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