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