Polytope of Type {6,147}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope