Polytope of Type {162,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {162,6}*1944b
if this polytope has a name.
Group : SmallGroup(1944,955)
Rank : 3
Schlafli Type : {162,6}
Number of vertices, edges, etc : 162, 486, 6
Order of s₀s₁s₂ : 162
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {81,6}*972
   3-fold quotients : {162,2}*648, {54,6}*648b
   6-fold quotients : {81,2}*324, {27,6}*324
   9-fold quotients : {54,2}*216, {18,6}*216b
   18-fold quotients : {27,2}*108, {9,6}*108
   27-fold quotients : {18,2}*72, {6,6}*72c
   54-fold quotients : {9,2}*36, {3,6}*36
   81-fold quotients : {6,2}*24
   162-fold quotients : {3,2}*12
   243-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2,  3)(  4,  8)(  5,  7)(  6,  9)( 10, 23)( 11, 22)( 12, 24)( 13, 20)
( 14, 19)( 15, 21)( 16, 27)( 17, 26)( 18, 25)( 28, 55)( 29, 57)( 30, 56)
( 31, 62)( 32, 61)( 33, 63)( 34, 59)( 35, 58)( 36, 60)( 37, 77)( 38, 76)
( 39, 78)( 40, 74)( 41, 73)( 42, 75)( 43, 81)( 44, 80)( 45, 79)( 46, 68)
( 47, 67)( 48, 69)( 49, 65)( 50, 64)( 51, 66)( 52, 72)( 53, 71)( 54, 70)
( 82,176)( 83,175)( 84,177)( 85,173)( 86,172)( 87,174)( 88,180)( 89,179)
( 90,178)( 91,167)( 92,166)( 93,168)( 94,164)( 95,163)( 96,165)( 97,171)
( 98,170)( 99,169)(100,189)(101,188)(102,187)(103,186)(104,185)(105,184)
(106,183)(107,182)(108,181)(109,230)(110,229)(111,231)(112,227)(113,226)
(114,228)(115,234)(116,233)(117,232)(118,221)(119,220)(120,222)(121,218)
(122,217)(123,219)(124,225)(125,224)(126,223)(127,243)(128,242)(129,241)
(130,240)(131,239)(132,238)(133,237)(134,236)(135,235)(136,203)(137,202)
(138,204)(139,200)(140,199)(141,201)(142,207)(143,206)(144,205)(145,194)
(146,193)(147,195)(148,191)(149,190)(150,192)(151,198)(152,197)(153,196)
(154,216)(155,215)(156,214)(157,213)(158,212)(159,211)(160,210)(161,209)
(162,208)(245,246)(247,251)(248,250)(249,252)(253,266)(254,265)(255,267)
(256,263)(257,262)(258,264)(259,270)(260,269)(261,268)(271,298)(272,300)
(273,299)(274,305)(275,304)(276,306)(277,302)(278,301)(279,303)(280,320)
(281,319)(282,321)(283,317)(284,316)(285,318)(286,324)(287,323)(288,322)
(289,311)(290,310)(291,312)(292,308)(293,307)(294,309)(295,315)(296,314)
(297,313)(325,419)(326,418)(327,420)(328,416)(329,415)(330,417)(331,423)
(332,422)(333,421)(334,410)(335,409)(336,411)(337,407)(338,406)(339,408)
(340,414)(341,413)(342,412)(343,432)(344,431)(345,430)(346,429)(347,428)
(348,427)(349,426)(350,425)(351,424)(352,473)(353,472)(354,474)(355,470)
(356,469)(357,471)(358,477)(359,476)(360,475)(361,464)(362,463)(363,465)
(364,461)(365,460)(366,462)(367,468)(368,467)(369,466)(370,486)(371,485)
(372,484)(373,483)(374,482)(375,481)(376,480)(377,479)(378,478)(379,446)
(380,445)(381,447)(382,443)(383,442)(384,444)(385,450)(386,449)(387,448)
(388,437)(389,436)(390,438)(391,434)(392,433)(393,435)(394,441)(395,440)
(396,439)(397,459)(398,458)(399,457)(400,456)(401,455)(402,454)(403,453)
(404,452)(405,451);;
s1 := (  1,352)(  2,354)(  3,353)(  4,359)(  5,358)(  6,360)(  7,356)(  8,355)
(  9,357)( 10,374)( 11,373)( 12,375)( 13,371)( 14,370)( 15,372)( 16,378)
( 17,377)( 18,376)( 19,365)( 20,364)( 21,366)( 22,362)( 23,361)( 24,363)
( 25,369)( 26,368)( 27,367)( 28,325)( 29,327)( 30,326)( 31,332)( 32,331)
( 33,333)( 34,329)( 35,328)( 36,330)( 37,347)( 38,346)( 39,348)( 40,344)
( 41,343)( 42,345)( 43,351)( 44,350)( 45,349)( 46,338)( 47,337)( 48,339)
( 49,335)( 50,334)( 51,336)( 52,342)( 53,341)( 54,340)( 55,379)( 56,381)
( 57,380)( 58,386)( 59,385)( 60,387)( 61,383)( 62,382)( 63,384)( 64,401)
( 65,400)( 66,402)( 67,398)( 68,397)( 69,399)( 70,405)( 71,404)( 72,403)
( 73,392)( 74,391)( 75,393)( 76,389)( 77,388)( 78,390)( 79,396)( 80,395)
( 81,394)( 82,271)( 83,273)( 84,272)( 85,278)( 86,277)( 87,279)( 88,275)
( 89,274)( 90,276)( 91,293)( 92,292)( 93,294)( 94,290)( 95,289)( 96,291)
( 97,297)( 98,296)( 99,295)(100,284)(101,283)(102,285)(103,281)(104,280)
(105,282)(106,288)(107,287)(108,286)(109,244)(110,246)(111,245)(112,251)
(113,250)(114,252)(115,248)(116,247)(117,249)(118,266)(119,265)(120,267)
(121,263)(122,262)(123,264)(124,270)(125,269)(126,268)(127,257)(128,256)
(129,258)(130,254)(131,253)(132,255)(133,261)(134,260)(135,259)(136,298)
(137,300)(138,299)(139,305)(140,304)(141,306)(142,302)(143,301)(144,303)
(145,320)(146,319)(147,321)(148,317)(149,316)(150,318)(151,324)(152,323)
(153,322)(154,311)(155,310)(156,312)(157,308)(158,307)(159,309)(160,315)
(161,314)(162,313)(163,446)(164,445)(165,447)(166,443)(167,442)(168,444)
(169,450)(170,449)(171,448)(172,437)(173,436)(174,438)(175,434)(176,433)
(177,435)(178,441)(179,440)(180,439)(181,459)(182,458)(183,457)(184,456)
(185,455)(186,454)(187,453)(188,452)(189,451)(190,419)(191,418)(192,420)
(193,416)(194,415)(195,417)(196,423)(197,422)(198,421)(199,410)(200,409)
(201,411)(202,407)(203,406)(204,408)(205,414)(206,413)(207,412)(208,432)
(209,431)(210,430)(211,429)(212,428)(213,427)(214,426)(215,425)(216,424)
(217,473)(218,472)(219,474)(220,470)(221,469)(222,471)(223,477)(224,476)
(225,475)(226,464)(227,463)(228,465)(229,461)(230,460)(231,462)(232,468)
(233,467)(234,466)(235,486)(236,485)(237,484)(238,483)(239,482)(240,481)
(241,480)(242,479)(243,478);;
s2 := ( 28, 55)( 29, 56)( 30, 57)( 31, 58)( 32, 59)( 33, 60)( 34, 61)( 35, 62)
( 36, 63)( 37, 64)( 38, 65)( 39, 66)( 40, 67)( 41, 68)( 42, 69)( 43, 70)
( 44, 71)( 45, 72)( 46, 73)( 47, 74)( 48, 75)( 49, 76)( 50, 77)( 51, 78)
( 52, 79)( 53, 80)( 54, 81)(109,136)(110,137)(111,138)(112,139)(113,140)
(114,141)(115,142)(116,143)(117,144)(118,145)(119,146)(120,147)(121,148)
(122,149)(123,150)(124,151)(125,152)(126,153)(127,154)(128,155)(129,156)
(130,157)(131,158)(132,159)(133,160)(134,161)(135,162)(190,217)(191,218)
(192,219)(193,220)(194,221)(195,222)(196,223)(197,224)(198,225)(199,226)
(200,227)(201,228)(202,229)(203,230)(204,231)(205,232)(206,233)(207,234)
(208,235)(209,236)(210,237)(211,238)(212,239)(213,240)(214,241)(215,242)
(216,243)(271,298)(272,299)(273,300)(274,301)(275,302)(276,303)(277,304)
(278,305)(279,306)(280,307)(281,308)(282,309)(283,310)(284,311)(285,312)
(286,313)(287,314)(288,315)(289,316)(290,317)(291,318)(292,319)(293,320)
(294,321)(295,322)(296,323)(297,324)(352,379)(353,380)(354,381)(355,382)
(356,383)(357,384)(358,385)(359,386)(360,387)(361,388)(362,389)(363,390)
(364,391)(365,392)(366,393)(367,394)(368,395)(369,396)(370,397)(371,398)
(372,399)(373,400)(374,401)(375,402)(376,403)(377,404)(378,405)(433,460)
(434,461)(435,462)(436,463)(437,464)(438,465)(439,466)(440,467)(441,468)
(442,469)(443,470)(444,471)(445,472)(446,473)(447,474)(448,475)(449,476)
(450,477)(451,478)(452,479)(453,480)(454,481)(455,482)(456,483)(457,484)
(458,485)(459,486);;
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*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(486)!(  2,  3)(  4,  8)(  5,  7)(  6,  9)( 10, 23)( 11, 22)( 12, 24)
( 13, 20)( 14, 19)( 15, 21)( 16, 27)( 17, 26)( 18, 25)( 28, 55)( 29, 57)
( 30, 56)( 31, 62)( 32, 61)( 33, 63)( 34, 59)( 35, 58)( 36, 60)( 37, 77)
( 38, 76)( 39, 78)( 40, 74)( 41, 73)( 42, 75)( 43, 81)( 44, 80)( 45, 79)
( 46, 68)( 47, 67)( 48, 69)( 49, 65)( 50, 64)( 51, 66)( 52, 72)( 53, 71)
( 54, 70)( 82,176)( 83,175)( 84,177)( 85,173)( 86,172)( 87,174)( 88,180)
( 89,179)( 90,178)( 91,167)( 92,166)( 93,168)( 94,164)( 95,163)( 96,165)
( 97,171)( 98,170)( 99,169)(100,189)(101,188)(102,187)(103,186)(104,185)
(105,184)(106,183)(107,182)(108,181)(109,230)(110,229)(111,231)(112,227)
(113,226)(114,228)(115,234)(116,233)(117,232)(118,221)(119,220)(120,222)
(121,218)(122,217)(123,219)(124,225)(125,224)(126,223)(127,243)(128,242)
(129,241)(130,240)(131,239)(132,238)(133,237)(134,236)(135,235)(136,203)
(137,202)(138,204)(139,200)(140,199)(141,201)(142,207)(143,206)(144,205)
(145,194)(146,193)(147,195)(148,191)(149,190)(150,192)(151,198)(152,197)
(153,196)(154,216)(155,215)(156,214)(157,213)(158,212)(159,211)(160,210)
(161,209)(162,208)(245,246)(247,251)(248,250)(249,252)(253,266)(254,265)
(255,267)(256,263)(257,262)(258,264)(259,270)(260,269)(261,268)(271,298)
(272,300)(273,299)(274,305)(275,304)(276,306)(277,302)(278,301)(279,303)
(280,320)(281,319)(282,321)(283,317)(284,316)(285,318)(286,324)(287,323)
(288,322)(289,311)(290,310)(291,312)(292,308)(293,307)(294,309)(295,315)
(296,314)(297,313)(325,419)(326,418)(327,420)(328,416)(329,415)(330,417)
(331,423)(332,422)(333,421)(334,410)(335,409)(336,411)(337,407)(338,406)
(339,408)(340,414)(341,413)(342,412)(343,432)(344,431)(345,430)(346,429)
(347,428)(348,427)(349,426)(350,425)(351,424)(352,473)(353,472)(354,474)
(355,470)(356,469)(357,471)(358,477)(359,476)(360,475)(361,464)(362,463)
(363,465)(364,461)(365,460)(366,462)(367,468)(368,467)(369,466)(370,486)
(371,485)(372,484)(373,483)(374,482)(375,481)(376,480)(377,479)(378,478)
(379,446)(380,445)(381,447)(382,443)(383,442)(384,444)(385,450)(386,449)
(387,448)(388,437)(389,436)(390,438)(391,434)(392,433)(393,435)(394,441)
(395,440)(396,439)(397,459)(398,458)(399,457)(400,456)(401,455)(402,454)
(403,453)(404,452)(405,451);
s1 := Sym(486)!(  1,352)(  2,354)(  3,353)(  4,359)(  5,358)(  6,360)(  7,356)
(  8,355)(  9,357)( 10,374)( 11,373)( 12,375)( 13,371)( 14,370)( 15,372)
( 16,378)( 17,377)( 18,376)( 19,365)( 20,364)( 21,366)( 22,362)( 23,361)
( 24,363)( 25,369)( 26,368)( 27,367)( 28,325)( 29,327)( 30,326)( 31,332)
( 32,331)( 33,333)( 34,329)( 35,328)( 36,330)( 37,347)( 38,346)( 39,348)
( 40,344)( 41,343)( 42,345)( 43,351)( 44,350)( 45,349)( 46,338)( 47,337)
( 48,339)( 49,335)( 50,334)( 51,336)( 52,342)( 53,341)( 54,340)( 55,379)
( 56,381)( 57,380)( 58,386)( 59,385)( 60,387)( 61,383)( 62,382)( 63,384)
( 64,401)( 65,400)( 66,402)( 67,398)( 68,397)( 69,399)( 70,405)( 71,404)
( 72,403)( 73,392)( 74,391)( 75,393)( 76,389)( 77,388)( 78,390)( 79,396)
( 80,395)( 81,394)( 82,271)( 83,273)( 84,272)( 85,278)( 86,277)( 87,279)
( 88,275)( 89,274)( 90,276)( 91,293)( 92,292)( 93,294)( 94,290)( 95,289)
( 96,291)( 97,297)( 98,296)( 99,295)(100,284)(101,283)(102,285)(103,281)
(104,280)(105,282)(106,288)(107,287)(108,286)(109,244)(110,246)(111,245)
(112,251)(113,250)(114,252)(115,248)(116,247)(117,249)(118,266)(119,265)
(120,267)(121,263)(122,262)(123,264)(124,270)(125,269)(126,268)(127,257)
(128,256)(129,258)(130,254)(131,253)(132,255)(133,261)(134,260)(135,259)
(136,298)(137,300)(138,299)(139,305)(140,304)(141,306)(142,302)(143,301)
(144,303)(145,320)(146,319)(147,321)(148,317)(149,316)(150,318)(151,324)
(152,323)(153,322)(154,311)(155,310)(156,312)(157,308)(158,307)(159,309)
(160,315)(161,314)(162,313)(163,446)(164,445)(165,447)(166,443)(167,442)
(168,444)(169,450)(170,449)(171,448)(172,437)(173,436)(174,438)(175,434)
(176,433)(177,435)(178,441)(179,440)(180,439)(181,459)(182,458)(183,457)
(184,456)(185,455)(186,454)(187,453)(188,452)(189,451)(190,419)(191,418)
(192,420)(193,416)(194,415)(195,417)(196,423)(197,422)(198,421)(199,410)
(200,409)(201,411)(202,407)(203,406)(204,408)(205,414)(206,413)(207,412)
(208,432)(209,431)(210,430)(211,429)(212,428)(213,427)(214,426)(215,425)
(216,424)(217,473)(218,472)(219,474)(220,470)(221,469)(222,471)(223,477)
(224,476)(225,475)(226,464)(227,463)(228,465)(229,461)(230,460)(231,462)
(232,468)(233,467)(234,466)(235,486)(236,485)(237,484)(238,483)(239,482)
(240,481)(241,480)(242,479)(243,478);
s2 := Sym(486)!( 28, 55)( 29, 56)( 30, 57)( 31, 58)( 32, 59)( 33, 60)( 34, 61)
( 35, 62)( 36, 63)( 37, 64)( 38, 65)( 39, 66)( 40, 67)( 41, 68)( 42, 69)
( 43, 70)( 44, 71)( 45, 72)( 46, 73)( 47, 74)( 48, 75)( 49, 76)( 50, 77)
( 51, 78)( 52, 79)( 53, 80)( 54, 81)(109,136)(110,137)(111,138)(112,139)
(113,140)(114,141)(115,142)(116,143)(117,144)(118,145)(119,146)(120,147)
(121,148)(122,149)(123,150)(124,151)(125,152)(126,153)(127,154)(128,155)
(129,156)(130,157)(131,158)(132,159)(133,160)(134,161)(135,162)(190,217)
(191,218)(192,219)(193,220)(194,221)(195,222)(196,223)(197,224)(198,225)
(199,226)(200,227)(201,228)(202,229)(203,230)(204,231)(205,232)(206,233)
(207,234)(208,235)(209,236)(210,237)(211,238)(212,239)(213,240)(214,241)
(215,242)(216,243)(271,298)(272,299)(273,300)(274,301)(275,302)(276,303)
(277,304)(278,305)(279,306)(280,307)(281,308)(282,309)(283,310)(284,311)
(285,312)(286,313)(287,314)(288,315)(289,316)(290,317)(291,318)(292,319)
(293,320)(294,321)(295,322)(296,323)(297,324)(352,379)(353,380)(354,381)
(355,382)(356,383)(357,384)(358,385)(359,386)(360,387)(361,388)(362,389)
(363,390)(364,391)(365,392)(366,393)(367,394)(368,395)(369,396)(370,397)
(371,398)(372,399)(373,400)(374,401)(375,402)(376,403)(377,404)(378,405)
(433,460)(434,461)(435,462)(436,463)(437,464)(438,465)(439,466)(440,467)
(441,468)(442,469)(443,470)(444,471)(445,472)(446,473)(447,474)(448,475)
(449,476)(450,477)(451,478)(452,479)(453,480)(454,481)(455,482)(456,483)
(457,484)(458,485)(459,486);
poly := sub<Sym(486)|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*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope