Polytope of Type {18,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,6}*1944l
if this polytope has a name.
Group : SmallGroup(1944,956)
Rank : 3
Schlafli Type : {18,6}
Number of vertices, edges, etc : 162, 486, 54
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 18
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}*972e
   3-fold quotients : {18,6}*648g
   6-fold quotients : {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,  7)(  5,  9)(  6,  8)( 10, 20)( 11, 19)( 12, 21)( 13, 26)
( 14, 25)( 15, 27)( 16, 23)( 17, 22)( 18, 24)( 29, 30)( 31, 34)( 32, 36)
( 33, 35)( 37, 47)( 38, 46)( 39, 48)( 40, 53)( 41, 52)( 42, 54)( 43, 50)
( 44, 49)( 45, 51)( 56, 57)( 58, 61)( 59, 63)( 60, 62)( 64, 74)( 65, 73)
( 66, 75)( 67, 80)( 68, 79)( 69, 81)( 70, 77)( 71, 76)( 72, 78)( 82,166)
( 83,168)( 84,167)( 85,163)( 86,165)( 87,164)( 88,169)( 89,171)( 90,170)
( 91,185)( 92,184)( 93,186)( 94,182)( 95,181)( 96,183)( 97,188)( 98,187)
( 99,189)(100,176)(101,175)(102,177)(103,173)(104,172)(105,174)(106,179)
(107,178)(108,180)(109,195)(110,194)(111,193)(112,192)(113,191)(114,190)
(115,198)(116,197)(117,196)(118,211)(119,213)(120,212)(121,208)(122,210)
(123,209)(124,214)(125,216)(126,215)(127,202)(128,204)(129,203)(130,199)
(131,201)(132,200)(133,205)(134,207)(135,206)(136,221)(137,220)(138,222)
(139,218)(140,217)(141,219)(142,224)(143,223)(144,225)(145,240)(146,239)
(147,238)(148,237)(149,236)(150,235)(151,243)(152,242)(153,241)(154,231)
(155,230)(156,229)(157,228)(158,227)(159,226)(160,234)(161,233)(162,232)
(245,246)(247,250)(248,252)(249,251)(253,263)(254,262)(255,264)(256,269)
(257,268)(258,270)(259,266)(260,265)(261,267)(272,273)(274,277)(275,279)
(276,278)(280,290)(281,289)(282,291)(283,296)(284,295)(285,297)(286,293)
(287,292)(288,294)(299,300)(301,304)(302,306)(303,305)(307,317)(308,316)
(309,318)(310,323)(311,322)(312,324)(313,320)(314,319)(315,321)(325,409)
(326,411)(327,410)(328,406)(329,408)(330,407)(331,412)(332,414)(333,413)
(334,428)(335,427)(336,429)(337,425)(338,424)(339,426)(340,431)(341,430)
(342,432)(343,419)(344,418)(345,420)(346,416)(347,415)(348,417)(349,422)
(350,421)(351,423)(352,438)(353,437)(354,436)(355,435)(356,434)(357,433)
(358,441)(359,440)(360,439)(361,454)(362,456)(363,455)(364,451)(365,453)
(366,452)(367,457)(368,459)(369,458)(370,445)(371,447)(372,446)(373,442)
(374,444)(375,443)(376,448)(377,450)(378,449)(379,464)(380,463)(381,465)
(382,461)(383,460)(384,462)(385,467)(386,466)(387,468)(388,483)(389,482)
(390,481)(391,480)(392,479)(393,478)(394,486)(395,485)(396,484)(397,474)
(398,473)(399,472)(400,471)(401,470)(402,469)(403,477)(404,476)(405,475);;
s1 := (  1, 82)(  2, 83)(  3, 84)(  4, 88)(  5, 89)(  6, 90)(  7, 85)(  8, 86)
(  9, 87)( 10, 91)( 11, 92)( 12, 93)( 13, 97)( 14, 98)( 15, 99)( 16, 94)
( 17, 95)( 18, 96)( 19,100)( 20,101)( 21,102)( 22,106)( 23,107)( 24,108)
( 25,103)( 26,104)( 27,105)( 28,158)( 29,159)( 30,157)( 31,155)( 32,156)
( 33,154)( 34,161)( 35,162)( 36,160)( 37,139)( 38,140)( 39,141)( 40,136)
( 41,137)( 42,138)( 43,142)( 44,143)( 45,144)( 46,148)( 47,149)( 48,150)
( 49,145)( 50,146)( 51,147)( 52,151)( 53,152)( 54,153)( 55,121)( 56,122)
( 57,123)( 58,118)( 59,119)( 60,120)( 61,124)( 62,125)( 63,126)( 64,130)
( 65,131)( 66,132)( 67,127)( 68,128)( 69,129)( 70,133)( 71,134)( 72,135)
( 73,114)( 74,112)( 75,113)( 76,111)( 77,109)( 78,110)( 79,117)( 80,115)
( 81,116)(163,166)(164,167)(165,168)(172,175)(173,176)(174,177)(181,184)
(182,185)(183,186)(190,243)(191,241)(192,242)(193,240)(194,238)(195,239)
(196,237)(197,235)(198,236)(199,224)(200,225)(201,223)(202,221)(203,222)
(204,220)(205,218)(206,219)(207,217)(208,233)(209,234)(210,232)(211,230)
(212,231)(213,229)(214,227)(215,228)(216,226)(244,325)(245,326)(246,327)
(247,331)(248,332)(249,333)(250,328)(251,329)(252,330)(253,334)(254,335)
(255,336)(256,340)(257,341)(258,342)(259,337)(260,338)(261,339)(262,343)
(263,344)(264,345)(265,349)(266,350)(267,351)(268,346)(269,347)(270,348)
(271,401)(272,402)(273,400)(274,398)(275,399)(276,397)(277,404)(278,405)
(279,403)(280,382)(281,383)(282,384)(283,379)(284,380)(285,381)(286,385)
(287,386)(288,387)(289,391)(290,392)(291,393)(292,388)(293,389)(294,390)
(295,394)(296,395)(297,396)(298,364)(299,365)(300,366)(301,361)(302,362)
(303,363)(304,367)(305,368)(306,369)(307,373)(308,374)(309,375)(310,370)
(311,371)(312,372)(313,376)(314,377)(315,378)(316,357)(317,355)(318,356)
(319,354)(320,352)(321,353)(322,360)(323,358)(324,359)(406,409)(407,410)
(408,411)(415,418)(416,419)(417,420)(424,427)(425,428)(426,429)(433,486)
(434,484)(435,485)(436,483)(437,481)(438,482)(439,480)(440,478)(441,479)
(442,467)(443,468)(444,466)(445,464)(446,465)(447,463)(448,461)(449,462)
(450,460)(451,476)(452,477)(453,475)(454,473)(455,474)(456,472)(457,470)
(458,471)(459,469);;
s2 := (  1,271)(  2,273)(  3,272)(  4,276)(  5,275)(  6,274)(  7,278)(  8,277)
(  9,279)( 10,294)( 11,293)( 12,292)( 13,296)( 14,295)( 15,297)( 16,289)
( 17,291)( 18,290)( 19,286)( 20,288)( 21,287)( 22,282)( 23,281)( 24,280)
( 25,284)( 26,283)( 27,285)( 28,244)( 29,246)( 30,245)( 31,249)( 32,248)
( 33,247)( 34,251)( 35,250)( 36,252)( 37,267)( 38,266)( 39,265)( 40,269)
( 41,268)( 42,270)( 43,262)( 44,264)( 45,263)( 46,259)( 47,261)( 48,260)
( 49,255)( 50,254)( 51,253)( 52,257)( 53,256)( 54,258)( 55,298)( 56,300)
( 57,299)( 58,303)( 59,302)( 60,301)( 61,305)( 62,304)( 63,306)( 64,321)
( 65,320)( 66,319)( 67,323)( 68,322)( 69,324)( 70,316)( 71,318)( 72,317)
( 73,313)( 74,315)( 75,314)( 76,309)( 77,308)( 78,307)( 79,311)( 80,310)
( 81,312)( 82,352)( 83,354)( 84,353)( 85,357)( 86,356)( 87,355)( 88,359)
( 89,358)( 90,360)( 91,375)( 92,374)( 93,373)( 94,377)( 95,376)( 96,378)
( 97,370)( 98,372)( 99,371)(100,367)(101,369)(102,368)(103,363)(104,362)
(105,361)(106,365)(107,364)(108,366)(109,325)(110,327)(111,326)(112,330)
(113,329)(114,328)(115,332)(116,331)(117,333)(118,348)(119,347)(120,346)
(121,350)(122,349)(123,351)(124,343)(125,345)(126,344)(127,340)(128,342)
(129,341)(130,336)(131,335)(132,334)(133,338)(134,337)(135,339)(136,379)
(137,381)(138,380)(139,384)(140,383)(141,382)(142,386)(143,385)(144,387)
(145,402)(146,401)(147,400)(148,404)(149,403)(150,405)(151,397)(152,399)
(153,398)(154,394)(155,396)(156,395)(157,390)(158,389)(159,388)(160,392)
(161,391)(162,393)(163,433)(164,435)(165,434)(166,438)(167,437)(168,436)
(169,440)(170,439)(171,441)(172,456)(173,455)(174,454)(175,458)(176,457)
(177,459)(178,451)(179,453)(180,452)(181,448)(182,450)(183,449)(184,444)
(185,443)(186,442)(187,446)(188,445)(189,447)(190,406)(191,408)(192,407)
(193,411)(194,410)(195,409)(196,413)(197,412)(198,414)(199,429)(200,428)
(201,427)(202,431)(203,430)(204,432)(205,424)(206,426)(207,425)(208,421)
(209,423)(210,422)(211,417)(212,416)(213,415)(214,419)(215,418)(216,420)
(217,460)(218,462)(219,461)(220,465)(221,464)(222,463)(223,467)(224,466)
(225,468)(226,483)(227,482)(228,481)(229,485)(230,484)(231,486)(232,478)
(233,480)(234,479)(235,475)(236,477)(237,476)(238,471)(239,470)(240,469)
(241,473)(242,472)(243,474);;
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, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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,  7)(  5,  9)(  6,  8)( 10, 20)( 11, 19)( 12, 21)
( 13, 26)( 14, 25)( 15, 27)( 16, 23)( 17, 22)( 18, 24)( 29, 30)( 31, 34)
( 32, 36)( 33, 35)( 37, 47)( 38, 46)( 39, 48)( 40, 53)( 41, 52)( 42, 54)
( 43, 50)( 44, 49)( 45, 51)( 56, 57)( 58, 61)( 59, 63)( 60, 62)( 64, 74)
( 65, 73)( 66, 75)( 67, 80)( 68, 79)( 69, 81)( 70, 77)( 71, 76)( 72, 78)
( 82,166)( 83,168)( 84,167)( 85,163)( 86,165)( 87,164)( 88,169)( 89,171)
( 90,170)( 91,185)( 92,184)( 93,186)( 94,182)( 95,181)( 96,183)( 97,188)
( 98,187)( 99,189)(100,176)(101,175)(102,177)(103,173)(104,172)(105,174)
(106,179)(107,178)(108,180)(109,195)(110,194)(111,193)(112,192)(113,191)
(114,190)(115,198)(116,197)(117,196)(118,211)(119,213)(120,212)(121,208)
(122,210)(123,209)(124,214)(125,216)(126,215)(127,202)(128,204)(129,203)
(130,199)(131,201)(132,200)(133,205)(134,207)(135,206)(136,221)(137,220)
(138,222)(139,218)(140,217)(141,219)(142,224)(143,223)(144,225)(145,240)
(146,239)(147,238)(148,237)(149,236)(150,235)(151,243)(152,242)(153,241)
(154,231)(155,230)(156,229)(157,228)(158,227)(159,226)(160,234)(161,233)
(162,232)(245,246)(247,250)(248,252)(249,251)(253,263)(254,262)(255,264)
(256,269)(257,268)(258,270)(259,266)(260,265)(261,267)(272,273)(274,277)
(275,279)(276,278)(280,290)(281,289)(282,291)(283,296)(284,295)(285,297)
(286,293)(287,292)(288,294)(299,300)(301,304)(302,306)(303,305)(307,317)
(308,316)(309,318)(310,323)(311,322)(312,324)(313,320)(314,319)(315,321)
(325,409)(326,411)(327,410)(328,406)(329,408)(330,407)(331,412)(332,414)
(333,413)(334,428)(335,427)(336,429)(337,425)(338,424)(339,426)(340,431)
(341,430)(342,432)(343,419)(344,418)(345,420)(346,416)(347,415)(348,417)
(349,422)(350,421)(351,423)(352,438)(353,437)(354,436)(355,435)(356,434)
(357,433)(358,441)(359,440)(360,439)(361,454)(362,456)(363,455)(364,451)
(365,453)(366,452)(367,457)(368,459)(369,458)(370,445)(371,447)(372,446)
(373,442)(374,444)(375,443)(376,448)(377,450)(378,449)(379,464)(380,463)
(381,465)(382,461)(383,460)(384,462)(385,467)(386,466)(387,468)(388,483)
(389,482)(390,481)(391,480)(392,479)(393,478)(394,486)(395,485)(396,484)
(397,474)(398,473)(399,472)(400,471)(401,470)(402,469)(403,477)(404,476)
(405,475);
s1 := Sym(486)!(  1, 82)(  2, 83)(  3, 84)(  4, 88)(  5, 89)(  6, 90)(  7, 85)
(  8, 86)(  9, 87)( 10, 91)( 11, 92)( 12, 93)( 13, 97)( 14, 98)( 15, 99)
( 16, 94)( 17, 95)( 18, 96)( 19,100)( 20,101)( 21,102)( 22,106)( 23,107)
( 24,108)( 25,103)( 26,104)( 27,105)( 28,158)( 29,159)( 30,157)( 31,155)
( 32,156)( 33,154)( 34,161)( 35,162)( 36,160)( 37,139)( 38,140)( 39,141)
( 40,136)( 41,137)( 42,138)( 43,142)( 44,143)( 45,144)( 46,148)( 47,149)
( 48,150)( 49,145)( 50,146)( 51,147)( 52,151)( 53,152)( 54,153)( 55,121)
( 56,122)( 57,123)( 58,118)( 59,119)( 60,120)( 61,124)( 62,125)( 63,126)
( 64,130)( 65,131)( 66,132)( 67,127)( 68,128)( 69,129)( 70,133)( 71,134)
( 72,135)( 73,114)( 74,112)( 75,113)( 76,111)( 77,109)( 78,110)( 79,117)
( 80,115)( 81,116)(163,166)(164,167)(165,168)(172,175)(173,176)(174,177)
(181,184)(182,185)(183,186)(190,243)(191,241)(192,242)(193,240)(194,238)
(195,239)(196,237)(197,235)(198,236)(199,224)(200,225)(201,223)(202,221)
(203,222)(204,220)(205,218)(206,219)(207,217)(208,233)(209,234)(210,232)
(211,230)(212,231)(213,229)(214,227)(215,228)(216,226)(244,325)(245,326)
(246,327)(247,331)(248,332)(249,333)(250,328)(251,329)(252,330)(253,334)
(254,335)(255,336)(256,340)(257,341)(258,342)(259,337)(260,338)(261,339)
(262,343)(263,344)(264,345)(265,349)(266,350)(267,351)(268,346)(269,347)
(270,348)(271,401)(272,402)(273,400)(274,398)(275,399)(276,397)(277,404)
(278,405)(279,403)(280,382)(281,383)(282,384)(283,379)(284,380)(285,381)
(286,385)(287,386)(288,387)(289,391)(290,392)(291,393)(292,388)(293,389)
(294,390)(295,394)(296,395)(297,396)(298,364)(299,365)(300,366)(301,361)
(302,362)(303,363)(304,367)(305,368)(306,369)(307,373)(308,374)(309,375)
(310,370)(311,371)(312,372)(313,376)(314,377)(315,378)(316,357)(317,355)
(318,356)(319,354)(320,352)(321,353)(322,360)(323,358)(324,359)(406,409)
(407,410)(408,411)(415,418)(416,419)(417,420)(424,427)(425,428)(426,429)
(433,486)(434,484)(435,485)(436,483)(437,481)(438,482)(439,480)(440,478)
(441,479)(442,467)(443,468)(444,466)(445,464)(446,465)(447,463)(448,461)
(449,462)(450,460)(451,476)(452,477)(453,475)(454,473)(455,474)(456,472)
(457,470)(458,471)(459,469);
s2 := Sym(486)!(  1,271)(  2,273)(  3,272)(  4,276)(  5,275)(  6,274)(  7,278)
(  8,277)(  9,279)( 10,294)( 11,293)( 12,292)( 13,296)( 14,295)( 15,297)
( 16,289)( 17,291)( 18,290)( 19,286)( 20,288)( 21,287)( 22,282)( 23,281)
( 24,280)( 25,284)( 26,283)( 27,285)( 28,244)( 29,246)( 30,245)( 31,249)
( 32,248)( 33,247)( 34,251)( 35,250)( 36,252)( 37,267)( 38,266)( 39,265)
( 40,269)( 41,268)( 42,270)( 43,262)( 44,264)( 45,263)( 46,259)( 47,261)
( 48,260)( 49,255)( 50,254)( 51,253)( 52,257)( 53,256)( 54,258)( 55,298)
( 56,300)( 57,299)( 58,303)( 59,302)( 60,301)( 61,305)( 62,304)( 63,306)
( 64,321)( 65,320)( 66,319)( 67,323)( 68,322)( 69,324)( 70,316)( 71,318)
( 72,317)( 73,313)( 74,315)( 75,314)( 76,309)( 77,308)( 78,307)( 79,311)
( 80,310)( 81,312)( 82,352)( 83,354)( 84,353)( 85,357)( 86,356)( 87,355)
( 88,359)( 89,358)( 90,360)( 91,375)( 92,374)( 93,373)( 94,377)( 95,376)
( 96,378)( 97,370)( 98,372)( 99,371)(100,367)(101,369)(102,368)(103,363)
(104,362)(105,361)(106,365)(107,364)(108,366)(109,325)(110,327)(111,326)
(112,330)(113,329)(114,328)(115,332)(116,331)(117,333)(118,348)(119,347)
(120,346)(121,350)(122,349)(123,351)(124,343)(125,345)(126,344)(127,340)
(128,342)(129,341)(130,336)(131,335)(132,334)(133,338)(134,337)(135,339)
(136,379)(137,381)(138,380)(139,384)(140,383)(141,382)(142,386)(143,385)
(144,387)(145,402)(146,401)(147,400)(148,404)(149,403)(150,405)(151,397)
(152,399)(153,398)(154,394)(155,396)(156,395)(157,390)(158,389)(159,388)
(160,392)(161,391)(162,393)(163,433)(164,435)(165,434)(166,438)(167,437)
(168,436)(169,440)(170,439)(171,441)(172,456)(173,455)(174,454)(175,458)
(176,457)(177,459)(178,451)(179,453)(180,452)(181,448)(182,450)(183,449)
(184,444)(185,443)(186,442)(187,446)(188,445)(189,447)(190,406)(191,408)
(192,407)(193,411)(194,410)(195,409)(196,413)(197,412)(198,414)(199,429)
(200,428)(201,427)(202,431)(203,430)(204,432)(205,424)(206,426)(207,425)
(208,421)(209,423)(210,422)(211,417)(212,416)(213,415)(214,419)(215,418)
(216,420)(217,460)(218,462)(219,461)(220,465)(221,464)(222,463)(223,467)
(224,466)(225,468)(226,483)(227,482)(228,481)(229,485)(230,484)(231,486)
(232,478)(233,480)(234,479)(235,475)(236,477)(237,476)(238,471)(239,470)
(240,469)(241,473)(242,472)(243,474);
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, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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