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