
(283,408)(284,407)(285,404)(286,403)(287,402)(288,401)(289,353)(290,354)
(291,355)(292,356)(293,360)(294,359)(295,358)(296,357)(297,363)(298,364)
(299,361)(300,362)(301,366)(302,365)(303,368)(304,367)(305,384)(306,383)
(307,382)(308,381)(309,378)(310,377)(311,380)(312,379)(313,374)(314,373)
(315,376)(316,375)(317,372)(318,371)(319,370)(320,369);;
s1 := ( 1,193)( 2,194)( 3,212)( 4,211)( 5,213)( 6,214)( 7,200)( 8,199)
( 9,224)( 10,223)( 11,205)( 12,206)( 13,203)( 14,204)( 15,218)( 16,217)
( 17,210)( 18,209)( 19,196)( 20,195)( 21,197)( 22,198)( 23,215)( 24,216)
( 25,208)( 26,207)( 27,222)( 28,221)( 29,220)( 30,219)( 31,202)( 32,201)
( 33,161)( 34,162)( 35,180)( 36,179)( 37,181)( 38,182)( 39,168)( 40,167)
( 41,192)( 42,191)( 43,173)( 44,174)( 45,171)( 46,172)( 47,186)( 48,185)
( 49,178)( 50,177)( 51,164)( 52,163)( 53,165)( 54,166)( 55,183)( 56,184)
( 57,176)( 58,175)( 59,190)( 60,189)( 61,188)( 62,187)( 63,170)( 64,169)
( 65,289)( 66,290)( 67,308)( 68,307)( 69,309)( 70,310)( 71,296)( 72,295)
( 73,320)( 74,319)( 75,301)( 76,302)( 77,299)( 78,300)( 79,314)( 80,313)
( 81,306)( 82,305)( 83,292)( 84,291)( 85,293)( 86,294)( 87,311)( 88,312)
( 89,304)( 90,303)( 91,318)( 92,317)( 93,316)( 94,315)( 95,298)( 96,297)
( 97,257)( 98,258)( 99,276)(100,275)(101,277)(102,278)(103,264)(104,263)
(105,288)(106,287)(107,269)(108,270)(109,267)(110,268)(111,282)(112,281)
(113,274)(114,273)(115,260)(116,259)(117,261)(118,262)(119,279)(120,280)
(121,272)(122,271)(123,286)(124,285)(125,284)(126,283)(127,266)(128,265)
(129,225)(130,226)(131,244)(132,243)(133,245)(134,246)(135,232)(136,231)
(137,256)(138,255)(139,237)(140,238)(141,235)(142,236)(143,250)(144,249)
(145,242)(146,241)(147,228)(148,227)(149,229)(150,230)(151,247)(152,248)
(153,240)(154,239)(155,254)(156,253)(157,252)(158,251)(159,234)(160,233)
(321,353)(322,354)(323,372)(324,371)(325,373)(326,374)(327,360)(328,359)
(329,384)(330,383)(331,365)(332,366)(333,363)(334,364)(335,378)(336,377)
(337,370)(338,369)(339,356)(340,355)(341,357)(342,358)(343,375)(344,376)
(345,368)(346,367)(347,382)(348,381)(349,380)(350,379)(351,362)(352,361)
(385,449)(386,450)(387,468)(388,467)(389,469)(390,470)(391,456)(392,455)
(393,480)(394,479)(395,461)(396,462)(397,459)(398,460)(399,474)(400,473)
(401,466)(402,465)(403,452)(404,451)(405,453)(406,454)(407,471)(408,472)
(409,464)(410,463)(411,478)(412,477)(413,476)(414,475)(415,458)(416,457)
(419,436)(420,435)(421,437)(422,438)(423,424)(425,448)(426,447)(427,429)
(428,430)(431,442)(432,441)(433,434)(443,446)(444,445);;
s2 := ( 1, 3)( 2, 4)( 5, 6)( 7, 8)( 13, 16)( 14, 15)( 17, 30)( 18, 29)
( 19, 32)( 20, 31)( 21, 28)( 22, 27)( 23, 26)( 24, 25)( 33,131)( 34,132)
( 35,129)( 36,130)( 37,134)( 38,133)( 39,136)( 40,135)( 41,137)( 42,138)
( 43,139)( 44,140)( 45,144)( 46,143)( 47,142)( 48,141)( 49,158)( 50,157)
( 51,160)( 52,159)( 53,156)( 54,155)( 55,154)( 56,153)( 57,152)( 58,151)
( 59,150)( 60,149)( 61,146)( 62,145)( 63,148)( 64,147)( 65, 99)( 66,100)
( 67, 97)( 68, 98)( 69,102)( 70,101)( 71,104)( 72,103)( 73,105)( 74,106)
( 75,107)( 76,108)( 77,112)( 78,111)( 79,110)( 80,109)( 81,126)( 82,125)
( 83,128)( 84,127)( 85,124)( 86,123)( 87,122)( 88,121)( 89,120)( 90,119)
( 91,118)( 92,117)( 93,114)( 94,113)( 95,116)( 96,115)(161,163)(162,164)
(165,166)(167,168)(173,176)(174,175)(177,190)(178,189)(179,192)(180,191)
(181,188)(182,187)(183,186)(184,185)(193,291)(194,292)(195,289)(196,290)
(197,294)(198,293)(199,296)(200,295)(201,297)(202,298)(203,299)(204,300)
(205,304)(206,303)(207,302)(208,301)(209,318)(210,317)(211,320)(212,319)
(213,316)(214,315)(215,314)(216,313)(217,312)(218,311)(219,310)(220,309)
(221,306)(222,305)(223,308)(224,307)(225,259)(226,260)(227,257)(228,258)
(229,262)(230,261)(231,264)(232,263)(233,265)(234,266)(235,267)(236,268)
(237,272)(238,271)(239,270)(240,269)(241,286)(242,285)(243,288)(244,287)
(245,284)(246,283)(247,282)(248,281)(249,280)(250,279)(251,278)(252,277)
(253,274)(254,273)(255,276)(256,275)(321,323)(322,324)(325,326)(327,328)
(333,336)(334,335)(337,350)(338,349)(339,352)(340,351)(341,348)(342,347)
(343,346)(344,345)(353,451)(354,452)(355,449)(356,450)(357,454)(358,453)
(359,456)(360,455)(361,457)(362,458)(363,459)(364,460)(365,464)(366,463)
(367,462)(368,461)(369,478)(370,477)(371,480)(372,479)(373,476)(374,475)
(375,474)(376,473)(377,472)(378,471)(379,470)(380,469)(381,466)(382,465)
(383,468)(384,467)(385,419)(386,420)(387,417)(388,418)(389,422)(390,421)
(391,424)(392,423)(393,425)(394,426)(395,427)(396,428)(397,432)(398,431)
(399,430)(400,429)(401,446)(402,445)(403,448)(404,447)(405,444)(406,443)
(407,442)(408,441)(409,440)(410,439)(411,438)(412,437)(413,434)(414,433)
(415,436)(416,435);;
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*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(480)!( 5, 8)( 6, 7)( 9, 11)( 10, 12)( 13, 14)( 15, 16)( 17, 32)
( 18, 31)( 19, 30)( 20, 29)( 21, 26)( 22, 25)( 23, 28)( 24, 27)( 33,129)
( 34,130)( 35,131)( 36,132)( 37,136)( 38,135)( 39,134)( 40,133)( 41,139)
( 42,140)( 43,137)( 44,138)( 45,142)( 46,141)( 47,144)( 48,143)( 49,160)
( 50,159)( 51,158)( 52,157)( 53,154)( 54,153)( 55,156)( 56,155)( 57,150)
( 58,149)( 59,152)( 60,151)( 61,148)( 62,147)( 63,146)( 64,145)( 65, 97)
( 66, 98)( 67, 99)( 68,100)( 69,104)( 70,103)( 71,102)( 72,101)( 73,107)
( 74,108)( 75,105)( 76,106)( 77,110)( 78,109)( 79,112)( 80,111)( 81,128)
( 82,127)( 83,126)( 84,125)( 85,122)( 86,121)( 87,124)( 88,123)( 89,118)
( 90,117)( 91,120)( 92,119)( 93,116)( 94,115)( 95,114)( 96,113)(161,321)
(162,322)(163,323)(164,324)(165,328)(166,327)(167,326)(168,325)(169,331)
(170,332)(171,329)(172,330)(173,334)(174,333)(175,336)(176,335)(177,352)
(178,351)(179,350)(180,349)(181,346)(182,345)(183,348)(184,347)(185,342)
(186,341)(187,344)(188,343)(189,340)(190,339)(191,338)(192,337)(193,449)
(194,450)(195,451)(196,452)(197,456)(198,455)(199,454)(200,453)(201,459)
(202,460)(203,457)(204,458)(205,462)(206,461)(207,464)(208,463)(209,480)
(210,479)(211,478)(212,477)(213,474)(214,473)(215,476)(216,475)(217,470)
(218,469)(219,472)(220,471)(221,468)(222,467)(223,466)(224,465)(225,417)
(226,418)(227,419)(228,420)(229,424)(230,423)(231,422)(232,421)(233,427)
(234,428)(235,425)(236,426)(237,430)(238,429)(239,432)(240,431)(241,448)
(242,447)(243,446)(244,445)(245,442)(246,441)(247,444)(248,443)(249,438)
(250,437)(251,440)(252,439)(253,436)(254,435)(255,434)(256,433)(257,385)
(258,386)(259,387)(260,388)(261,392)(262,391)(263,390)(264,389)(265,395)
(266,396)(267,393)(268,394)(269,398)(270,397)(271,400)(272,399)(273,416)
(274,415)(275,414)(276,413)(277,410)(278,409)(279,412)(280,411)(281,406)
(282,405)(283,408)(284,407)(285,404)(286,403)(287,402)(288,401)(289,353)
(290,354)(291,355)(292,356)(293,360)(294,359)(295,358)(296,357)(297,363)
(298,364)(299,361)(300,362)(301,366)(302,365)(303,368)(304,367)(305,384)
(306,383)(307,382)(308,381)(309,378)(310,377)(311,380)(312,379)(313,374)
(314,373)(315,376)(316,375)(317,372)(318,371)(319,370)(320,369);
s1 := Sym(480)!( 1,193)( 2,194)( 3,212)( 4,211)( 5,213)( 6,214)( 7,200)
( 8,199)( 9,224)( 10,223)( 11,205)( 12,206)( 13,203)( 14,204)( 15,218)
( 16,217)( 17,210)( 18,209)( 19,196)( 20,195)( 21,197)( 22,198)( 23,215)
( 24,216)( 25,208)( 26,207)( 27,222)( 28,221)( 29,220)( 30,219)( 31,202)
( 32,201)( 33,161)( 34,162)( 35,180)( 36,179)( 37,181)( 38,182)( 39,168)
( 40,167)( 41,192)( 42,191)( 43,173)( 44,174)( 45,171)( 46,172)( 47,186)
( 48,185)( 49,178)( 50,177)( 51,164)( 52,163)( 53,165)( 54,166)( 55,183)
( 56,184)( 57,176)( 58,175)( 59,190)( 60,189)( 61,188)( 62,187)( 63,170)
( 64,169)( 65,289)( 66,290)( 67,308)( 68,307)( 69,309)( 70,310)( 71,296)
( 72,295)( 73,320)( 74,319)( 75,301)( 76,302)( 77,299)( 78,300)( 79,314)
( 80,313)( 81,306)( 82,305)( 83,292)( 84,291)( 85,293)( 86,294)( 87,311)
( 88,312)( 89,304)( 90,303)( 91,318)( 92,317)( 93,316)( 94,315)( 95,298)
( 96,297)( 97,257)( 98,258)( 99,276)(100,275)(101,277)(102,278)(103,264)
(104,263)(105,288)(106,287)(107,269)(108,270)(109,267)(110,268)(111,282)
(112,281)(113,274)(114,273)(115,260)(116,259)(117,261)(118,262)(119,279)
(120,280)(121,272)(122,271)(123,286)(124,285)(125,284)(126,283)(127,266)
(128,265)(129,225)(130,226)(131,244)(132,243)(133,245)(134,246)(135,232)
(136,231)(137,256)(138,255)(139,237)(140,238)(141,235)(142,236)(143,250)
(144,249)(145,242)(146,241)(147,228)(148,227)(149,229)(150,230)(151,247)
(152,248)(153,240)(154,239)(155,254)(156,253)(157,252)(158,251)(159,234)
(160,233)(321,353)(322,354)(323,372)(324,371)(325,373)(326,374)(327,360)
(328,359)(329,384)(330,383)(331,365)(332,366)(333,363)(334,364)(335,378)
(336,377)(337,370)(338,369)(339,356)(340,355)(341,357)(342,358)(343,375)
(344,376)(345,368)(346,367)(347,382)(348,381)(349,380)(350,379)(351,362)
(352,361)(385,449)(386,450)(387,468)(388,467)(389,469)(390,470)(391,456)
(392,455)(393,480)(394,479)(395,461)(396,462)(397,459)(398,460)(399,474)
(400,473)(401,466)(402,465)(403,452)(404,451)(405,453)(406,454)(407,471)
(408,472)(409,464)(410,463)(411,478)(412,477)(413,476)(414,475)(415,458)
(416,457)(419,436)(420,435)(421,437)(422,438)(423,424)(425,448)(426,447)
(427,429)(428,430)(431,442)(432,441)(433,434)(443,446)(444,445);
s2 := Sym(480)!( 1, 3)( 2, 4)( 5, 6)( 7, 8)( 13, 16)( 14, 15)( 17, 30)
( 18, 29)( 19, 32)( 20, 31)( 21, 28)( 22, 27)( 23, 26)( 24, 25)( 33,131)
( 34,132)( 35,129)( 36,130)( 37,134)( 38,133)( 39,136)( 40,135)( 41,137)
( 42,138)( 43,139)( 44,140)( 45,144)( 46,143)( 47,142)( 48,141)( 49,158)
( 50,157)( 51,160)( 52,159)( 53,156)( 54,155)( 55,154)( 56,153)( 57,152)
( 58,151)( 59,150)( 60,149)( 61,146)( 62,145)( 63,148)( 64,147)( 65, 99)
( 66,100)( 67, 97)( 68, 98)( 69,102)( 70,101)( 71,104)( 72,103)( 73,105)
( 74,106)( 75,107)( 76,108)( 77,112)( 78,111)( 79,110)( 80,109)( 81,126)
( 82,125)( 83,128)( 84,127)( 85,124)( 86,123)( 87,122)( 88,121)( 89,120)
( 90,119)( 91,118)( 92,117)( 93,114)( 94,113)( 95,116)( 96,115)(161,163)
(162,164)(165,166)(167,168)(173,176)(174,175)(177,190)(178,189)(179,192)
(180,191)(181,188)(182,187)(183,186)(184,185)(193,291)(194,292)(195,289)
(196,290)(197,294)(198,293)(199,296)(200,295)(201,297)(202,298)(203,299)
(204,300)(205,304)(206,303)(207,302)(208,301)(209,318)(210,317)(211,320)
(212,319)(213,316)(214,315)(215,314)(216,313)(217,312)(218,311)(219,310)
(220,309)(221,306)(222,305)(223,308)(224,307)(225,259)(226,260)(227,257)
(228,258)(229,262)(230,261)(231,264)(232,263)(233,265)(234,266)(235,267)
(236,268)(237,272)(238,271)(239,270)(240,269)(241,286)(242,285)(243,288)
(244,287)(245,284)(246,283)(247,282)(248,281)(249,280)(250,279)(251,278)
(252,277)(253,274)(254,273)(255,276)(256,275)(321,323)(322,324)(325,326)
(327,328)(333,336)(334,335)(337,350)(338,349)(339,352)(340,351)(341,348)
(342,347)(343,346)(344,345)(353,451)(354,452)(355,449)(356,450)(357,454)
(358,453)(359,456)(360,455)(361,457)(362,458)(363,459)(364,460)(365,464)
(366,463)(367,462)(368,461)(369,478)(370,477)(371,480)(372,479)(373,476)
(374,475)(375,474)(376,473)(377,472)(378,471)(379,470)(380,469)(381,466)
(382,465)(383,468)(384,467)(385,419)(386,420)(387,417)(388,418)(389,422)
(390,421)(391,424)(392,423)(393,425)(394,426)(395,427)(396,428)(397,432)
(398,431)(399,430)(400,429)(401,446)(402,445)(403,448)(404,447)(405,444)
(406,443)(407,442)(408,441)(409,440)(410,439)(411,438)(412,437)(413,434)
(414,433)(415,436)(416,435);
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*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s0*s1 >;
References : None.
to this polytope