Polytope of Type {18,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,6}*1944e
if this polytope has a name.
Group : SmallGroup(1944,944)
Rank : 3
Schlafli Type : {18,6}
Number of vertices, edges, etc : 162, 486, 54
Order of s0s1s2 : 18
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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 : {18,6}*972b
3-fold quotients : {6,6}*648a, {18,6}*648g
6-fold quotients : {6,6}*324b, {18,6}*324c
9-fold quotients : {6,6}*216b
18-fold quotients : {6,6}*108
27-fold quotients : {6,6}*72a
81-fold quotients : {2,6}*24, {6,2}*24
162-fold quotients : {2,3}*12, {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, 6)( 7, 8)( 10, 19)( 11, 21)( 12, 20)( 13, 24)( 14, 23)
( 15, 22)( 16, 26)( 17, 25)( 18, 27)( 28, 56)( 29, 55)( 30, 57)( 31, 58)
( 32, 60)( 33, 59)( 34, 63)( 35, 62)( 36, 61)( 37, 74)( 38, 73)( 39, 75)
( 40, 76)( 41, 78)( 42, 77)( 43, 81)( 44, 80)( 45, 79)( 46, 65)( 47, 64)
( 48, 66)( 49, 67)( 50, 69)( 51, 68)( 52, 72)( 53, 71)( 54, 70)( 83, 84)
( 85, 87)( 88, 89)( 91,100)( 92,102)( 93,101)( 94,105)( 95,104)( 96,103)
( 97,107)( 98,106)( 99,108)(109,137)(110,136)(111,138)(112,139)(113,141)
(114,140)(115,144)(116,143)(117,142)(118,155)(119,154)(120,156)(121,157)
(122,159)(123,158)(124,162)(125,161)(126,160)(127,146)(128,145)(129,147)
(130,148)(131,150)(132,149)(133,153)(134,152)(135,151)(164,165)(166,168)
(169,170)(172,181)(173,183)(174,182)(175,186)(176,185)(177,184)(178,188)
(179,187)(180,189)(190,218)(191,217)(192,219)(193,220)(194,222)(195,221)
(196,225)(197,224)(198,223)(199,236)(200,235)(201,237)(202,238)(203,240)
(204,239)(205,243)(206,242)(207,241)(208,227)(209,226)(210,228)(211,229)
(212,231)(213,230)(214,234)(215,233)(216,232)(245,246)(247,249)(250,251)
(253,262)(254,264)(255,263)(256,267)(257,266)(258,265)(259,269)(260,268)
(261,270)(271,299)(272,298)(273,300)(274,301)(275,303)(276,302)(277,306)
(278,305)(279,304)(280,317)(281,316)(282,318)(283,319)(284,321)(285,320)
(286,324)(287,323)(288,322)(289,308)(290,307)(291,309)(292,310)(293,312)
(294,311)(295,315)(296,314)(297,313)(326,327)(328,330)(331,332)(334,343)
(335,345)(336,344)(337,348)(338,347)(339,346)(340,350)(341,349)(342,351)
(352,380)(353,379)(354,381)(355,382)(356,384)(357,383)(358,387)(359,386)
(360,385)(361,398)(362,397)(363,399)(364,400)(365,402)(366,401)(367,405)
(368,404)(369,403)(370,389)(371,388)(372,390)(373,391)(374,393)(375,392)
(376,396)(377,395)(378,394)(407,408)(409,411)(412,413)(415,424)(416,426)
(417,425)(418,429)(419,428)(420,427)(421,431)(422,430)(423,432)(433,461)
(434,460)(435,462)(436,463)(437,465)(438,464)(439,468)(440,467)(441,466)
(442,479)(443,478)(444,480)(445,481)(446,483)(447,482)(448,486)(449,485)
(450,484)(451,470)(452,469)(453,471)(454,472)(455,474)(456,473)(457,477)
(458,476)(459,475);;
s1 := ( 1, 28)( 2, 30)( 3, 29)( 4, 34)( 5, 36)( 6, 35)( 7, 31)( 8, 33)
( 9, 32)( 10, 45)( 11, 44)( 12, 43)( 13, 42)( 14, 41)( 15, 40)( 16, 39)
( 17, 38)( 18, 37)( 19, 50)( 20, 49)( 21, 51)( 22, 47)( 23, 46)( 24, 48)
( 25, 53)( 26, 52)( 27, 54)( 55, 56)( 58, 62)( 59, 61)( 60, 63)( 64, 70)
( 65, 72)( 66, 71)( 68, 69)( 73, 78)( 74, 77)( 75, 76)( 79, 81)( 82,190)
( 83,192)( 84,191)( 85,196)( 86,198)( 87,197)( 88,193)( 89,195)( 90,194)
( 91,207)( 92,206)( 93,205)( 94,204)( 95,203)( 96,202)( 97,201)( 98,200)
( 99,199)(100,212)(101,211)(102,213)(103,209)(104,208)(105,210)(106,215)
(107,214)(108,216)(109,163)(110,165)(111,164)(112,169)(113,171)(114,170)
(115,166)(116,168)(117,167)(118,180)(119,179)(120,178)(121,177)(122,176)
(123,175)(124,174)(125,173)(126,172)(127,185)(128,184)(129,186)(130,182)
(131,181)(132,183)(133,188)(134,187)(135,189)(136,218)(137,217)(138,219)
(139,224)(140,223)(141,225)(142,221)(143,220)(144,222)(145,232)(146,234)
(147,233)(148,229)(149,231)(150,230)(151,226)(152,228)(153,227)(154,240)
(155,239)(156,238)(157,237)(158,236)(159,235)(160,243)(161,242)(162,241)
(244,271)(245,273)(246,272)(247,277)(248,279)(249,278)(250,274)(251,276)
(252,275)(253,288)(254,287)(255,286)(256,285)(257,284)(258,283)(259,282)
(260,281)(261,280)(262,293)(263,292)(264,294)(265,290)(266,289)(267,291)
(268,296)(269,295)(270,297)(298,299)(301,305)(302,304)(303,306)(307,313)
(308,315)(309,314)(311,312)(316,321)(317,320)(318,319)(322,324)(325,433)
(326,435)(327,434)(328,439)(329,441)(330,440)(331,436)(332,438)(333,437)
(334,450)(335,449)(336,448)(337,447)(338,446)(339,445)(340,444)(341,443)
(342,442)(343,455)(344,454)(345,456)(346,452)(347,451)(348,453)(349,458)
(350,457)(351,459)(352,406)(353,408)(354,407)(355,412)(356,414)(357,413)
(358,409)(359,411)(360,410)(361,423)(362,422)(363,421)(364,420)(365,419)
(366,418)(367,417)(368,416)(369,415)(370,428)(371,427)(372,429)(373,425)
(374,424)(375,426)(376,431)(377,430)(378,432)(379,461)(380,460)(381,462)
(382,467)(383,466)(384,468)(385,464)(386,463)(387,465)(388,475)(389,477)
(390,476)(391,472)(392,474)(393,473)(394,469)(395,471)(396,470)(397,483)
(398,482)(399,481)(400,480)(401,479)(402,478)(403,486)(404,485)(405,484);;
s2 := ( 1,325)( 2,326)( 3,327)( 4,332)( 5,333)( 6,331)( 7,330)( 8,328)
( 9,329)( 10,345)( 11,343)( 12,344)( 13,349)( 14,350)( 15,351)( 16,347)
( 17,348)( 18,346)( 19,335)( 20,336)( 21,334)( 22,342)( 23,340)( 24,341)
( 25,337)( 26,338)( 27,339)( 28,364)( 29,365)( 30,366)( 31,362)( 32,363)
( 33,361)( 34,369)( 35,367)( 36,368)( 37,357)( 38,355)( 39,356)( 40,352)
( 41,353)( 42,354)( 43,359)( 44,360)( 45,358)( 46,374)( 47,375)( 48,373)
( 49,372)( 50,370)( 51,371)( 52,376)( 53,377)( 54,378)( 55,402)( 56,400)
( 57,401)( 58,397)( 59,398)( 60,399)( 61,404)( 62,405)( 63,403)( 64,392)
( 65,393)( 66,391)( 67,390)( 68,388)( 69,389)( 70,394)( 71,395)( 72,396)
( 73,382)( 74,383)( 75,384)( 76,380)( 77,381)( 78,379)( 79,387)( 80,385)
( 81,386)( 82,244)( 83,245)( 84,246)( 85,251)( 86,252)( 87,250)( 88,249)
( 89,247)( 90,248)( 91,264)( 92,262)( 93,263)( 94,268)( 95,269)( 96,270)
( 97,266)( 98,267)( 99,265)(100,254)(101,255)(102,253)(103,261)(104,259)
(105,260)(106,256)(107,257)(108,258)(109,283)(110,284)(111,285)(112,281)
(113,282)(114,280)(115,288)(116,286)(117,287)(118,276)(119,274)(120,275)
(121,271)(122,272)(123,273)(124,278)(125,279)(126,277)(127,293)(128,294)
(129,292)(130,291)(131,289)(132,290)(133,295)(134,296)(135,297)(136,321)
(137,319)(138,320)(139,316)(140,317)(141,318)(142,323)(143,324)(144,322)
(145,311)(146,312)(147,310)(148,309)(149,307)(150,308)(151,313)(152,314)
(153,315)(154,301)(155,302)(156,303)(157,299)(158,300)(159,298)(160,306)
(161,304)(162,305)(163,406)(164,407)(165,408)(166,413)(167,414)(168,412)
(169,411)(170,409)(171,410)(172,426)(173,424)(174,425)(175,430)(176,431)
(177,432)(178,428)(179,429)(180,427)(181,416)(182,417)(183,415)(184,423)
(185,421)(186,422)(187,418)(188,419)(189,420)(190,445)(191,446)(192,447)
(193,443)(194,444)(195,442)(196,450)(197,448)(198,449)(199,438)(200,436)
(201,437)(202,433)(203,434)(204,435)(205,440)(206,441)(207,439)(208,455)
(209,456)(210,454)(211,453)(212,451)(213,452)(214,457)(215,458)(216,459)
(217,483)(218,481)(219,482)(220,478)(221,479)(222,480)(223,485)(224,486)
(225,484)(226,473)(227,474)(228,472)(229,471)(230,469)(231,470)(232,475)
(233,476)(234,477)(235,463)(236,464)(237,465)(238,461)(239,462)(240,460)
(241,468)(242,466)(243,467);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(486)!( 2, 3)( 4, 6)( 7, 8)( 10, 19)( 11, 21)( 12, 20)( 13, 24)
( 14, 23)( 15, 22)( 16, 26)( 17, 25)( 18, 27)( 28, 56)( 29, 55)( 30, 57)
( 31, 58)( 32, 60)( 33, 59)( 34, 63)( 35, 62)( 36, 61)( 37, 74)( 38, 73)
( 39, 75)( 40, 76)( 41, 78)( 42, 77)( 43, 81)( 44, 80)( 45, 79)( 46, 65)
( 47, 64)( 48, 66)( 49, 67)( 50, 69)( 51, 68)( 52, 72)( 53, 71)( 54, 70)
( 83, 84)( 85, 87)( 88, 89)( 91,100)( 92,102)( 93,101)( 94,105)( 95,104)
( 96,103)( 97,107)( 98,106)( 99,108)(109,137)(110,136)(111,138)(112,139)
(113,141)(114,140)(115,144)(116,143)(117,142)(118,155)(119,154)(120,156)
(121,157)(122,159)(123,158)(124,162)(125,161)(126,160)(127,146)(128,145)
(129,147)(130,148)(131,150)(132,149)(133,153)(134,152)(135,151)(164,165)
(166,168)(169,170)(172,181)(173,183)(174,182)(175,186)(176,185)(177,184)
(178,188)(179,187)(180,189)(190,218)(191,217)(192,219)(193,220)(194,222)
(195,221)(196,225)(197,224)(198,223)(199,236)(200,235)(201,237)(202,238)
(203,240)(204,239)(205,243)(206,242)(207,241)(208,227)(209,226)(210,228)
(211,229)(212,231)(213,230)(214,234)(215,233)(216,232)(245,246)(247,249)
(250,251)(253,262)(254,264)(255,263)(256,267)(257,266)(258,265)(259,269)
(260,268)(261,270)(271,299)(272,298)(273,300)(274,301)(275,303)(276,302)
(277,306)(278,305)(279,304)(280,317)(281,316)(282,318)(283,319)(284,321)
(285,320)(286,324)(287,323)(288,322)(289,308)(290,307)(291,309)(292,310)
(293,312)(294,311)(295,315)(296,314)(297,313)(326,327)(328,330)(331,332)
(334,343)(335,345)(336,344)(337,348)(338,347)(339,346)(340,350)(341,349)
(342,351)(352,380)(353,379)(354,381)(355,382)(356,384)(357,383)(358,387)
(359,386)(360,385)(361,398)(362,397)(363,399)(364,400)(365,402)(366,401)
(367,405)(368,404)(369,403)(370,389)(371,388)(372,390)(373,391)(374,393)
(375,392)(376,396)(377,395)(378,394)(407,408)(409,411)(412,413)(415,424)
(416,426)(417,425)(418,429)(419,428)(420,427)(421,431)(422,430)(423,432)
(433,461)(434,460)(435,462)(436,463)(437,465)(438,464)(439,468)(440,467)
(441,466)(442,479)(443,478)(444,480)(445,481)(446,483)(447,482)(448,486)
(449,485)(450,484)(451,470)(452,469)(453,471)(454,472)(455,474)(456,473)
(457,477)(458,476)(459,475);
s1 := Sym(486)!( 1, 28)( 2, 30)( 3, 29)( 4, 34)( 5, 36)( 6, 35)( 7, 31)
( 8, 33)( 9, 32)( 10, 45)( 11, 44)( 12, 43)( 13, 42)( 14, 41)( 15, 40)
( 16, 39)( 17, 38)( 18, 37)( 19, 50)( 20, 49)( 21, 51)( 22, 47)( 23, 46)
( 24, 48)( 25, 53)( 26, 52)( 27, 54)( 55, 56)( 58, 62)( 59, 61)( 60, 63)
( 64, 70)( 65, 72)( 66, 71)( 68, 69)( 73, 78)( 74, 77)( 75, 76)( 79, 81)
( 82,190)( 83,192)( 84,191)( 85,196)( 86,198)( 87,197)( 88,193)( 89,195)
( 90,194)( 91,207)( 92,206)( 93,205)( 94,204)( 95,203)( 96,202)( 97,201)
( 98,200)( 99,199)(100,212)(101,211)(102,213)(103,209)(104,208)(105,210)
(106,215)(107,214)(108,216)(109,163)(110,165)(111,164)(112,169)(113,171)
(114,170)(115,166)(116,168)(117,167)(118,180)(119,179)(120,178)(121,177)
(122,176)(123,175)(124,174)(125,173)(126,172)(127,185)(128,184)(129,186)
(130,182)(131,181)(132,183)(133,188)(134,187)(135,189)(136,218)(137,217)
(138,219)(139,224)(140,223)(141,225)(142,221)(143,220)(144,222)(145,232)
(146,234)(147,233)(148,229)(149,231)(150,230)(151,226)(152,228)(153,227)
(154,240)(155,239)(156,238)(157,237)(158,236)(159,235)(160,243)(161,242)
(162,241)(244,271)(245,273)(246,272)(247,277)(248,279)(249,278)(250,274)
(251,276)(252,275)(253,288)(254,287)(255,286)(256,285)(257,284)(258,283)
(259,282)(260,281)(261,280)(262,293)(263,292)(264,294)(265,290)(266,289)
(267,291)(268,296)(269,295)(270,297)(298,299)(301,305)(302,304)(303,306)
(307,313)(308,315)(309,314)(311,312)(316,321)(317,320)(318,319)(322,324)
(325,433)(326,435)(327,434)(328,439)(329,441)(330,440)(331,436)(332,438)
(333,437)(334,450)(335,449)(336,448)(337,447)(338,446)(339,445)(340,444)
(341,443)(342,442)(343,455)(344,454)(345,456)(346,452)(347,451)(348,453)
(349,458)(350,457)(351,459)(352,406)(353,408)(354,407)(355,412)(356,414)
(357,413)(358,409)(359,411)(360,410)(361,423)(362,422)(363,421)(364,420)
(365,419)(366,418)(367,417)(368,416)(369,415)(370,428)(371,427)(372,429)
(373,425)(374,424)(375,426)(376,431)(377,430)(378,432)(379,461)(380,460)
(381,462)(382,467)(383,466)(384,468)(385,464)(386,463)(387,465)(388,475)
(389,477)(390,476)(391,472)(392,474)(393,473)(394,469)(395,471)(396,470)
(397,483)(398,482)(399,481)(400,480)(401,479)(402,478)(403,486)(404,485)
(405,484);
s2 := Sym(486)!( 1,325)( 2,326)( 3,327)( 4,332)( 5,333)( 6,331)( 7,330)
( 8,328)( 9,329)( 10,345)( 11,343)( 12,344)( 13,349)( 14,350)( 15,351)
( 16,347)( 17,348)( 18,346)( 19,335)( 20,336)( 21,334)( 22,342)( 23,340)
( 24,341)( 25,337)( 26,338)( 27,339)( 28,364)( 29,365)( 30,366)( 31,362)
( 32,363)( 33,361)( 34,369)( 35,367)( 36,368)( 37,357)( 38,355)( 39,356)
( 40,352)( 41,353)( 42,354)( 43,359)( 44,360)( 45,358)( 46,374)( 47,375)
( 48,373)( 49,372)( 50,370)( 51,371)( 52,376)( 53,377)( 54,378)( 55,402)
( 56,400)( 57,401)( 58,397)( 59,398)( 60,399)( 61,404)( 62,405)( 63,403)
( 64,392)( 65,393)( 66,391)( 67,390)( 68,388)( 69,389)( 70,394)( 71,395)
( 72,396)( 73,382)( 74,383)( 75,384)( 76,380)( 77,381)( 78,379)( 79,387)
( 80,385)( 81,386)( 82,244)( 83,245)( 84,246)( 85,251)( 86,252)( 87,250)
( 88,249)( 89,247)( 90,248)( 91,264)( 92,262)( 93,263)( 94,268)( 95,269)
( 96,270)( 97,266)( 98,267)( 99,265)(100,254)(101,255)(102,253)(103,261)
(104,259)(105,260)(106,256)(107,257)(108,258)(109,283)(110,284)(111,285)
(112,281)(113,282)(114,280)(115,288)(116,286)(117,287)(118,276)(119,274)
(120,275)(121,271)(122,272)(123,273)(124,278)(125,279)(126,277)(127,293)
(128,294)(129,292)(130,291)(131,289)(132,290)(133,295)(134,296)(135,297)
(136,321)(137,319)(138,320)(139,316)(140,317)(141,318)(142,323)(143,324)
(144,322)(145,311)(146,312)(147,310)(148,309)(149,307)(150,308)(151,313)
(152,314)(153,315)(154,301)(155,302)(156,303)(157,299)(158,300)(159,298)
(160,306)(161,304)(162,305)(163,406)(164,407)(165,408)(166,413)(167,414)
(168,412)(169,411)(170,409)(171,410)(172,426)(173,424)(174,425)(175,430)
(176,431)(177,432)(178,428)(179,429)(180,427)(181,416)(182,417)(183,415)
(184,423)(185,421)(186,422)(187,418)(188,419)(189,420)(190,445)(191,446)
(192,447)(193,443)(194,444)(195,442)(196,450)(197,448)(198,449)(199,438)
(200,436)(201,437)(202,433)(203,434)(204,435)(205,440)(206,441)(207,439)
(208,455)(209,456)(210,454)(211,453)(212,451)(213,452)(214,457)(215,458)
(216,459)(217,483)(218,481)(219,482)(220,478)(221,479)(222,480)(223,485)
(224,486)(225,484)(226,473)(227,474)(228,472)(229,471)(230,469)(231,470)
(232,475)(233,476)(234,477)(235,463)(236,464)(237,465)(238,461)(239,462)
(240,460)(241,468)(242,466)(243,467);
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope