Polytope of Type {147,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {147,6}*1764
if this polytope has a name.
Group : SmallGroup(1764,36)
Rank : 3
Schlafli Type : {147,6}
Number of vertices, edges, etc : 147, 441, 6
Order of s₀s₁s₂ : 294
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 : {147,2}*588
   7-fold quotients : {21,6}*252
   9-fold quotients : {49,2}*196
   21-fold quotients : {21,2}*84
   49-fold quotients : {3,6}*36
   63-fold quotients : {7,2}*28
   147-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope