Polytope of Type {18,52}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,52}*1872a
Also Known As : {18,52|2}. if this polytope has another name.
Group : SmallGroup(1872,189)
Rank : 3
Schlafli Type : {18,52}
Number of vertices, edges, etc : 18, 468, 52
Order of s0s1s2 : 468
Order of s0s1s2s1 : 2
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) :
2-fold quotients : {18,26}*936
3-fold quotients : {6,52}*624a
6-fold quotients : {6,26}*312
9-fold quotients : {2,52}*208
13-fold quotients : {18,4}*144a
18-fold quotients : {2,26}*104
26-fold quotients : {18,2}*72
36-fold quotients : {2,13}*52
39-fold quotients : {6,4}*48a
52-fold quotients : {9,2}*36
78-fold quotients : {6,2}*24
117-fold quotients : {2,4}*16
156-fold quotients : {3,2}*12
234-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 3)( 5, 6)( 8, 9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)( 23, 24)
( 26, 27)( 29, 30)( 32, 33)( 35, 36)( 38, 39)( 40, 81)( 41, 80)( 42, 79)
( 43, 84)( 44, 83)( 45, 82)( 46, 87)( 47, 86)( 48, 85)( 49, 90)( 50, 89)
( 51, 88)( 52, 93)( 53, 92)( 54, 91)( 55, 96)( 56, 95)( 57, 94)( 58, 99)
( 59, 98)( 60, 97)( 61,102)( 62,101)( 63,100)( 64,105)( 65,104)( 66,103)
( 67,108)( 68,107)( 69,106)( 70,111)( 71,110)( 72,109)( 73,114)( 74,113)
( 75,112)( 76,117)( 77,116)( 78,115)(119,120)(122,123)(125,126)(128,129)
(131,132)(134,135)(137,138)(140,141)(143,144)(146,147)(149,150)(152,153)
(155,156)(157,198)(158,197)(159,196)(160,201)(161,200)(162,199)(163,204)
(164,203)(165,202)(166,207)(167,206)(168,205)(169,210)(170,209)(171,208)
(172,213)(173,212)(174,211)(175,216)(176,215)(177,214)(178,219)(179,218)
(180,217)(181,222)(182,221)(183,220)(184,225)(185,224)(186,223)(187,228)
(188,227)(189,226)(190,231)(191,230)(192,229)(193,234)(194,233)(195,232)
(236,237)(239,240)(242,243)(245,246)(248,249)(251,252)(254,255)(257,258)
(260,261)(263,264)(266,267)(269,270)(272,273)(274,315)(275,314)(276,313)
(277,318)(278,317)(279,316)(280,321)(281,320)(282,319)(283,324)(284,323)
(285,322)(286,327)(287,326)(288,325)(289,330)(290,329)(291,328)(292,333)
(293,332)(294,331)(295,336)(296,335)(297,334)(298,339)(299,338)(300,337)
(301,342)(302,341)(303,340)(304,345)(305,344)(306,343)(307,348)(308,347)
(309,346)(310,351)(311,350)(312,349)(353,354)(356,357)(359,360)(362,363)
(365,366)(368,369)(371,372)(374,375)(377,378)(380,381)(383,384)(386,387)
(389,390)(391,432)(392,431)(393,430)(394,435)(395,434)(396,433)(397,438)
(398,437)(399,436)(400,441)(401,440)(402,439)(403,444)(404,443)(405,442)
(406,447)(407,446)(408,445)(409,450)(410,449)(411,448)(412,453)(413,452)
(414,451)(415,456)(416,455)(417,454)(418,459)(419,458)(420,457)(421,462)
(422,461)(423,460)(424,465)(425,464)(426,463)(427,468)(428,467)(429,466);;
s1 := ( 1, 40)( 2, 42)( 3, 41)( 4, 76)( 5, 78)( 6, 77)( 7, 73)( 8, 75)
( 9, 74)( 10, 70)( 11, 72)( 12, 71)( 13, 67)( 14, 69)( 15, 68)( 16, 64)
( 17, 66)( 18, 65)( 19, 61)( 20, 63)( 21, 62)( 22, 58)( 23, 60)( 24, 59)
( 25, 55)( 26, 57)( 27, 56)( 28, 52)( 29, 54)( 30, 53)( 31, 49)( 32, 51)
( 33, 50)( 34, 46)( 35, 48)( 36, 47)( 37, 43)( 38, 45)( 39, 44)( 79, 81)
( 82,117)( 83,116)( 84,115)( 85,114)( 86,113)( 87,112)( 88,111)( 89,110)
( 90,109)( 91,108)( 92,107)( 93,106)( 94,105)( 95,104)( 96,103)( 97,102)
( 98,101)( 99,100)(118,157)(119,159)(120,158)(121,193)(122,195)(123,194)
(124,190)(125,192)(126,191)(127,187)(128,189)(129,188)(130,184)(131,186)
(132,185)(133,181)(134,183)(135,182)(136,178)(137,180)(138,179)(139,175)
(140,177)(141,176)(142,172)(143,174)(144,173)(145,169)(146,171)(147,170)
(148,166)(149,168)(150,167)(151,163)(152,165)(153,164)(154,160)(155,162)
(156,161)(196,198)(199,234)(200,233)(201,232)(202,231)(203,230)(204,229)
(205,228)(206,227)(207,226)(208,225)(209,224)(210,223)(211,222)(212,221)
(213,220)(214,219)(215,218)(216,217)(235,391)(236,393)(237,392)(238,427)
(239,429)(240,428)(241,424)(242,426)(243,425)(244,421)(245,423)(246,422)
(247,418)(248,420)(249,419)(250,415)(251,417)(252,416)(253,412)(254,414)
(255,413)(256,409)(257,411)(258,410)(259,406)(260,408)(261,407)(262,403)
(263,405)(264,404)(265,400)(266,402)(267,401)(268,397)(269,399)(270,398)
(271,394)(272,396)(273,395)(274,352)(275,354)(276,353)(277,388)(278,390)
(279,389)(280,385)(281,387)(282,386)(283,382)(284,384)(285,383)(286,379)
(287,381)(288,380)(289,376)(290,378)(291,377)(292,373)(293,375)(294,374)
(295,370)(296,372)(297,371)(298,367)(299,369)(300,368)(301,364)(302,366)
(303,365)(304,361)(305,363)(306,362)(307,358)(308,360)(309,359)(310,355)
(311,357)(312,356)(313,432)(314,431)(315,430)(316,468)(317,467)(318,466)
(319,465)(320,464)(321,463)(322,462)(323,461)(324,460)(325,459)(326,458)
(327,457)(328,456)(329,455)(330,454)(331,453)(332,452)(333,451)(334,450)
(335,449)(336,448)(337,447)(338,446)(339,445)(340,444)(341,443)(342,442)
(343,441)(344,440)(345,439)(346,438)(347,437)(348,436)(349,435)(350,434)
(351,433);;
s2 := ( 1,238)( 2,239)( 3,240)( 4,235)( 5,236)( 6,237)( 7,271)( 8,272)
( 9,273)( 10,268)( 11,269)( 12,270)( 13,265)( 14,266)( 15,267)( 16,262)
( 17,263)( 18,264)( 19,259)( 20,260)( 21,261)( 22,256)( 23,257)( 24,258)
( 25,253)( 26,254)( 27,255)( 28,250)( 29,251)( 30,252)( 31,247)( 32,248)
( 33,249)( 34,244)( 35,245)( 36,246)( 37,241)( 38,242)( 39,243)( 40,277)
( 41,278)( 42,279)( 43,274)( 44,275)( 45,276)( 46,310)( 47,311)( 48,312)
( 49,307)( 50,308)( 51,309)( 52,304)( 53,305)( 54,306)( 55,301)( 56,302)
( 57,303)( 58,298)( 59,299)( 60,300)( 61,295)( 62,296)( 63,297)( 64,292)
( 65,293)( 66,294)( 67,289)( 68,290)( 69,291)( 70,286)( 71,287)( 72,288)
( 73,283)( 74,284)( 75,285)( 76,280)( 77,281)( 78,282)( 79,316)( 80,317)
( 81,318)( 82,313)( 83,314)( 84,315)( 85,349)( 86,350)( 87,351)( 88,346)
( 89,347)( 90,348)( 91,343)( 92,344)( 93,345)( 94,340)( 95,341)( 96,342)
( 97,337)( 98,338)( 99,339)(100,334)(101,335)(102,336)(103,331)(104,332)
(105,333)(106,328)(107,329)(108,330)(109,325)(110,326)(111,327)(112,322)
(113,323)(114,324)(115,319)(116,320)(117,321)(118,355)(119,356)(120,357)
(121,352)(122,353)(123,354)(124,388)(125,389)(126,390)(127,385)(128,386)
(129,387)(130,382)(131,383)(132,384)(133,379)(134,380)(135,381)(136,376)
(137,377)(138,378)(139,373)(140,374)(141,375)(142,370)(143,371)(144,372)
(145,367)(146,368)(147,369)(148,364)(149,365)(150,366)(151,361)(152,362)
(153,363)(154,358)(155,359)(156,360)(157,394)(158,395)(159,396)(160,391)
(161,392)(162,393)(163,427)(164,428)(165,429)(166,424)(167,425)(168,426)
(169,421)(170,422)(171,423)(172,418)(173,419)(174,420)(175,415)(176,416)
(177,417)(178,412)(179,413)(180,414)(181,409)(182,410)(183,411)(184,406)
(185,407)(186,408)(187,403)(188,404)(189,405)(190,400)(191,401)(192,402)
(193,397)(194,398)(195,399)(196,433)(197,434)(198,435)(199,430)(200,431)
(201,432)(202,466)(203,467)(204,468)(205,463)(206,464)(207,465)(208,460)
(209,461)(210,462)(211,457)(212,458)(213,459)(214,454)(215,455)(216,456)
(217,451)(218,452)(219,453)(220,448)(221,449)(222,450)(223,445)(224,446)
(225,447)(226,442)(227,443)(228,444)(229,439)(230,440)(231,441)(232,436)
(233,437)(234,438);;
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, s0*s1*s2*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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(468)!( 2, 3)( 5, 6)( 8, 9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)
( 23, 24)( 26, 27)( 29, 30)( 32, 33)( 35, 36)( 38, 39)( 40, 81)( 41, 80)
( 42, 79)( 43, 84)( 44, 83)( 45, 82)( 46, 87)( 47, 86)( 48, 85)( 49, 90)
( 50, 89)( 51, 88)( 52, 93)( 53, 92)( 54, 91)( 55, 96)( 56, 95)( 57, 94)
( 58, 99)( 59, 98)( 60, 97)( 61,102)( 62,101)( 63,100)( 64,105)( 65,104)
( 66,103)( 67,108)( 68,107)( 69,106)( 70,111)( 71,110)( 72,109)( 73,114)
( 74,113)( 75,112)( 76,117)( 77,116)( 78,115)(119,120)(122,123)(125,126)
(128,129)(131,132)(134,135)(137,138)(140,141)(143,144)(146,147)(149,150)
(152,153)(155,156)(157,198)(158,197)(159,196)(160,201)(161,200)(162,199)
(163,204)(164,203)(165,202)(166,207)(167,206)(168,205)(169,210)(170,209)
(171,208)(172,213)(173,212)(174,211)(175,216)(176,215)(177,214)(178,219)
(179,218)(180,217)(181,222)(182,221)(183,220)(184,225)(185,224)(186,223)
(187,228)(188,227)(189,226)(190,231)(191,230)(192,229)(193,234)(194,233)
(195,232)(236,237)(239,240)(242,243)(245,246)(248,249)(251,252)(254,255)
(257,258)(260,261)(263,264)(266,267)(269,270)(272,273)(274,315)(275,314)
(276,313)(277,318)(278,317)(279,316)(280,321)(281,320)(282,319)(283,324)
(284,323)(285,322)(286,327)(287,326)(288,325)(289,330)(290,329)(291,328)
(292,333)(293,332)(294,331)(295,336)(296,335)(297,334)(298,339)(299,338)
(300,337)(301,342)(302,341)(303,340)(304,345)(305,344)(306,343)(307,348)
(308,347)(309,346)(310,351)(311,350)(312,349)(353,354)(356,357)(359,360)
(362,363)(365,366)(368,369)(371,372)(374,375)(377,378)(380,381)(383,384)
(386,387)(389,390)(391,432)(392,431)(393,430)(394,435)(395,434)(396,433)
(397,438)(398,437)(399,436)(400,441)(401,440)(402,439)(403,444)(404,443)
(405,442)(406,447)(407,446)(408,445)(409,450)(410,449)(411,448)(412,453)
(413,452)(414,451)(415,456)(416,455)(417,454)(418,459)(419,458)(420,457)
(421,462)(422,461)(423,460)(424,465)(425,464)(426,463)(427,468)(428,467)
(429,466);
s1 := Sym(468)!( 1, 40)( 2, 42)( 3, 41)( 4, 76)( 5, 78)( 6, 77)( 7, 73)
( 8, 75)( 9, 74)( 10, 70)( 11, 72)( 12, 71)( 13, 67)( 14, 69)( 15, 68)
( 16, 64)( 17, 66)( 18, 65)( 19, 61)( 20, 63)( 21, 62)( 22, 58)( 23, 60)
( 24, 59)( 25, 55)( 26, 57)( 27, 56)( 28, 52)( 29, 54)( 30, 53)( 31, 49)
( 32, 51)( 33, 50)( 34, 46)( 35, 48)( 36, 47)( 37, 43)( 38, 45)( 39, 44)
( 79, 81)( 82,117)( 83,116)( 84,115)( 85,114)( 86,113)( 87,112)( 88,111)
( 89,110)( 90,109)( 91,108)( 92,107)( 93,106)( 94,105)( 95,104)( 96,103)
( 97,102)( 98,101)( 99,100)(118,157)(119,159)(120,158)(121,193)(122,195)
(123,194)(124,190)(125,192)(126,191)(127,187)(128,189)(129,188)(130,184)
(131,186)(132,185)(133,181)(134,183)(135,182)(136,178)(137,180)(138,179)
(139,175)(140,177)(141,176)(142,172)(143,174)(144,173)(145,169)(146,171)
(147,170)(148,166)(149,168)(150,167)(151,163)(152,165)(153,164)(154,160)
(155,162)(156,161)(196,198)(199,234)(200,233)(201,232)(202,231)(203,230)
(204,229)(205,228)(206,227)(207,226)(208,225)(209,224)(210,223)(211,222)
(212,221)(213,220)(214,219)(215,218)(216,217)(235,391)(236,393)(237,392)
(238,427)(239,429)(240,428)(241,424)(242,426)(243,425)(244,421)(245,423)
(246,422)(247,418)(248,420)(249,419)(250,415)(251,417)(252,416)(253,412)
(254,414)(255,413)(256,409)(257,411)(258,410)(259,406)(260,408)(261,407)
(262,403)(263,405)(264,404)(265,400)(266,402)(267,401)(268,397)(269,399)
(270,398)(271,394)(272,396)(273,395)(274,352)(275,354)(276,353)(277,388)
(278,390)(279,389)(280,385)(281,387)(282,386)(283,382)(284,384)(285,383)
(286,379)(287,381)(288,380)(289,376)(290,378)(291,377)(292,373)(293,375)
(294,374)(295,370)(296,372)(297,371)(298,367)(299,369)(300,368)(301,364)
(302,366)(303,365)(304,361)(305,363)(306,362)(307,358)(308,360)(309,359)
(310,355)(311,357)(312,356)(313,432)(314,431)(315,430)(316,468)(317,467)
(318,466)(319,465)(320,464)(321,463)(322,462)(323,461)(324,460)(325,459)
(326,458)(327,457)(328,456)(329,455)(330,454)(331,453)(332,452)(333,451)
(334,450)(335,449)(336,448)(337,447)(338,446)(339,445)(340,444)(341,443)
(342,442)(343,441)(344,440)(345,439)(346,438)(347,437)(348,436)(349,435)
(350,434)(351,433);
s2 := Sym(468)!( 1,238)( 2,239)( 3,240)( 4,235)( 5,236)( 6,237)( 7,271)
( 8,272)( 9,273)( 10,268)( 11,269)( 12,270)( 13,265)( 14,266)( 15,267)
( 16,262)( 17,263)( 18,264)( 19,259)( 20,260)( 21,261)( 22,256)( 23,257)
( 24,258)( 25,253)( 26,254)( 27,255)( 28,250)( 29,251)( 30,252)( 31,247)
( 32,248)( 33,249)( 34,244)( 35,245)( 36,246)( 37,241)( 38,242)( 39,243)
( 40,277)( 41,278)( 42,279)( 43,274)( 44,275)( 45,276)( 46,310)( 47,311)
( 48,312)( 49,307)( 50,308)( 51,309)( 52,304)( 53,305)( 54,306)( 55,301)
( 56,302)( 57,303)( 58,298)( 59,299)( 60,300)( 61,295)( 62,296)( 63,297)
( 64,292)( 65,293)( 66,294)( 67,289)( 68,290)( 69,291)( 70,286)( 71,287)
( 72,288)( 73,283)( 74,284)( 75,285)( 76,280)( 77,281)( 78,282)( 79,316)
( 80,317)( 81,318)( 82,313)( 83,314)( 84,315)( 85,349)( 86,350)( 87,351)
( 88,346)( 89,347)( 90,348)( 91,343)( 92,344)( 93,345)( 94,340)( 95,341)
( 96,342)( 97,337)( 98,338)( 99,339)(100,334)(101,335)(102,336)(103,331)
(104,332)(105,333)(106,328)(107,329)(108,330)(109,325)(110,326)(111,327)
(112,322)(113,323)(114,324)(115,319)(116,320)(117,321)(118,355)(119,356)
(120,357)(121,352)(122,353)(123,354)(124,388)(125,389)(126,390)(127,385)
(128,386)(129,387)(130,382)(131,383)(132,384)(133,379)(134,380)(135,381)
(136,376)(137,377)(138,378)(139,373)(140,374)(141,375)(142,370)(143,371)
(144,372)(145,367)(146,368)(147,369)(148,364)(149,365)(150,366)(151,361)
(152,362)(153,363)(154,358)(155,359)(156,360)(157,394)(158,395)(159,396)
(160,391)(161,392)(162,393)(163,427)(164,428)(165,429)(166,424)(167,425)
(168,426)(169,421)(170,422)(171,423)(172,418)(173,419)(174,420)(175,415)
(176,416)(177,417)(178,412)(179,413)(180,414)(181,409)(182,410)(183,411)
(184,406)(185,407)(186,408)(187,403)(188,404)(189,405)(190,400)(191,401)
(192,402)(193,397)(194,398)(195,399)(196,433)(197,434)(198,435)(199,430)
(200,431)(201,432)(202,466)(203,467)(204,468)(205,463)(206,464)(207,465)
(208,460)(209,461)(210,462)(211,457)(212,458)(213,459)(214,454)(215,455)
(216,456)(217,451)(218,452)(219,453)(220,448)(221,449)(222,450)(223,445)
(224,446)(225,447)(226,442)(227,443)(228,444)(229,439)(230,440)(231,441)
(232,436)(233,437)(234,438);
poly := sub<Sym(468)|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, s0*s1*s2*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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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