Polytope of Type {6,159}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,159}*1908
if this polytope has a name.
Group : SmallGroup(1908,28)
Rank : 3
Schlafli Type : {6,159}
Number of vertices, edges, etc : 6, 477, 159
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 : {2,159}*636
9-fold quotients : {2,53}*212
53-fold quotients : {6,3}*36
159-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 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);;
s1 := ( 1, 54)( 2,106)( 3,105)( 4,104)( 5,103)( 6,102)( 7,101)( 8,100)
( 9, 99)( 10, 98)( 11, 97)( 12, 96)( 13, 95)( 14, 94)( 15, 93)( 16, 92)
( 17, 91)( 18, 90)( 19, 89)( 20, 88)( 21, 87)( 22, 86)( 23, 85)( 24, 84)
( 25, 83)( 26, 82)( 27, 81)( 28, 80)( 29, 79)( 30, 78)( 31, 77)( 32, 76)
( 33, 75)( 34, 74)( 35, 73)( 36, 72)( 37, 71)( 38, 70)( 39, 69)( 40, 68)
( 41, 67)( 42, 66)( 43, 65)( 44, 64)( 45, 63)( 46, 62)( 47, 61)( 48, 60)
( 49, 59)( 50, 58)( 51, 57)( 52, 56)( 53, 55)(108,159)(109,158)(110,157)
(111,156)(112,155)(113,154)(114,153)(115,152)(116,151)(117,150)(118,149)
(119,148)(120,147)(121,146)(122,145)(123,144)(124,143)(125,142)(126,141)
(127,140)(128,139)(129,138)(130,137)(131,136)(132,135)(133,134)(160,372)
(161,424)(162,423)(163,422)(164,421)(165,420)(166,419)(167,418)(168,417)
(169,416)(170,415)(171,414)(172,413)(173,412)(174,411)(175,410)(176,409)
(177,408)(178,407)(179,406)(180,405)(181,404)(182,403)(183,402)(184,401)
(185,400)(186,399)(187,398)(188,397)(189,396)(190,395)(191,394)(192,393)
(193,392)(194,391)(195,390)(196,389)(197,388)(198,387)(199,386)(200,385)
(201,384)(202,383)(203,382)(204,381)(205,380)(206,379)(207,378)(208,377)
(209,376)(210,375)(211,374)(212,373)(213,319)(214,371)(215,370)(216,369)
(217,368)(218,367)(219,366)(220,365)(221,364)(222,363)(223,362)(224,361)
(225,360)(226,359)(227,358)(228,357)(229,356)(230,355)(231,354)(232,353)
(233,352)(234,351)(235,350)(236,349)(237,348)(238,347)(239,346)(240,345)
(241,344)(242,343)(243,342)(244,341)(245,340)(246,339)(247,338)(248,337)
(249,336)(250,335)(251,334)(252,333)(253,332)(254,331)(255,330)(256,329)
(257,328)(258,327)(259,326)(260,325)(261,324)(262,323)(263,322)(264,321)
(265,320)(266,425)(267,477)(268,476)(269,475)(270,474)(271,473)(272,472)
(273,471)(274,470)(275,469)(276,468)(277,467)(278,466)(279,465)(280,464)
(281,463)(282,462)(283,461)(284,460)(285,459)(286,458)(287,457)(288,456)
(289,455)(290,454)(291,453)(292,452)(293,451)(294,450)(295,449)(296,448)
(297,447)(298,446)(299,445)(300,444)(301,443)(302,442)(303,441)(304,440)
(305,439)(306,438)(307,437)(308,436)(309,435)(310,434)(311,433)(312,432)
(313,431)(314,430)(315,429)(316,428)(317,427)(318,426);;
s2 := ( 1,161)( 2,160)( 3,212)( 4,211)( 5,210)( 6,209)( 7,208)( 8,207)
( 9,206)( 10,205)( 11,204)( 12,203)( 13,202)( 14,201)( 15,200)( 16,199)
( 17,198)( 18,197)( 19,196)( 20,195)( 21,194)( 22,193)( 23,192)( 24,191)
( 25,190)( 26,189)( 27,188)( 28,187)( 29,186)( 30,185)( 31,184)( 32,183)
( 33,182)( 34,181)( 35,180)( 36,179)( 37,178)( 38,177)( 39,176)( 40,175)
( 41,174)( 42,173)( 43,172)( 44,171)( 45,170)( 46,169)( 47,168)( 48,167)
( 49,166)( 50,165)( 51,164)( 52,163)( 53,162)( 54,267)( 55,266)( 56,318)
( 57,317)( 58,316)( 59,315)( 60,314)( 61,313)( 62,312)( 63,311)( 64,310)
( 65,309)( 66,308)( 67,307)( 68,306)( 69,305)( 70,304)( 71,303)( 72,302)
( 73,301)( 74,300)( 75,299)( 76,298)( 77,297)( 78,296)( 79,295)( 80,294)
( 81,293)( 82,292)( 83,291)( 84,290)( 85,289)( 86,288)( 87,287)( 88,286)
( 89,285)( 90,284)( 91,283)( 92,282)( 93,281)( 94,280)( 95,279)( 96,278)
( 97,277)( 98,276)( 99,275)(100,274)(101,273)(102,272)(103,271)(104,270)
(105,269)(106,268)(107,214)(108,213)(109,265)(110,264)(111,263)(112,262)
(113,261)(114,260)(115,259)(116,258)(117,257)(118,256)(119,255)(120,254)
(121,253)(122,252)(123,251)(124,250)(125,249)(126,248)(127,247)(128,246)
(129,245)(130,244)(131,243)(132,242)(133,241)(134,240)(135,239)(136,238)
(137,237)(138,236)(139,235)(140,234)(141,233)(142,232)(143,231)(144,230)
(145,229)(146,228)(147,227)(148,226)(149,225)(150,224)(151,223)(152,222)
(153,221)(154,220)(155,219)(156,218)(157,217)(158,216)(159,215)(319,320)
(321,371)(322,370)(323,369)(324,368)(325,367)(326,366)(327,365)(328,364)
(329,363)(330,362)(331,361)(332,360)(333,359)(334,358)(335,357)(336,356)
(337,355)(338,354)(339,353)(340,352)(341,351)(342,350)(343,349)(344,348)
(345,347)(372,426)(373,425)(374,477)(375,476)(376,475)(377,474)(378,473)
(379,472)(380,471)(381,470)(382,469)(383,468)(384,467)(385,466)(386,465)
(387,464)(388,463)(389,462)(390,461)(391,460)(392,459)(393,458)(394,457)
(395,456)(396,455)(397,454)(398,453)(399,452)(400,451)(401,450)(402,449)
(403,448)(404,447)(405,446)(406,445)(407,444)(408,443)(409,442)(410,441)
(411,440)(412,439)(413,438)(414,437)(415,436)(416,435)(417,434)(418,433)
(419,432)(420,431)(421,430)(422,429)(423,428)(424,427);;
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*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s0*s1*s0*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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);
s1 := Sym(477)!( 1, 54)( 2,106)( 3,105)( 4,104)( 5,103)( 6,102)( 7,101)
( 8,100)( 9, 99)( 10, 98)( 11, 97)( 12, 96)( 13, 95)( 14, 94)( 15, 93)
( 16, 92)( 17, 91)( 18, 90)( 19, 89)( 20, 88)( 21, 87)( 22, 86)( 23, 85)
( 24, 84)( 25, 83)( 26, 82)( 27, 81)( 28, 80)( 29, 79)( 30, 78)( 31, 77)
( 32, 76)( 33, 75)( 34, 74)( 35, 73)( 36, 72)( 37, 71)( 38, 70)( 39, 69)
( 40, 68)( 41, 67)( 42, 66)( 43, 65)( 44, 64)( 45, 63)( 46, 62)( 47, 61)
( 48, 60)( 49, 59)( 50, 58)( 51, 57)( 52, 56)( 53, 55)(108,159)(109,158)
(110,157)(111,156)(112,155)(113,154)(114,153)(115,152)(116,151)(117,150)
(118,149)(119,148)(120,147)(121,146)(122,145)(123,144)(124,143)(125,142)
(126,141)(127,140)(128,139)(129,138)(130,137)(131,136)(132,135)(133,134)
(160,372)(161,424)(162,423)(163,422)(164,421)(165,420)(166,419)(167,418)
(168,417)(169,416)(170,415)(171,414)(172,413)(173,412)(174,411)(175,410)
(176,409)(177,408)(178,407)(179,406)(180,405)(181,404)(182,403)(183,402)
(184,401)(185,400)(186,399)(187,398)(188,397)(189,396)(190,395)(191,394)
(192,393)(193,392)(194,391)(195,390)(196,389)(197,388)(198,387)(199,386)
(200,385)(201,384)(202,383)(203,382)(204,381)(205,380)(206,379)(207,378)
(208,377)(209,376)(210,375)(211,374)(212,373)(213,319)(214,371)(215,370)
(216,369)(217,368)(218,367)(219,366)(220,365)(221,364)(222,363)(223,362)
(224,361)(225,360)(226,359)(227,358)(228,357)(229,356)(230,355)(231,354)
(232,353)(233,352)(234,351)(235,350)(236,349)(237,348)(238,347)(239,346)
(240,345)(241,344)(242,343)(243,342)(244,341)(245,340)(246,339)(247,338)
(248,337)(249,336)(250,335)(251,334)(252,333)(253,332)(254,331)(255,330)
(256,329)(257,328)(258,327)(259,326)(260,325)(261,324)(262,323)(263,322)
(264,321)(265,320)(266,425)(267,477)(268,476)(269,475)(270,474)(271,473)
(272,472)(273,471)(274,470)(275,469)(276,468)(277,467)(278,466)(279,465)
(280,464)(281,463)(282,462)(283,461)(284,460)(285,459)(286,458)(287,457)
(288,456)(289,455)(290,454)(291,453)(292,452)(293,451)(294,450)(295,449)
(296,448)(297,447)(298,446)(299,445)(300,444)(301,443)(302,442)(303,441)
(304,440)(305,439)(306,438)(307,437)(308,436)(309,435)(310,434)(311,433)
(312,432)(313,431)(314,430)(315,429)(316,428)(317,427)(318,426);
s2 := Sym(477)!( 1,161)( 2,160)( 3,212)( 4,211)( 5,210)( 6,209)( 7,208)
( 8,207)( 9,206)( 10,205)( 11,204)( 12,203)( 13,202)( 14,201)( 15,200)
( 16,199)( 17,198)( 18,197)( 19,196)( 20,195)( 21,194)( 22,193)( 23,192)
( 24,191)( 25,190)( 26,189)( 27,188)( 28,187)( 29,186)( 30,185)( 31,184)
( 32,183)( 33,182)( 34,181)( 35,180)( 36,179)( 37,178)( 38,177)( 39,176)
( 40,175)( 41,174)( 42,173)( 43,172)( 44,171)( 45,170)( 46,169)( 47,168)
( 48,167)( 49,166)( 50,165)( 51,164)( 52,163)( 53,162)( 54,267)( 55,266)
( 56,318)( 57,317)( 58,316)( 59,315)( 60,314)( 61,313)( 62,312)( 63,311)
( 64,310)( 65,309)( 66,308)( 67,307)( 68,306)( 69,305)( 70,304)( 71,303)
( 72,302)( 73,301)( 74,300)( 75,299)( 76,298)( 77,297)( 78,296)( 79,295)
( 80,294)( 81,293)( 82,292)( 83,291)( 84,290)( 85,289)( 86,288)( 87,287)
( 88,286)( 89,285)( 90,284)( 91,283)( 92,282)( 93,281)( 94,280)( 95,279)
( 96,278)( 97,277)( 98,276)( 99,275)(100,274)(101,273)(102,272)(103,271)
(104,270)(105,269)(106,268)(107,214)(108,213)(109,265)(110,264)(111,263)
(112,262)(113,261)(114,260)(115,259)(116,258)(117,257)(118,256)(119,255)
(120,254)(121,253)(122,252)(123,251)(124,250)(125,249)(126,248)(127,247)
(128,246)(129,245)(130,244)(131,243)(132,242)(133,241)(134,240)(135,239)
(136,238)(137,237)(138,236)(139,235)(140,234)(141,233)(142,232)(143,231)
(144,230)(145,229)(146,228)(147,227)(148,226)(149,225)(150,224)(151,223)
(152,222)(153,221)(154,220)(155,219)(156,218)(157,217)(158,216)(159,215)
(319,320)(321,371)(322,370)(323,369)(324,368)(325,367)(326,366)(327,365)
(328,364)(329,363)(330,362)(331,361)(332,360)(333,359)(334,358)(335,357)
(336,356)(337,355)(338,354)(339,353)(340,352)(341,351)(342,350)(343,349)
(344,348)(345,347)(372,426)(373,425)(374,477)(375,476)(376,475)(377,474)
(378,473)(379,472)(380,471)(381,470)(382,469)(383,468)(384,467)(385,466)
(386,465)(387,464)(388,463)(389,462)(390,461)(391,460)(392,459)(393,458)
(394,457)(395,456)(396,455)(397,454)(398,453)(399,452)(400,451)(401,450)
(402,449)(403,448)(404,447)(405,446)(406,445)(407,444)(408,443)(409,442)
(410,441)(411,440)(412,439)(413,438)(414,437)(415,436)(416,435)(417,434)
(418,433)(419,432)(420,431)(421,430)(422,429)(423,428)(424,427);
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*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s0*s1*s0*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope