Polytope of Type {159,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {159,6}*1908
if this polytope has a name.
Group : SmallGroup(1908,28)
Rank : 3
Schlafli Type : {159,6}
Number of vertices, edges, etc : 159, 477, 6
Order of s₀s₁s₂ : 318
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {159,2}*636
   9-fold quotients : {53,2}*212
   53-fold quotients : {3,6}*36
   159-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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