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