Polytope of Type {18,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,6}*1944a
if this polytope has a name.
Group : SmallGroup(1944,941)
Rank : 3
Schlafli Type : {18,6}
Number of vertices, edges, etc : 162, 486, 54
Order of s0s1s2 : 6
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 : {9,6}*972a
3-fold quotients : {18,6}*648c, {18,6}*648d
6-fold quotients : {9,6}*324b, {9,6}*324c
9-fold quotients : {6,6}*216c
18-fold quotients : {3,6}*108
27-fold quotients : {6,6}*72c
54-fold quotients : {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, 7)( 5, 9)( 6, 8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)
( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 28, 55)( 29, 57)( 30, 56)( 31, 61)
( 32, 63)( 33, 62)( 34, 58)( 35, 60)( 36, 59)( 37, 64)( 38, 66)( 39, 65)
( 40, 70)( 41, 72)( 42, 71)( 43, 67)( 44, 69)( 45, 68)( 46, 73)( 47, 75)
( 48, 74)( 49, 79)( 50, 81)( 51, 80)( 52, 76)( 53, 78)( 54, 77)( 82,163)
( 83,165)( 84,164)( 85,169)( 86,171)( 87,170)( 88,166)( 89,168)( 90,167)
( 91,172)( 92,174)( 93,173)( 94,178)( 95,180)( 96,179)( 97,175)( 98,177)
( 99,176)(100,181)(101,183)(102,182)(103,187)(104,189)(105,188)(106,184)
(107,186)(108,185)(109,217)(110,219)(111,218)(112,223)(113,225)(114,224)
(115,220)(116,222)(117,221)(118,226)(119,228)(120,227)(121,232)(122,234)
(123,233)(124,229)(125,231)(126,230)(127,235)(128,237)(129,236)(130,241)
(131,243)(132,242)(133,238)(134,240)(135,239)(136,190)(137,192)(138,191)
(139,196)(140,198)(141,197)(142,193)(143,195)(144,194)(145,199)(146,201)
(147,200)(148,205)(149,207)(150,206)(151,202)(152,204)(153,203)(154,208)
(155,210)(156,209)(157,214)(158,216)(159,215)(160,211)(161,213)(162,212)
(245,246)(247,250)(248,252)(249,251)(254,255)(256,259)(257,261)(258,260)
(263,264)(265,268)(266,270)(267,269)(271,298)(272,300)(273,299)(274,304)
(275,306)(276,305)(277,301)(278,303)(279,302)(280,307)(281,309)(282,308)
(283,313)(284,315)(285,314)(286,310)(287,312)(288,311)(289,316)(290,318)
(291,317)(292,322)(293,324)(294,323)(295,319)(296,321)(297,320)(325,406)
(326,408)(327,407)(328,412)(329,414)(330,413)(331,409)(332,411)(333,410)
(334,415)(335,417)(336,416)(337,421)(338,423)(339,422)(340,418)(341,420)
(342,419)(343,424)(344,426)(345,425)(346,430)(347,432)(348,431)(349,427)
(350,429)(351,428)(352,460)(353,462)(354,461)(355,466)(356,468)(357,467)
(358,463)(359,465)(360,464)(361,469)(362,471)(363,470)(364,475)(365,477)
(366,476)(367,472)(368,474)(369,473)(370,478)(371,480)(372,479)(373,484)
(374,486)(375,485)(376,481)(377,483)(378,482)(379,433)(380,435)(381,434)
(382,439)(383,441)(384,440)(385,436)(386,438)(387,437)(388,442)(389,444)
(390,443)(391,448)(392,450)(393,449)(394,445)(395,447)(396,446)(397,451)
(398,453)(399,452)(400,457)(401,459)(402,458)(403,454)(404,456)(405,455);;
s1 := ( 1,442)( 2,444)( 3,443)( 4,448)( 5,450)( 6,449)( 7,445)( 8,447)
( 9,446)( 10,458)( 11,457)( 12,459)( 13,455)( 14,454)( 15,456)( 16,452)
( 17,451)( 18,453)( 19,438)( 20,437)( 21,436)( 22,435)( 23,434)( 24,433)
( 25,441)( 26,440)( 27,439)( 28,429)( 29,428)( 30,427)( 31,426)( 32,425)
( 33,424)( 34,432)( 35,431)( 36,430)( 37,406)( 38,408)( 39,407)( 40,412)
( 41,414)( 42,413)( 43,409)( 44,411)( 45,410)( 46,422)( 47,421)( 48,423)
( 49,419)( 50,418)( 51,420)( 52,416)( 53,415)( 54,417)( 55,462)( 56,461)
( 57,460)( 58,468)( 59,467)( 60,466)( 61,465)( 62,464)( 63,463)( 64,475)
( 65,477)( 66,476)( 67,472)( 68,474)( 69,473)( 70,469)( 71,471)( 72,470)
( 73,482)( 74,481)( 75,483)( 76,479)( 77,478)( 78,480)( 79,485)( 80,484)
( 81,486)( 82,361)( 83,363)( 84,362)( 85,367)( 86,369)( 87,368)( 88,364)
( 89,366)( 90,365)( 91,377)( 92,376)( 93,378)( 94,374)( 95,373)( 96,375)
( 97,371)( 98,370)( 99,372)(100,357)(101,356)(102,355)(103,354)(104,353)
(105,352)(106,360)(107,359)(108,358)(109,348)(110,347)(111,346)(112,345)
(113,344)(114,343)(115,351)(116,350)(117,349)(118,325)(119,327)(120,326)
(121,331)(122,333)(123,332)(124,328)(125,330)(126,329)(127,341)(128,340)
(129,342)(130,338)(131,337)(132,339)(133,335)(134,334)(135,336)(136,381)
(137,380)(138,379)(139,387)(140,386)(141,385)(142,384)(143,383)(144,382)
(145,394)(146,396)(147,395)(148,391)(149,393)(150,392)(151,388)(152,390)
(153,389)(154,401)(155,400)(156,402)(157,398)(158,397)(159,399)(160,404)
(161,403)(162,405)(163,280)(164,282)(165,281)(166,286)(167,288)(168,287)
(169,283)(170,285)(171,284)(172,296)(173,295)(174,297)(175,293)(176,292)
(177,294)(178,290)(179,289)(180,291)(181,276)(182,275)(183,274)(184,273)
(185,272)(186,271)(187,279)(188,278)(189,277)(190,267)(191,266)(192,265)
(193,264)(194,263)(195,262)(196,270)(197,269)(198,268)(199,244)(200,246)
(201,245)(202,250)(203,252)(204,251)(205,247)(206,249)(207,248)(208,260)
(209,259)(210,261)(211,257)(212,256)(213,258)(214,254)(215,253)(216,255)
(217,300)(218,299)(219,298)(220,306)(221,305)(222,304)(223,303)(224,302)
(225,301)(226,313)(227,315)(228,314)(229,310)(230,312)(231,311)(232,307)
(233,309)(234,308)(235,320)(236,319)(237,321)(238,317)(239,316)(240,318)
(241,323)(242,322)(243,324);;
s2 := ( 4, 8)( 5, 9)( 6, 7)( 10, 19)( 11, 20)( 12, 21)( 13, 26)( 14, 27)
( 15, 25)( 16, 24)( 17, 22)( 18, 23)( 31, 35)( 32, 36)( 33, 34)( 37, 46)
( 38, 47)( 39, 48)( 40, 53)( 41, 54)( 42, 52)( 43, 51)( 44, 49)( 45, 50)
( 58, 62)( 59, 63)( 60, 61)( 64, 73)( 65, 74)( 66, 75)( 67, 80)( 68, 81)
( 69, 79)( 70, 78)( 71, 76)( 72, 77)( 82,163)( 83,164)( 84,165)( 85,170)
( 86,171)( 87,169)( 88,168)( 89,166)( 90,167)( 91,181)( 92,182)( 93,183)
( 94,188)( 95,189)( 96,187)( 97,186)( 98,184)( 99,185)(100,172)(101,173)
(102,174)(103,179)(104,180)(105,178)(106,177)(107,175)(108,176)(109,190)
(110,191)(111,192)(112,197)(113,198)(114,196)(115,195)(116,193)(117,194)
(118,208)(119,209)(120,210)(121,215)(122,216)(123,214)(124,213)(125,211)
(126,212)(127,199)(128,200)(129,201)(130,206)(131,207)(132,205)(133,204)
(134,202)(135,203)(136,217)(137,218)(138,219)(139,224)(140,225)(141,223)
(142,222)(143,220)(144,221)(145,235)(146,236)(147,237)(148,242)(149,243)
(150,241)(151,240)(152,238)(153,239)(154,226)(155,227)(156,228)(157,233)
(158,234)(159,232)(160,231)(161,229)(162,230)(247,251)(248,252)(249,250)
(253,262)(254,263)(255,264)(256,269)(257,270)(258,268)(259,267)(260,265)
(261,266)(274,278)(275,279)(276,277)(280,289)(281,290)(282,291)(283,296)
(284,297)(285,295)(286,294)(287,292)(288,293)(301,305)(302,306)(303,304)
(307,316)(308,317)(309,318)(310,323)(311,324)(312,322)(313,321)(314,319)
(315,320)(325,406)(326,407)(327,408)(328,413)(329,414)(330,412)(331,411)
(332,409)(333,410)(334,424)(335,425)(336,426)(337,431)(338,432)(339,430)
(340,429)(341,427)(342,428)(343,415)(344,416)(345,417)(346,422)(347,423)
(348,421)(349,420)(350,418)(351,419)(352,433)(353,434)(354,435)(355,440)
(356,441)(357,439)(358,438)(359,436)(360,437)(361,451)(362,452)(363,453)
(364,458)(365,459)(366,457)(367,456)(368,454)(369,455)(370,442)(371,443)
(372,444)(373,449)(374,450)(375,448)(376,447)(377,445)(378,446)(379,460)
(380,461)(381,462)(382,467)(383,468)(384,466)(385,465)(386,463)(387,464)
(388,478)(389,479)(390,480)(391,485)(392,486)(393,484)(394,483)(395,481)
(396,482)(397,469)(398,470)(399,471)(400,476)(401,477)(402,475)(403,474)
(404,472)(405,473);;
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*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(486)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 11, 12)( 13, 16)( 14, 18)
( 15, 17)( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 28, 55)( 29, 57)( 30, 56)
( 31, 61)( 32, 63)( 33, 62)( 34, 58)( 35, 60)( 36, 59)( 37, 64)( 38, 66)
( 39, 65)( 40, 70)( 41, 72)( 42, 71)( 43, 67)( 44, 69)( 45, 68)( 46, 73)
( 47, 75)( 48, 74)( 49, 79)( 50, 81)( 51, 80)( 52, 76)( 53, 78)( 54, 77)
( 82,163)( 83,165)( 84,164)( 85,169)( 86,171)( 87,170)( 88,166)( 89,168)
( 90,167)( 91,172)( 92,174)( 93,173)( 94,178)( 95,180)( 96,179)( 97,175)
( 98,177)( 99,176)(100,181)(101,183)(102,182)(103,187)(104,189)(105,188)
(106,184)(107,186)(108,185)(109,217)(110,219)(111,218)(112,223)(113,225)
(114,224)(115,220)(116,222)(117,221)(118,226)(119,228)(120,227)(121,232)
(122,234)(123,233)(124,229)(125,231)(126,230)(127,235)(128,237)(129,236)
(130,241)(131,243)(132,242)(133,238)(134,240)(135,239)(136,190)(137,192)
(138,191)(139,196)(140,198)(141,197)(142,193)(143,195)(144,194)(145,199)
(146,201)(147,200)(148,205)(149,207)(150,206)(151,202)(152,204)(153,203)
(154,208)(155,210)(156,209)(157,214)(158,216)(159,215)(160,211)(161,213)
(162,212)(245,246)(247,250)(248,252)(249,251)(254,255)(256,259)(257,261)
(258,260)(263,264)(265,268)(266,270)(267,269)(271,298)(272,300)(273,299)
(274,304)(275,306)(276,305)(277,301)(278,303)(279,302)(280,307)(281,309)
(282,308)(283,313)(284,315)(285,314)(286,310)(287,312)(288,311)(289,316)
(290,318)(291,317)(292,322)(293,324)(294,323)(295,319)(296,321)(297,320)
(325,406)(326,408)(327,407)(328,412)(329,414)(330,413)(331,409)(332,411)
(333,410)(334,415)(335,417)(336,416)(337,421)(338,423)(339,422)(340,418)
(341,420)(342,419)(343,424)(344,426)(345,425)(346,430)(347,432)(348,431)
(349,427)(350,429)(351,428)(352,460)(353,462)(354,461)(355,466)(356,468)
(357,467)(358,463)(359,465)(360,464)(361,469)(362,471)(363,470)(364,475)
(365,477)(366,476)(367,472)(368,474)(369,473)(370,478)(371,480)(372,479)
(373,484)(374,486)(375,485)(376,481)(377,483)(378,482)(379,433)(380,435)
(381,434)(382,439)(383,441)(384,440)(385,436)(386,438)(387,437)(388,442)
(389,444)(390,443)(391,448)(392,450)(393,449)(394,445)(395,447)(396,446)
(397,451)(398,453)(399,452)(400,457)(401,459)(402,458)(403,454)(404,456)
(405,455);
s1 := Sym(486)!( 1,442)( 2,444)( 3,443)( 4,448)( 5,450)( 6,449)( 7,445)
( 8,447)( 9,446)( 10,458)( 11,457)( 12,459)( 13,455)( 14,454)( 15,456)
( 16,452)( 17,451)( 18,453)( 19,438)( 20,437)( 21,436)( 22,435)( 23,434)
( 24,433)( 25,441)( 26,440)( 27,439)( 28,429)( 29,428)( 30,427)( 31,426)
( 32,425)( 33,424)( 34,432)( 35,431)( 36,430)( 37,406)( 38,408)( 39,407)
( 40,412)( 41,414)( 42,413)( 43,409)( 44,411)( 45,410)( 46,422)( 47,421)
( 48,423)( 49,419)( 50,418)( 51,420)( 52,416)( 53,415)( 54,417)( 55,462)
( 56,461)( 57,460)( 58,468)( 59,467)( 60,466)( 61,465)( 62,464)( 63,463)
( 64,475)( 65,477)( 66,476)( 67,472)( 68,474)( 69,473)( 70,469)( 71,471)
( 72,470)( 73,482)( 74,481)( 75,483)( 76,479)( 77,478)( 78,480)( 79,485)
( 80,484)( 81,486)( 82,361)( 83,363)( 84,362)( 85,367)( 86,369)( 87,368)
( 88,364)( 89,366)( 90,365)( 91,377)( 92,376)( 93,378)( 94,374)( 95,373)
( 96,375)( 97,371)( 98,370)( 99,372)(100,357)(101,356)(102,355)(103,354)
(104,353)(105,352)(106,360)(107,359)(108,358)(109,348)(110,347)(111,346)
(112,345)(113,344)(114,343)(115,351)(116,350)(117,349)(118,325)(119,327)
(120,326)(121,331)(122,333)(123,332)(124,328)(125,330)(126,329)(127,341)
(128,340)(129,342)(130,338)(131,337)(132,339)(133,335)(134,334)(135,336)
(136,381)(137,380)(138,379)(139,387)(140,386)(141,385)(142,384)(143,383)
(144,382)(145,394)(146,396)(147,395)(148,391)(149,393)(150,392)(151,388)
(152,390)(153,389)(154,401)(155,400)(156,402)(157,398)(158,397)(159,399)
(160,404)(161,403)(162,405)(163,280)(164,282)(165,281)(166,286)(167,288)
(168,287)(169,283)(170,285)(171,284)(172,296)(173,295)(174,297)(175,293)
(176,292)(177,294)(178,290)(179,289)(180,291)(181,276)(182,275)(183,274)
(184,273)(185,272)(186,271)(187,279)(188,278)(189,277)(190,267)(191,266)
(192,265)(193,264)(194,263)(195,262)(196,270)(197,269)(198,268)(199,244)
(200,246)(201,245)(202,250)(203,252)(204,251)(205,247)(206,249)(207,248)
(208,260)(209,259)(210,261)(211,257)(212,256)(213,258)(214,254)(215,253)
(216,255)(217,300)(218,299)(219,298)(220,306)(221,305)(222,304)(223,303)
(224,302)(225,301)(226,313)(227,315)(228,314)(229,310)(230,312)(231,311)
(232,307)(233,309)(234,308)(235,320)(236,319)(237,321)(238,317)(239,316)
(240,318)(241,323)(242,322)(243,324);
s2 := Sym(486)!( 4, 8)( 5, 9)( 6, 7)( 10, 19)( 11, 20)( 12, 21)( 13, 26)
( 14, 27)( 15, 25)( 16, 24)( 17, 22)( 18, 23)( 31, 35)( 32, 36)( 33, 34)
( 37, 46)( 38, 47)( 39, 48)( 40, 53)( 41, 54)( 42, 52)( 43, 51)( 44, 49)
( 45, 50)( 58, 62)( 59, 63)( 60, 61)( 64, 73)( 65, 74)( 66, 75)( 67, 80)
( 68, 81)( 69, 79)( 70, 78)( 71, 76)( 72, 77)( 82,163)( 83,164)( 84,165)
( 85,170)( 86,171)( 87,169)( 88,168)( 89,166)( 90,167)( 91,181)( 92,182)
( 93,183)( 94,188)( 95,189)( 96,187)( 97,186)( 98,184)( 99,185)(100,172)
(101,173)(102,174)(103,179)(104,180)(105,178)(106,177)(107,175)(108,176)
(109,190)(110,191)(111,192)(112,197)(113,198)(114,196)(115,195)(116,193)
(117,194)(118,208)(119,209)(120,210)(121,215)(122,216)(123,214)(124,213)
(125,211)(126,212)(127,199)(128,200)(129,201)(130,206)(131,207)(132,205)
(133,204)(134,202)(135,203)(136,217)(137,218)(138,219)(139,224)(140,225)
(141,223)(142,222)(143,220)(144,221)(145,235)(146,236)(147,237)(148,242)
(149,243)(150,241)(151,240)(152,238)(153,239)(154,226)(155,227)(156,228)
(157,233)(158,234)(159,232)(160,231)(161,229)(162,230)(247,251)(248,252)
(249,250)(253,262)(254,263)(255,264)(256,269)(257,270)(258,268)(259,267)
(260,265)(261,266)(274,278)(275,279)(276,277)(280,289)(281,290)(282,291)
(283,296)(284,297)(285,295)(286,294)(287,292)(288,293)(301,305)(302,306)
(303,304)(307,316)(308,317)(309,318)(310,323)(311,324)(312,322)(313,321)
(314,319)(315,320)(325,406)(326,407)(327,408)(328,413)(329,414)(330,412)
(331,411)(332,409)(333,410)(334,424)(335,425)(336,426)(337,431)(338,432)
(339,430)(340,429)(341,427)(342,428)(343,415)(344,416)(345,417)(346,422)
(347,423)(348,421)(349,420)(350,418)(351,419)(352,433)(353,434)(354,435)
(355,440)(356,441)(357,439)(358,438)(359,436)(360,437)(361,451)(362,452)
(363,453)(364,458)(365,459)(366,457)(367,456)(368,454)(369,455)(370,442)
(371,443)(372,444)(373,449)(374,450)(375,448)(376,447)(377,445)(378,446)
(379,460)(380,461)(381,462)(382,467)(383,468)(384,466)(385,465)(386,463)
(387,464)(388,478)(389,479)(390,480)(391,485)(392,486)(393,484)(394,483)
(395,481)(396,482)(397,469)(398,470)(399,471)(400,476)(401,477)(402,475)
(403,474)(404,472)(405,473);
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*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;
References : None.
to this polytope