Polytope of Type {46,18}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {46,18}*1656
Also Known As : {46,18|2}. if this polytope has another name.
Group : SmallGroup(1656,40)
Rank : 3
Schlafli Type : {46,18}
Number of vertices, edges, etc : 46, 414, 18
Order of s0s1s2 : 414
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) :
3-fold quotients : {46,6}*552
9-fold quotients : {46,2}*184
18-fold quotients : {23,2}*92
23-fold quotients : {2,18}*72
46-fold quotients : {2,9}*36
69-fold quotients : {2,6}*24
138-fold quotients : {2,3}*12
207-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 4, 67)( 5, 68)( 6, 69)( 7, 64)( 8, 65)( 9, 66)( 10, 61)( 11, 62)
( 12, 63)( 13, 58)( 14, 59)( 15, 60)( 16, 55)( 17, 56)( 18, 57)( 19, 52)
( 20, 53)( 21, 54)( 22, 49)( 23, 50)( 24, 51)( 25, 46)( 26, 47)( 27, 48)
( 28, 43)( 29, 44)( 30, 45)( 31, 40)( 32, 41)( 33, 42)( 34, 37)( 35, 38)
( 36, 39)( 73,136)( 74,137)( 75,138)( 76,133)( 77,134)( 78,135)( 79,130)
( 80,131)( 81,132)( 82,127)( 83,128)( 84,129)( 85,124)( 86,125)( 87,126)
( 88,121)( 89,122)( 90,123)( 91,118)( 92,119)( 93,120)( 94,115)( 95,116)
( 96,117)( 97,112)( 98,113)( 99,114)(100,109)(101,110)(102,111)(103,106)
(104,107)(105,108)(142,205)(143,206)(144,207)(145,202)(146,203)(147,204)
(148,199)(149,200)(150,201)(151,196)(152,197)(153,198)(154,193)(155,194)
(156,195)(157,190)(158,191)(159,192)(160,187)(161,188)(162,189)(163,184)
(164,185)(165,186)(166,181)(167,182)(168,183)(169,178)(170,179)(171,180)
(172,175)(173,176)(174,177)(211,274)(212,275)(213,276)(214,271)(215,272)
(216,273)(217,268)(218,269)(219,270)(220,265)(221,266)(222,267)(223,262)
(224,263)(225,264)(226,259)(227,260)(228,261)(229,256)(230,257)(231,258)
(232,253)(233,254)(234,255)(235,250)(236,251)(237,252)(238,247)(239,248)
(240,249)(241,244)(242,245)(243,246)(280,343)(281,344)(282,345)(283,340)
(284,341)(285,342)(286,337)(287,338)(288,339)(289,334)(290,335)(291,336)
(292,331)(293,332)(294,333)(295,328)(296,329)(297,330)(298,325)(299,326)
(300,327)(301,322)(302,323)(303,324)(304,319)(305,320)(306,321)(307,316)
(308,317)(309,318)(310,313)(311,314)(312,315)(349,412)(350,413)(351,414)
(352,409)(353,410)(354,411)(355,406)(356,407)(357,408)(358,403)(359,404)
(360,405)(361,400)(362,401)(363,402)(364,397)(365,398)(366,399)(367,394)
(368,395)(369,396)(370,391)(371,392)(372,393)(373,388)(374,389)(375,390)
(376,385)(377,386)(378,387)(379,382)(380,383)(381,384);;
s1 := ( 1, 4)( 2, 6)( 3, 5)( 7, 67)( 8, 69)( 9, 68)( 10, 64)( 11, 66)
( 12, 65)( 13, 61)( 14, 63)( 15, 62)( 16, 58)( 17, 60)( 18, 59)( 19, 55)
( 20, 57)( 21, 56)( 22, 52)( 23, 54)( 24, 53)( 25, 49)( 26, 51)( 27, 50)
( 28, 46)( 29, 48)( 30, 47)( 31, 43)( 32, 45)( 33, 44)( 34, 40)( 35, 42)
( 36, 41)( 38, 39)( 70,143)( 71,142)( 72,144)( 73,140)( 74,139)( 75,141)
( 76,206)( 77,205)( 78,207)( 79,203)( 80,202)( 81,204)( 82,200)( 83,199)
( 84,201)( 85,197)( 86,196)( 87,198)( 88,194)( 89,193)( 90,195)( 91,191)
( 92,190)( 93,192)( 94,188)( 95,187)( 96,189)( 97,185)( 98,184)( 99,186)
(100,182)(101,181)(102,183)(103,179)(104,178)(105,180)(106,176)(107,175)
(108,177)(109,173)(110,172)(111,174)(112,170)(113,169)(114,171)(115,167)
(116,166)(117,168)(118,164)(119,163)(120,165)(121,161)(122,160)(123,162)
(124,158)(125,157)(126,159)(127,155)(128,154)(129,156)(130,152)(131,151)
(132,153)(133,149)(134,148)(135,150)(136,146)(137,145)(138,147)(208,211)
(209,213)(210,212)(214,274)(215,276)(216,275)(217,271)(218,273)(219,272)
(220,268)(221,270)(222,269)(223,265)(224,267)(225,266)(226,262)(227,264)
(228,263)(229,259)(230,261)(231,260)(232,256)(233,258)(234,257)(235,253)
(236,255)(237,254)(238,250)(239,252)(240,251)(241,247)(242,249)(243,248)
(245,246)(277,350)(278,349)(279,351)(280,347)(281,346)(282,348)(283,413)
(284,412)(285,414)(286,410)(287,409)(288,411)(289,407)(290,406)(291,408)
(292,404)(293,403)(294,405)(295,401)(296,400)(297,402)(298,398)(299,397)
(300,399)(301,395)(302,394)(303,396)(304,392)(305,391)(306,393)(307,389)
(308,388)(309,390)(310,386)(311,385)(312,387)(313,383)(314,382)(315,384)
(316,380)(317,379)(318,381)(319,377)(320,376)(321,378)(322,374)(323,373)
(324,375)(325,371)(326,370)(327,372)(328,368)(329,367)(330,369)(331,365)
(332,364)(333,366)(334,362)(335,361)(336,363)(337,359)(338,358)(339,360)
(340,356)(341,355)(342,357)(343,353)(344,352)(345,354);;
s2 := ( 1,277)( 2,279)( 3,278)( 4,280)( 5,282)( 6,281)( 7,283)( 8,285)
( 9,284)( 10,286)( 11,288)( 12,287)( 13,289)( 14,291)( 15,290)( 16,292)
( 17,294)( 18,293)( 19,295)( 20,297)( 21,296)( 22,298)( 23,300)( 24,299)
( 25,301)( 26,303)( 27,302)( 28,304)( 29,306)( 30,305)( 31,307)( 32,309)
( 33,308)( 34,310)( 35,312)( 36,311)( 37,313)( 38,315)( 39,314)( 40,316)
( 41,318)( 42,317)( 43,319)( 44,321)( 45,320)( 46,322)( 47,324)( 48,323)
( 49,325)( 50,327)( 51,326)( 52,328)( 53,330)( 54,329)( 55,331)( 56,333)
( 57,332)( 58,334)( 59,336)( 60,335)( 61,337)( 62,339)( 63,338)( 64,340)
( 65,342)( 66,341)( 67,343)( 68,345)( 69,344)( 70,208)( 71,210)( 72,209)
( 73,211)( 74,213)( 75,212)( 76,214)( 77,216)( 78,215)( 79,217)( 80,219)
( 81,218)( 82,220)( 83,222)( 84,221)( 85,223)( 86,225)( 87,224)( 88,226)
( 89,228)( 90,227)( 91,229)( 92,231)( 93,230)( 94,232)( 95,234)( 96,233)
( 97,235)( 98,237)( 99,236)(100,238)(101,240)(102,239)(103,241)(104,243)
(105,242)(106,244)(107,246)(108,245)(109,247)(110,249)(111,248)(112,250)
(113,252)(114,251)(115,253)(116,255)(117,254)(118,256)(119,258)(120,257)
(121,259)(122,261)(123,260)(124,262)(125,264)(126,263)(127,265)(128,267)
(129,266)(130,268)(131,270)(132,269)(133,271)(134,273)(135,272)(136,274)
(137,276)(138,275)(139,347)(140,346)(141,348)(142,350)(143,349)(144,351)
(145,353)(146,352)(147,354)(148,356)(149,355)(150,357)(151,359)(152,358)
(153,360)(154,362)(155,361)(156,363)(157,365)(158,364)(159,366)(160,368)
(161,367)(162,369)(163,371)(164,370)(165,372)(166,374)(167,373)(168,375)
(169,377)(170,376)(171,378)(172,380)(173,379)(174,381)(175,383)(176,382)
(177,384)(178,386)(179,385)(180,387)(181,389)(182,388)(183,390)(184,392)
(185,391)(186,393)(187,395)(188,394)(189,396)(190,398)(191,397)(192,399)
(193,401)(194,400)(195,402)(196,404)(197,403)(198,405)(199,407)(200,406)
(201,408)(202,410)(203,409)(204,411)(205,413)(206,412)(207,414);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(414)!( 4, 67)( 5, 68)( 6, 69)( 7, 64)( 8, 65)( 9, 66)( 10, 61)
( 11, 62)( 12, 63)( 13, 58)( 14, 59)( 15, 60)( 16, 55)( 17, 56)( 18, 57)
( 19, 52)( 20, 53)( 21, 54)( 22, 49)( 23, 50)( 24, 51)( 25, 46)( 26, 47)
( 27, 48)( 28, 43)( 29, 44)( 30, 45)( 31, 40)( 32, 41)( 33, 42)( 34, 37)
( 35, 38)( 36, 39)( 73,136)( 74,137)( 75,138)( 76,133)( 77,134)( 78,135)
( 79,130)( 80,131)( 81,132)( 82,127)( 83,128)( 84,129)( 85,124)( 86,125)
( 87,126)( 88,121)( 89,122)( 90,123)( 91,118)( 92,119)( 93,120)( 94,115)
( 95,116)( 96,117)( 97,112)( 98,113)( 99,114)(100,109)(101,110)(102,111)
(103,106)(104,107)(105,108)(142,205)(143,206)(144,207)(145,202)(146,203)
(147,204)(148,199)(149,200)(150,201)(151,196)(152,197)(153,198)(154,193)
(155,194)(156,195)(157,190)(158,191)(159,192)(160,187)(161,188)(162,189)
(163,184)(164,185)(165,186)(166,181)(167,182)(168,183)(169,178)(170,179)
(171,180)(172,175)(173,176)(174,177)(211,274)(212,275)(213,276)(214,271)
(215,272)(216,273)(217,268)(218,269)(219,270)(220,265)(221,266)(222,267)
(223,262)(224,263)(225,264)(226,259)(227,260)(228,261)(229,256)(230,257)
(231,258)(232,253)(233,254)(234,255)(235,250)(236,251)(237,252)(238,247)
(239,248)(240,249)(241,244)(242,245)(243,246)(280,343)(281,344)(282,345)
(283,340)(284,341)(285,342)(286,337)(287,338)(288,339)(289,334)(290,335)
(291,336)(292,331)(293,332)(294,333)(295,328)(296,329)(297,330)(298,325)
(299,326)(300,327)(301,322)(302,323)(303,324)(304,319)(305,320)(306,321)
(307,316)(308,317)(309,318)(310,313)(311,314)(312,315)(349,412)(350,413)
(351,414)(352,409)(353,410)(354,411)(355,406)(356,407)(357,408)(358,403)
(359,404)(360,405)(361,400)(362,401)(363,402)(364,397)(365,398)(366,399)
(367,394)(368,395)(369,396)(370,391)(371,392)(372,393)(373,388)(374,389)
(375,390)(376,385)(377,386)(378,387)(379,382)(380,383)(381,384);
s1 := Sym(414)!( 1, 4)( 2, 6)( 3, 5)( 7, 67)( 8, 69)( 9, 68)( 10, 64)
( 11, 66)( 12, 65)( 13, 61)( 14, 63)( 15, 62)( 16, 58)( 17, 60)( 18, 59)
( 19, 55)( 20, 57)( 21, 56)( 22, 52)( 23, 54)( 24, 53)( 25, 49)( 26, 51)
( 27, 50)( 28, 46)( 29, 48)( 30, 47)( 31, 43)( 32, 45)( 33, 44)( 34, 40)
( 35, 42)( 36, 41)( 38, 39)( 70,143)( 71,142)( 72,144)( 73,140)( 74,139)
( 75,141)( 76,206)( 77,205)( 78,207)( 79,203)( 80,202)( 81,204)( 82,200)
( 83,199)( 84,201)( 85,197)( 86,196)( 87,198)( 88,194)( 89,193)( 90,195)
( 91,191)( 92,190)( 93,192)( 94,188)( 95,187)( 96,189)( 97,185)( 98,184)
( 99,186)(100,182)(101,181)(102,183)(103,179)(104,178)(105,180)(106,176)
(107,175)(108,177)(109,173)(110,172)(111,174)(112,170)(113,169)(114,171)
(115,167)(116,166)(117,168)(118,164)(119,163)(120,165)(121,161)(122,160)
(123,162)(124,158)(125,157)(126,159)(127,155)(128,154)(129,156)(130,152)
(131,151)(132,153)(133,149)(134,148)(135,150)(136,146)(137,145)(138,147)
(208,211)(209,213)(210,212)(214,274)(215,276)(216,275)(217,271)(218,273)
(219,272)(220,268)(221,270)(222,269)(223,265)(224,267)(225,266)(226,262)
(227,264)(228,263)(229,259)(230,261)(231,260)(232,256)(233,258)(234,257)
(235,253)(236,255)(237,254)(238,250)(239,252)(240,251)(241,247)(242,249)
(243,248)(245,246)(277,350)(278,349)(279,351)(280,347)(281,346)(282,348)
(283,413)(284,412)(285,414)(286,410)(287,409)(288,411)(289,407)(290,406)
(291,408)(292,404)(293,403)(294,405)(295,401)(296,400)(297,402)(298,398)
(299,397)(300,399)(301,395)(302,394)(303,396)(304,392)(305,391)(306,393)
(307,389)(308,388)(309,390)(310,386)(311,385)(312,387)(313,383)(314,382)
(315,384)(316,380)(317,379)(318,381)(319,377)(320,376)(321,378)(322,374)
(323,373)(324,375)(325,371)(326,370)(327,372)(328,368)(329,367)(330,369)
(331,365)(332,364)(333,366)(334,362)(335,361)(336,363)(337,359)(338,358)
(339,360)(340,356)(341,355)(342,357)(343,353)(344,352)(345,354);
s2 := Sym(414)!( 1,277)( 2,279)( 3,278)( 4,280)( 5,282)( 6,281)( 7,283)
( 8,285)( 9,284)( 10,286)( 11,288)( 12,287)( 13,289)( 14,291)( 15,290)
( 16,292)( 17,294)( 18,293)( 19,295)( 20,297)( 21,296)( 22,298)( 23,300)
( 24,299)( 25,301)( 26,303)( 27,302)( 28,304)( 29,306)( 30,305)( 31,307)
( 32,309)( 33,308)( 34,310)( 35,312)( 36,311)( 37,313)( 38,315)( 39,314)
( 40,316)( 41,318)( 42,317)( 43,319)( 44,321)( 45,320)( 46,322)( 47,324)
( 48,323)( 49,325)( 50,327)( 51,326)( 52,328)( 53,330)( 54,329)( 55,331)
( 56,333)( 57,332)( 58,334)( 59,336)( 60,335)( 61,337)( 62,339)( 63,338)
( 64,340)( 65,342)( 66,341)( 67,343)( 68,345)( 69,344)( 70,208)( 71,210)
( 72,209)( 73,211)( 74,213)( 75,212)( 76,214)( 77,216)( 78,215)( 79,217)
( 80,219)( 81,218)( 82,220)( 83,222)( 84,221)( 85,223)( 86,225)( 87,224)
( 88,226)( 89,228)( 90,227)( 91,229)( 92,231)( 93,230)( 94,232)( 95,234)
( 96,233)( 97,235)( 98,237)( 99,236)(100,238)(101,240)(102,239)(103,241)
(104,243)(105,242)(106,244)(107,246)(108,245)(109,247)(110,249)(111,248)
(112,250)(113,252)(114,251)(115,253)(116,255)(117,254)(118,256)(119,258)
(120,257)(121,259)(122,261)(123,260)(124,262)(125,264)(126,263)(127,265)
(128,267)(129,266)(130,268)(131,270)(132,269)(133,271)(134,273)(135,272)
(136,274)(137,276)(138,275)(139,347)(140,346)(141,348)(142,350)(143,349)
(144,351)(145,353)(146,352)(147,354)(148,356)(149,355)(150,357)(151,359)
(152,358)(153,360)(154,362)(155,361)(156,363)(157,365)(158,364)(159,366)
(160,368)(161,367)(162,369)(163,371)(164,370)(165,372)(166,374)(167,373)
(168,375)(169,377)(170,376)(171,378)(172,380)(173,379)(174,381)(175,383)
(176,382)(177,384)(178,386)(179,385)(180,387)(181,389)(182,388)(183,390)
(184,392)(185,391)(186,393)(187,395)(188,394)(189,396)(190,398)(191,397)
(192,399)(193,401)(194,400)(195,402)(196,404)(197,403)(198,405)(199,407)
(200,406)(201,408)(202,410)(203,409)(204,411)(205,413)(206,412)(207,414);
poly := sub<Sym(414)|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 >;
References : None.
to this polytope