Polytope of Type {15,8}

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