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