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# Polytope of Type {15,8}

Atlas Canonical Name : {15,8}*960b
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 : 15
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
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}*320a
6-fold quotients : {5,4}*160
Covers (Minimal Covers in Boldface) :
2-fold covers : {15,8}*1920b, {30,8}*1920i, {30,8}*1920k
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, 13)(  2, 14)(  3, 16)(  4, 15)(  5,  9)(  6, 10)(  7, 12)(  8, 11)
( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)( 23, 28)( 24, 27)
( 33, 45)( 34, 46)( 35, 48)( 36, 47)( 37, 41)( 38, 42)( 39, 44)( 40, 43)
( 49, 61)( 50, 62)( 51, 64)( 52, 63)( 53, 57)( 54, 58)( 55, 60)( 56, 59)
( 65, 77)( 66, 78)( 67, 80)( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)
( 81, 93)( 82, 94)( 83, 96)( 84, 95)( 85, 89)( 86, 90)( 87, 92)( 88, 91)
( 97,109)( 98,110)( 99,112)(100,111)(101,105)(102,106)(103,108)(104,107)
(113,125)(114,126)(115,128)(116,127)(117,121)(118,122)(119,124)(120,123)
(129,141)(130,142)(131,144)(132,143)(133,137)(134,138)(135,140)(136,139)
(145,157)(146,158)(147,160)(148,159)(149,153)(150,154)(151,156)(152,155)
(161,173)(162,174)(163,176)(164,175)(165,169)(166,170)(167,172)(168,171)
(177,189)(178,190)(179,192)(180,191)(181,185)(182,186)(183,188)(184,187)
(193,205)(194,206)(195,208)(196,207)(197,201)(198,202)(199,204)(200,203)
(209,221)(210,222)(211,224)(212,223)(213,217)(214,218)(215,220)(216,219)
(225,237)(226,238)(227,240)(228,239)(229,233)(230,234)(231,236)(232,235)
(241,253)(242,254)(243,256)(244,255)(245,249)(246,250)(247,252)(248,251)
(257,269)(258,270)(259,272)(260,271)(261,265)(262,266)(263,268)(264,267)
(273,285)(274,286)(275,288)(276,287)(277,281)(278,282)(279,284)(280,283)
(289,301)(290,302)(291,304)(292,303)(293,297)(294,298)(295,300)(296,299)
(305,317)(306,318)(307,320)(308,319)(309,313)(310,314)(311,316)(312,315)
(321,333)(322,334)(323,336)(324,335)(325,329)(326,330)(327,332)(328,331)
(337,349)(338,350)(339,352)(340,351)(341,345)(342,346)(343,348)(344,347)
(353,365)(354,366)(355,368)(356,367)(357,361)(358,362)(359,364)(360,363)
(369,381)(370,382)(371,384)(372,383)(373,377)(374,378)(375,380)(376,379)
(385,397)(386,398)(387,400)(388,399)(389,393)(390,394)(391,396)(392,395)
(401,413)(402,414)(403,416)(404,415)(405,409)(406,410)(407,412)(408,411)
(417,429)(418,430)(419,432)(420,431)(421,425)(422,426)(423,428)(424,427)
(433,445)(434,446)(435,448)(436,447)(437,441)(438,442)(439,444)(440,443)
(449,461)(450,462)(451,464)(452,463)(453,457)(454,458)(455,460)(456,459)
(465,477)(466,478)(467,480)(468,479)(469,473)(470,474)(471,476)(472,475);;
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,
s1*s2*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0,
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, 13)(  2, 14)(  3, 16)(  4, 15)(  5,  9)(  6, 10)(  7, 12)
(  8, 11)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)( 23, 28)
( 24, 27)( 33, 45)( 34, 46)( 35, 48)( 36, 47)( 37, 41)( 38, 42)( 39, 44)
( 40, 43)( 49, 61)( 50, 62)( 51, 64)( 52, 63)( 53, 57)( 54, 58)( 55, 60)
( 56, 59)( 65, 77)( 66, 78)( 67, 80)( 68, 79)( 69, 73)( 70, 74)( 71, 76)
( 72, 75)( 81, 93)( 82, 94)( 83, 96)( 84, 95)( 85, 89)( 86, 90)( 87, 92)
( 88, 91)( 97,109)( 98,110)( 99,112)(100,111)(101,105)(102,106)(103,108)
(104,107)(113,125)(114,126)(115,128)(116,127)(117,121)(118,122)(119,124)
(120,123)(129,141)(130,142)(131,144)(132,143)(133,137)(134,138)(135,140)
(136,139)(145,157)(146,158)(147,160)(148,159)(149,153)(150,154)(151,156)
(152,155)(161,173)(162,174)(163,176)(164,175)(165,169)(166,170)(167,172)
(168,171)(177,189)(178,190)(179,192)(180,191)(181,185)(182,186)(183,188)
(184,187)(193,205)(194,206)(195,208)(196,207)(197,201)(198,202)(199,204)
(200,203)(209,221)(210,222)(211,224)(212,223)(213,217)(214,218)(215,220)
(216,219)(225,237)(226,238)(227,240)(228,239)(229,233)(230,234)(231,236)
(232,235)(241,253)(242,254)(243,256)(244,255)(245,249)(246,250)(247,252)
(248,251)(257,269)(258,270)(259,272)(260,271)(261,265)(262,266)(263,268)
(264,267)(273,285)(274,286)(275,288)(276,287)(277,281)(278,282)(279,284)
(280,283)(289,301)(290,302)(291,304)(292,303)(293,297)(294,298)(295,300)
(296,299)(305,317)(306,318)(307,320)(308,319)(309,313)(310,314)(311,316)
(312,315)(321,333)(322,334)(323,336)(324,335)(325,329)(326,330)(327,332)
(328,331)(337,349)(338,350)(339,352)(340,351)(341,345)(342,346)(343,348)
(344,347)(353,365)(354,366)(355,368)(356,367)(357,361)(358,362)(359,364)
(360,363)(369,381)(370,382)(371,384)(372,383)(373,377)(374,378)(375,380)
(376,379)(385,397)(386,398)(387,400)(388,399)(389,393)(390,394)(391,396)
(392,395)(401,413)(402,414)(403,416)(404,415)(405,409)(406,410)(407,412)
(408,411)(417,429)(418,430)(419,432)(420,431)(421,425)(422,426)(423,428)
(424,427)(433,445)(434,446)(435,448)(436,447)(437,441)(438,442)(439,444)
(440,443)(449,461)(450,462)(451,464)(452,463)(453,457)(454,458)(455,460)
(456,459)(465,477)(466,478)(467,480)(468,479)(469,473)(470,474)(471,476)
(472,475);
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,
s1*s2*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0,
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