Polytope of Type {14,18}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,18}*1764
if this polytope has a name.
Group : SmallGroup(1764,66)
Rank : 3
Schlafli Type : {14,18}
Number of vertices, edges, etc : 49, 441, 63
Order of s0s1s2 : 9
Order of s0s1s2s1 : 14
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
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 : {14,6}*588
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 7)( 3, 6)( 4, 5)( 8, 43)( 9, 49)( 10, 48)( 11, 47)( 12, 46)
( 13, 45)( 14, 44)( 15, 36)( 16, 42)( 17, 41)( 18, 40)( 19, 39)( 20, 38)
( 21, 37)( 22, 29)( 23, 35)( 24, 34)( 25, 33)( 26, 32)( 27, 31)( 28, 30)
( 51, 56)( 52, 55)( 53, 54)( 57, 92)( 58, 98)( 59, 97)( 60, 96)( 61, 95)
( 62, 94)( 63, 93)( 64, 85)( 65, 91)( 66, 90)( 67, 89)( 68, 88)( 69, 87)
( 70, 86)( 71, 78)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)( 77, 79)
(100,105)(101,104)(102,103)(106,141)(107,147)(108,146)(109,145)(110,144)
(111,143)(112,142)(113,134)(114,140)(115,139)(116,138)(117,137)(118,136)
(119,135)(120,127)(121,133)(122,132)(123,131)(124,130)(125,129)(126,128)
(149,154)(150,153)(151,152)(155,190)(156,196)(157,195)(158,194)(159,193)
(160,192)(161,191)(162,183)(163,189)(164,188)(165,187)(166,186)(167,185)
(168,184)(169,176)(170,182)(171,181)(172,180)(173,179)(174,178)(175,177)
(198,203)(199,202)(200,201)(204,239)(205,245)(206,244)(207,243)(208,242)
(209,241)(210,240)(211,232)(212,238)(213,237)(214,236)(215,235)(216,234)
(217,233)(218,225)(219,231)(220,230)(221,229)(222,228)(223,227)(224,226)
(247,252)(248,251)(249,250)(253,288)(254,294)(255,293)(256,292)(257,291)
(258,290)(259,289)(260,281)(261,287)(262,286)(263,285)(264,284)(265,283)
(266,282)(267,274)(268,280)(269,279)(270,278)(271,277)(272,276)(273,275)
(296,301)(297,300)(298,299)(302,337)(303,343)(304,342)(305,341)(306,340)
(307,339)(308,338)(309,330)(310,336)(311,335)(312,334)(313,333)(314,332)
(315,331)(316,323)(317,329)(318,328)(319,327)(320,326)(321,325)(322,324)
(345,350)(346,349)(347,348)(351,386)(352,392)(353,391)(354,390)(355,389)
(356,388)(357,387)(358,379)(359,385)(360,384)(361,383)(362,382)(363,381)
(364,380)(365,372)(366,378)(367,377)(368,376)(369,375)(370,374)(371,373)
(394,399)(395,398)(396,397)(400,435)(401,441)(402,440)(403,439)(404,438)
(405,437)(406,436)(407,428)(408,434)(409,433)(410,432)(411,431)(412,430)
(413,429)(414,421)(415,427)(416,426)(417,425)(418,424)(419,423)(420,422);;
s1 := ( 1,156)( 2,149)( 3,191)( 4,184)( 5,177)( 6,170)( 7,163)( 8,155)
( 9,148)( 10,190)( 11,183)( 12,176)( 13,169)( 14,162)( 15,161)( 16,154)
( 17,196)( 18,189)( 19,182)( 20,175)( 21,168)( 22,160)( 23,153)( 24,195)
( 25,188)( 26,181)( 27,174)( 28,167)( 29,159)( 30,152)( 31,194)( 32,187)
( 33,180)( 34,173)( 35,166)( 36,158)( 37,151)( 38,193)( 39,186)( 40,179)
( 41,172)( 42,165)( 43,157)( 44,150)( 45,192)( 46,185)( 47,178)( 48,171)
( 49,164)( 50,254)( 51,247)( 52,289)( 53,282)( 54,275)( 55,268)( 56,261)
( 57,253)( 58,246)( 59,288)( 60,281)( 61,274)( 62,267)( 63,260)( 64,259)
( 65,252)( 66,294)( 67,287)( 68,280)( 69,273)( 70,266)( 71,258)( 72,251)
( 73,293)( 74,286)( 75,279)( 76,272)( 77,265)( 78,257)( 79,250)( 80,292)
( 81,285)( 82,278)( 83,271)( 84,264)( 85,256)( 86,249)( 87,291)( 88,284)
( 89,277)( 90,270)( 91,263)( 92,255)( 93,248)( 94,290)( 95,283)( 96,276)
( 97,269)( 98,262)( 99,205)(100,198)(101,240)(102,233)(103,226)(104,219)
(105,212)(106,204)(107,197)(108,239)(109,232)(110,225)(111,218)(112,211)
(113,210)(114,203)(115,245)(116,238)(117,231)(118,224)(119,217)(120,209)
(121,202)(122,244)(123,237)(124,230)(125,223)(126,216)(127,208)(128,201)
(129,243)(130,236)(131,229)(132,222)(133,215)(134,207)(135,200)(136,242)
(137,235)(138,228)(139,221)(140,214)(141,206)(142,199)(143,241)(144,234)
(145,227)(146,220)(147,213)(295,401)(296,394)(297,436)(298,429)(299,422)
(300,415)(301,408)(302,400)(303,393)(304,435)(305,428)(306,421)(307,414)
(308,407)(309,406)(310,399)(311,441)(312,434)(313,427)(314,420)(315,413)
(316,405)(317,398)(318,440)(319,433)(320,426)(321,419)(322,412)(323,404)
(324,397)(325,439)(326,432)(327,425)(328,418)(329,411)(330,403)(331,396)
(332,438)(333,431)(334,424)(335,417)(336,410)(337,402)(338,395)(339,437)
(340,430)(341,423)(342,416)(343,409)(344,352)(346,387)(347,380)(348,373)
(349,366)(350,359)(353,386)(354,379)(355,372)(356,365)(357,358)(360,392)
(361,385)(362,378)(363,371)(367,391)(368,384)(369,377)(374,390)(375,383)
(381,389);;
s2 := ( 2, 15)( 3, 29)( 4, 43)( 5, 8)( 6, 22)( 7, 36)( 9, 19)( 10, 33)
( 11, 47)( 13, 26)( 14, 40)( 17, 30)( 18, 44)( 20, 23)( 21, 37)( 24, 34)
( 25, 48)( 28, 41)( 32, 45)( 35, 38)( 39, 49)( 50, 99)( 51,113)( 52,127)
( 53,141)( 54,106)( 55,120)( 56,134)( 57,103)( 58,117)( 59,131)( 60,145)
( 61,110)( 62,124)( 63,138)( 64,100)( 65,114)( 66,128)( 67,142)( 68,107)
( 69,121)( 70,135)( 71,104)( 72,118)( 73,132)( 74,146)( 75,111)( 76,125)
( 77,139)( 78,101)( 79,115)( 80,129)( 81,143)( 82,108)( 83,122)( 84,136)
( 85,105)( 86,119)( 87,133)( 88,147)( 89,112)( 90,126)( 91,140)( 92,102)
( 93,116)( 94,130)( 95,144)( 96,109)( 97,123)( 98,137)(148,393)(149,407)
(150,421)(151,435)(152,400)(153,414)(154,428)(155,397)(156,411)(157,425)
(158,439)(159,404)(160,418)(161,432)(162,394)(163,408)(164,422)(165,436)
(166,401)(167,415)(168,429)(169,398)(170,412)(171,426)(172,440)(173,405)
(174,419)(175,433)(176,395)(177,409)(178,423)(179,437)(180,402)(181,416)
(182,430)(183,399)(184,413)(185,427)(186,441)(187,406)(188,420)(189,434)
(190,396)(191,410)(192,424)(193,438)(194,403)(195,417)(196,431)(197,344)
(198,358)(199,372)(200,386)(201,351)(202,365)(203,379)(204,348)(205,362)
(206,376)(207,390)(208,355)(209,369)(210,383)(211,345)(212,359)(213,373)
(214,387)(215,352)(216,366)(217,380)(218,349)(219,363)(220,377)(221,391)
(222,356)(223,370)(224,384)(225,346)(226,360)(227,374)(228,388)(229,353)
(230,367)(231,381)(232,350)(233,364)(234,378)(235,392)(236,357)(237,371)
(238,385)(239,347)(240,361)(241,375)(242,389)(243,354)(244,368)(245,382)
(246,295)(247,309)(248,323)(249,337)(250,302)(251,316)(252,330)(253,299)
(254,313)(255,327)(256,341)(257,306)(258,320)(259,334)(260,296)(261,310)
(262,324)(263,338)(264,303)(265,317)(266,331)(267,300)(268,314)(269,328)
(270,342)(271,307)(272,321)(273,335)(274,297)(275,311)(276,325)(277,339)
(278,304)(279,318)(280,332)(281,301)(282,315)(283,329)(284,343)(285,308)
(286,322)(287,336)(288,298)(289,312)(290,326)(291,340)(292,305)(293,319)
(294,333);;
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, s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(441)!( 2, 7)( 3, 6)( 4, 5)( 8, 43)( 9, 49)( 10, 48)( 11, 47)
( 12, 46)( 13, 45)( 14, 44)( 15, 36)( 16, 42)( 17, 41)( 18, 40)( 19, 39)
( 20, 38)( 21, 37)( 22, 29)( 23, 35)( 24, 34)( 25, 33)( 26, 32)( 27, 31)
( 28, 30)( 51, 56)( 52, 55)( 53, 54)( 57, 92)( 58, 98)( 59, 97)( 60, 96)
( 61, 95)( 62, 94)( 63, 93)( 64, 85)( 65, 91)( 66, 90)( 67, 89)( 68, 88)
( 69, 87)( 70, 86)( 71, 78)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)
( 77, 79)(100,105)(101,104)(102,103)(106,141)(107,147)(108,146)(109,145)
(110,144)(111,143)(112,142)(113,134)(114,140)(115,139)(116,138)(117,137)
(118,136)(119,135)(120,127)(121,133)(122,132)(123,131)(124,130)(125,129)
(126,128)(149,154)(150,153)(151,152)(155,190)(156,196)(157,195)(158,194)
(159,193)(160,192)(161,191)(162,183)(163,189)(164,188)(165,187)(166,186)
(167,185)(168,184)(169,176)(170,182)(171,181)(172,180)(173,179)(174,178)
(175,177)(198,203)(199,202)(200,201)(204,239)(205,245)(206,244)(207,243)
(208,242)(209,241)(210,240)(211,232)(212,238)(213,237)(214,236)(215,235)
(216,234)(217,233)(218,225)(219,231)(220,230)(221,229)(222,228)(223,227)
(224,226)(247,252)(248,251)(249,250)(253,288)(254,294)(255,293)(256,292)
(257,291)(258,290)(259,289)(260,281)(261,287)(262,286)(263,285)(264,284)
(265,283)(266,282)(267,274)(268,280)(269,279)(270,278)(271,277)(272,276)
(273,275)(296,301)(297,300)(298,299)(302,337)(303,343)(304,342)(305,341)
(306,340)(307,339)(308,338)(309,330)(310,336)(311,335)(312,334)(313,333)
(314,332)(315,331)(316,323)(317,329)(318,328)(319,327)(320,326)(321,325)
(322,324)(345,350)(346,349)(347,348)(351,386)(352,392)(353,391)(354,390)
(355,389)(356,388)(357,387)(358,379)(359,385)(360,384)(361,383)(362,382)
(363,381)(364,380)(365,372)(366,378)(367,377)(368,376)(369,375)(370,374)
(371,373)(394,399)(395,398)(396,397)(400,435)(401,441)(402,440)(403,439)
(404,438)(405,437)(406,436)(407,428)(408,434)(409,433)(410,432)(411,431)
(412,430)(413,429)(414,421)(415,427)(416,426)(417,425)(418,424)(419,423)
(420,422);
s1 := Sym(441)!( 1,156)( 2,149)( 3,191)( 4,184)( 5,177)( 6,170)( 7,163)
( 8,155)( 9,148)( 10,190)( 11,183)( 12,176)( 13,169)( 14,162)( 15,161)
( 16,154)( 17,196)( 18,189)( 19,182)( 20,175)( 21,168)( 22,160)( 23,153)
( 24,195)( 25,188)( 26,181)( 27,174)( 28,167)( 29,159)( 30,152)( 31,194)
( 32,187)( 33,180)( 34,173)( 35,166)( 36,158)( 37,151)( 38,193)( 39,186)
( 40,179)( 41,172)( 42,165)( 43,157)( 44,150)( 45,192)( 46,185)( 47,178)
( 48,171)( 49,164)( 50,254)( 51,247)( 52,289)( 53,282)( 54,275)( 55,268)
( 56,261)( 57,253)( 58,246)( 59,288)( 60,281)( 61,274)( 62,267)( 63,260)
( 64,259)( 65,252)( 66,294)( 67,287)( 68,280)( 69,273)( 70,266)( 71,258)
( 72,251)( 73,293)( 74,286)( 75,279)( 76,272)( 77,265)( 78,257)( 79,250)
( 80,292)( 81,285)( 82,278)( 83,271)( 84,264)( 85,256)( 86,249)( 87,291)
( 88,284)( 89,277)( 90,270)( 91,263)( 92,255)( 93,248)( 94,290)( 95,283)
( 96,276)( 97,269)( 98,262)( 99,205)(100,198)(101,240)(102,233)(103,226)
(104,219)(105,212)(106,204)(107,197)(108,239)(109,232)(110,225)(111,218)
(112,211)(113,210)(114,203)(115,245)(116,238)(117,231)(118,224)(119,217)
(120,209)(121,202)(122,244)(123,237)(124,230)(125,223)(126,216)(127,208)
(128,201)(129,243)(130,236)(131,229)(132,222)(133,215)(134,207)(135,200)
(136,242)(137,235)(138,228)(139,221)(140,214)(141,206)(142,199)(143,241)
(144,234)(145,227)(146,220)(147,213)(295,401)(296,394)(297,436)(298,429)
(299,422)(300,415)(301,408)(302,400)(303,393)(304,435)(305,428)(306,421)
(307,414)(308,407)(309,406)(310,399)(311,441)(312,434)(313,427)(314,420)
(315,413)(316,405)(317,398)(318,440)(319,433)(320,426)(321,419)(322,412)
(323,404)(324,397)(325,439)(326,432)(327,425)(328,418)(329,411)(330,403)
(331,396)(332,438)(333,431)(334,424)(335,417)(336,410)(337,402)(338,395)
(339,437)(340,430)(341,423)(342,416)(343,409)(344,352)(346,387)(347,380)
(348,373)(349,366)(350,359)(353,386)(354,379)(355,372)(356,365)(357,358)
(360,392)(361,385)(362,378)(363,371)(367,391)(368,384)(369,377)(374,390)
(375,383)(381,389);
s2 := Sym(441)!( 2, 15)( 3, 29)( 4, 43)( 5, 8)( 6, 22)( 7, 36)( 9, 19)
( 10, 33)( 11, 47)( 13, 26)( 14, 40)( 17, 30)( 18, 44)( 20, 23)( 21, 37)
( 24, 34)( 25, 48)( 28, 41)( 32, 45)( 35, 38)( 39, 49)( 50, 99)( 51,113)
( 52,127)( 53,141)( 54,106)( 55,120)( 56,134)( 57,103)( 58,117)( 59,131)
( 60,145)( 61,110)( 62,124)( 63,138)( 64,100)( 65,114)( 66,128)( 67,142)
( 68,107)( 69,121)( 70,135)( 71,104)( 72,118)( 73,132)( 74,146)( 75,111)
( 76,125)( 77,139)( 78,101)( 79,115)( 80,129)( 81,143)( 82,108)( 83,122)
( 84,136)( 85,105)( 86,119)( 87,133)( 88,147)( 89,112)( 90,126)( 91,140)
( 92,102)( 93,116)( 94,130)( 95,144)( 96,109)( 97,123)( 98,137)(148,393)
(149,407)(150,421)(151,435)(152,400)(153,414)(154,428)(155,397)(156,411)
(157,425)(158,439)(159,404)(160,418)(161,432)(162,394)(163,408)(164,422)
(165,436)(166,401)(167,415)(168,429)(169,398)(170,412)(171,426)(172,440)
(173,405)(174,419)(175,433)(176,395)(177,409)(178,423)(179,437)(180,402)
(181,416)(182,430)(183,399)(184,413)(185,427)(186,441)(187,406)(188,420)
(189,434)(190,396)(191,410)(192,424)(193,438)(194,403)(195,417)(196,431)
(197,344)(198,358)(199,372)(200,386)(201,351)(202,365)(203,379)(204,348)
(205,362)(206,376)(207,390)(208,355)(209,369)(210,383)(211,345)(212,359)
(213,373)(214,387)(215,352)(216,366)(217,380)(218,349)(219,363)(220,377)
(221,391)(222,356)(223,370)(224,384)(225,346)(226,360)(227,374)(228,388)
(229,353)(230,367)(231,381)(232,350)(233,364)(234,378)(235,392)(236,357)
(237,371)(238,385)(239,347)(240,361)(241,375)(242,389)(243,354)(244,368)
(245,382)(246,295)(247,309)(248,323)(249,337)(250,302)(251,316)(252,330)
(253,299)(254,313)(255,327)(256,341)(257,306)(258,320)(259,334)(260,296)
(261,310)(262,324)(263,338)(264,303)(265,317)(266,331)(267,300)(268,314)
(269,328)(270,342)(271,307)(272,321)(273,335)(274,297)(275,311)(276,325)
(277,339)(278,304)(279,318)(280,332)(281,301)(282,315)(283,329)(284,343)
(285,308)(286,322)(287,336)(288,298)(289,312)(290,326)(291,340)(292,305)
(293,319)(294,333);
poly := sub<Sym(441)|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, s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*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 >;
References : None.
to this polytope