Polytope of Type {63,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {63,4}*1008
if this polytope has a name.
Group : SmallGroup(1008,503)
Rank : 3
Schlafli Type : {63,4}
Number of vertices, edges, etc : 126, 252, 8
Order of s0s1s2 : 126
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {63,4}*504
3-fold quotients : {21,4}*336
4-fold quotients : {63,2}*252
6-fold quotients : {21,4}*168
7-fold quotients : {9,4}*144
12-fold quotients : {21,2}*84
14-fold quotients : {9,4}*72
21-fold quotients : {3,4}*48
28-fold quotients : {9,2}*36
36-fold quotients : {7,2}*28
42-fold quotients : {3,4}*24
84-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13, 73)( 14, 74)( 15, 76)
( 16, 75)( 17, 81)( 18, 82)( 19, 84)( 20, 83)( 21, 77)( 22, 78)( 23, 80)
( 24, 79)( 25, 61)( 26, 62)( 27, 64)( 28, 63)( 29, 69)( 30, 70)( 31, 72)
( 32, 71)( 33, 65)( 34, 66)( 35, 68)( 36, 67)( 37, 49)( 38, 50)( 39, 52)
( 40, 51)( 41, 57)( 42, 58)( 43, 60)( 44, 59)( 45, 53)( 46, 54)( 47, 56)
( 48, 55)( 85,177)( 86,178)( 87,180)( 88,179)( 89,173)( 90,174)( 91,176)
( 92,175)( 93,169)( 94,170)( 95,172)( 96,171)( 97,249)( 98,250)( 99,252)
(100,251)(101,245)(102,246)(103,248)(104,247)(105,241)(106,242)(107,244)
(108,243)(109,237)(110,238)(111,240)(112,239)(113,233)(114,234)(115,236)
(116,235)(117,229)(118,230)(119,232)(120,231)(121,225)(122,226)(123,228)
(124,227)(125,221)(126,222)(127,224)(128,223)(129,217)(130,218)(131,220)
(132,219)(133,213)(134,214)(135,216)(136,215)(137,209)(138,210)(139,212)
(140,211)(141,205)(142,206)(143,208)(144,207)(145,201)(146,202)(147,204)
(148,203)(149,197)(150,198)(151,200)(152,199)(153,193)(154,194)(155,196)
(156,195)(157,189)(158,190)(159,192)(160,191)(161,185)(162,186)(163,188)
(164,187)(165,181)(166,182)(167,184)(168,183)(255,256)(257,261)(258,262)
(259,264)(260,263)(265,325)(266,326)(267,328)(268,327)(269,333)(270,334)
(271,336)(272,335)(273,329)(274,330)(275,332)(276,331)(277,313)(278,314)
(279,316)(280,315)(281,321)(282,322)(283,324)(284,323)(285,317)(286,318)
(287,320)(288,319)(289,301)(290,302)(291,304)(292,303)(293,309)(294,310)
(295,312)(296,311)(297,305)(298,306)(299,308)(300,307)(337,429)(338,430)
(339,432)(340,431)(341,425)(342,426)(343,428)(344,427)(345,421)(346,422)
(347,424)(348,423)(349,501)(350,502)(351,504)(352,503)(353,497)(354,498)
(355,500)(356,499)(357,493)(358,494)(359,496)(360,495)(361,489)(362,490)
(363,492)(364,491)(365,485)(366,486)(367,488)(368,487)(369,481)(370,482)
(371,484)(372,483)(373,477)(374,478)(375,480)(376,479)(377,473)(378,474)
(379,476)(380,475)(381,469)(382,470)(383,472)(384,471)(385,465)(386,466)
(387,468)(388,467)(389,461)(390,462)(391,464)(392,463)(393,457)(394,458)
(395,460)(396,459)(397,453)(398,454)(399,456)(400,455)(401,449)(402,450)
(403,452)(404,451)(405,445)(406,446)(407,448)(408,447)(409,441)(410,442)
(411,444)(412,443)(413,437)(414,438)(415,440)(416,439)(417,433)(418,434)
(419,436)(420,435);;
s1 := ( 1, 97)( 2,100)( 3, 99)( 4, 98)( 5,105)( 6,108)( 7,107)( 8,106)
( 9,101)( 10,104)( 11,103)( 12,102)( 13, 85)( 14, 88)( 15, 87)( 16, 86)
( 17, 93)( 18, 96)( 19, 95)( 20, 94)( 21, 89)( 22, 92)( 23, 91)( 24, 90)
( 25,157)( 26,160)( 27,159)( 28,158)( 29,165)( 30,168)( 31,167)( 32,166)
( 33,161)( 34,164)( 35,163)( 36,162)( 37,145)( 38,148)( 39,147)( 40,146)
( 41,153)( 42,156)( 43,155)( 44,154)( 45,149)( 46,152)( 47,151)( 48,150)
( 49,133)( 50,136)( 51,135)( 52,134)( 53,141)( 54,144)( 55,143)( 56,142)
( 57,137)( 58,140)( 59,139)( 60,138)( 61,121)( 62,124)( 63,123)( 64,122)
( 65,129)( 66,132)( 67,131)( 68,130)( 69,125)( 70,128)( 71,127)( 72,126)
( 73,109)( 74,112)( 75,111)( 76,110)( 77,117)( 78,120)( 79,119)( 80,118)
( 81,113)( 82,116)( 83,115)( 84,114)(169,189)(170,192)(171,191)(172,190)
(173,185)(174,188)(175,187)(176,186)(177,181)(178,184)(179,183)(180,182)
(193,249)(194,252)(195,251)(196,250)(197,245)(198,248)(199,247)(200,246)
(201,241)(202,244)(203,243)(204,242)(205,237)(206,240)(207,239)(208,238)
(209,233)(210,236)(211,235)(212,234)(213,229)(214,232)(215,231)(216,230)
(217,225)(218,228)(219,227)(220,226)(222,224)(253,349)(254,352)(255,351)
(256,350)(257,357)(258,360)(259,359)(260,358)(261,353)(262,356)(263,355)
(264,354)(265,337)(266,340)(267,339)(268,338)(269,345)(270,348)(271,347)
(272,346)(273,341)(274,344)(275,343)(276,342)(277,409)(278,412)(279,411)
(280,410)(281,417)(282,420)(283,419)(284,418)(285,413)(286,416)(287,415)
(288,414)(289,397)(290,400)(291,399)(292,398)(293,405)(294,408)(295,407)
(296,406)(297,401)(298,404)(299,403)(300,402)(301,385)(302,388)(303,387)
(304,386)(305,393)(306,396)(307,395)(308,394)(309,389)(310,392)(311,391)
(312,390)(313,373)(314,376)(315,375)(316,374)(317,381)(318,384)(319,383)
(320,382)(321,377)(322,380)(323,379)(324,378)(325,361)(326,364)(327,363)
(328,362)(329,369)(330,372)(331,371)(332,370)(333,365)(334,368)(335,367)
(336,366)(421,441)(422,444)(423,443)(424,442)(425,437)(426,440)(427,439)
(428,438)(429,433)(430,436)(431,435)(432,434)(445,501)(446,504)(447,503)
(448,502)(449,497)(450,500)(451,499)(452,498)(453,493)(454,496)(455,495)
(456,494)(457,489)(458,492)(459,491)(460,490)(461,485)(462,488)(463,487)
(464,486)(465,481)(466,484)(467,483)(468,482)(469,477)(470,480)(471,479)
(472,478)(474,476);;
s2 := ( 1,254)( 2,253)( 3,256)( 4,255)( 5,258)( 6,257)( 7,260)( 8,259)
( 9,262)( 10,261)( 11,264)( 12,263)( 13,266)( 14,265)( 15,268)( 16,267)
( 17,270)( 18,269)( 19,272)( 20,271)( 21,274)( 22,273)( 23,276)( 24,275)
( 25,278)( 26,277)( 27,280)( 28,279)( 29,282)( 30,281)( 31,284)( 32,283)
( 33,286)( 34,285)( 35,288)( 36,287)( 37,290)( 38,289)( 39,292)( 40,291)
( 41,294)( 42,293)( 43,296)( 44,295)( 45,298)( 46,297)( 47,300)( 48,299)
( 49,302)( 50,301)( 51,304)( 52,303)( 53,306)( 54,305)( 55,308)( 56,307)
( 57,310)( 58,309)( 59,312)( 60,311)( 61,314)( 62,313)( 63,316)( 64,315)
( 65,318)( 66,317)( 67,320)( 68,319)( 69,322)( 70,321)( 71,324)( 72,323)
( 73,326)( 74,325)( 75,328)( 76,327)( 77,330)( 78,329)( 79,332)( 80,331)
( 81,334)( 82,333)( 83,336)( 84,335)( 85,338)( 86,337)( 87,340)( 88,339)
( 89,342)( 90,341)( 91,344)( 92,343)( 93,346)( 94,345)( 95,348)( 96,347)
( 97,350)( 98,349)( 99,352)(100,351)(101,354)(102,353)(103,356)(104,355)
(105,358)(106,357)(107,360)(108,359)(109,362)(110,361)(111,364)(112,363)
(113,366)(114,365)(115,368)(116,367)(117,370)(118,369)(119,372)(120,371)
(121,374)(122,373)(123,376)(124,375)(125,378)(126,377)(127,380)(128,379)
(129,382)(130,381)(131,384)(132,383)(133,386)(134,385)(135,388)(136,387)
(137,390)(138,389)(139,392)(140,391)(141,394)(142,393)(143,396)(144,395)
(145,398)(146,397)(147,400)(148,399)(149,402)(150,401)(151,404)(152,403)
(153,406)(154,405)(155,408)(156,407)(157,410)(158,409)(159,412)(160,411)
(161,414)(162,413)(163,416)(164,415)(165,418)(166,417)(167,420)(168,419)
(169,422)(170,421)(171,424)(172,423)(173,426)(174,425)(175,428)(176,427)
(177,430)(178,429)(179,432)(180,431)(181,434)(182,433)(183,436)(184,435)
(185,438)(186,437)(187,440)(188,439)(189,442)(190,441)(191,444)(192,443)
(193,446)(194,445)(195,448)(196,447)(197,450)(198,449)(199,452)(200,451)
(201,454)(202,453)(203,456)(204,455)(205,458)(206,457)(207,460)(208,459)
(209,462)(210,461)(211,464)(212,463)(213,466)(214,465)(215,468)(216,467)
(217,470)(218,469)(219,472)(220,471)(221,474)(222,473)(223,476)(224,475)
(225,478)(226,477)(227,480)(228,479)(229,482)(230,481)(231,484)(232,483)
(233,486)(234,485)(235,488)(236,487)(237,490)(238,489)(239,492)(240,491)
(241,494)(242,493)(243,496)(244,495)(245,498)(246,497)(247,500)(248,499)
(249,502)(250,501)(251,504)(252,503);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(504)!( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13, 73)( 14, 74)
( 15, 76)( 16, 75)( 17, 81)( 18, 82)( 19, 84)( 20, 83)( 21, 77)( 22, 78)
( 23, 80)( 24, 79)( 25, 61)( 26, 62)( 27, 64)( 28, 63)( 29, 69)( 30, 70)
( 31, 72)( 32, 71)( 33, 65)( 34, 66)( 35, 68)( 36, 67)( 37, 49)( 38, 50)
( 39, 52)( 40, 51)( 41, 57)( 42, 58)( 43, 60)( 44, 59)( 45, 53)( 46, 54)
( 47, 56)( 48, 55)( 85,177)( 86,178)( 87,180)( 88,179)( 89,173)( 90,174)
( 91,176)( 92,175)( 93,169)( 94,170)( 95,172)( 96,171)( 97,249)( 98,250)
( 99,252)(100,251)(101,245)(102,246)(103,248)(104,247)(105,241)(106,242)
(107,244)(108,243)(109,237)(110,238)(111,240)(112,239)(113,233)(114,234)
(115,236)(116,235)(117,229)(118,230)(119,232)(120,231)(121,225)(122,226)
(123,228)(124,227)(125,221)(126,222)(127,224)(128,223)(129,217)(130,218)
(131,220)(132,219)(133,213)(134,214)(135,216)(136,215)(137,209)(138,210)
(139,212)(140,211)(141,205)(142,206)(143,208)(144,207)(145,201)(146,202)
(147,204)(148,203)(149,197)(150,198)(151,200)(152,199)(153,193)(154,194)
(155,196)(156,195)(157,189)(158,190)(159,192)(160,191)(161,185)(162,186)
(163,188)(164,187)(165,181)(166,182)(167,184)(168,183)(255,256)(257,261)
(258,262)(259,264)(260,263)(265,325)(266,326)(267,328)(268,327)(269,333)
(270,334)(271,336)(272,335)(273,329)(274,330)(275,332)(276,331)(277,313)
(278,314)(279,316)(280,315)(281,321)(282,322)(283,324)(284,323)(285,317)
(286,318)(287,320)(288,319)(289,301)(290,302)(291,304)(292,303)(293,309)
(294,310)(295,312)(296,311)(297,305)(298,306)(299,308)(300,307)(337,429)
(338,430)(339,432)(340,431)(341,425)(342,426)(343,428)(344,427)(345,421)
(346,422)(347,424)(348,423)(349,501)(350,502)(351,504)(352,503)(353,497)
(354,498)(355,500)(356,499)(357,493)(358,494)(359,496)(360,495)(361,489)
(362,490)(363,492)(364,491)(365,485)(366,486)(367,488)(368,487)(369,481)
(370,482)(371,484)(372,483)(373,477)(374,478)(375,480)(376,479)(377,473)
(378,474)(379,476)(380,475)(381,469)(382,470)(383,472)(384,471)(385,465)
(386,466)(387,468)(388,467)(389,461)(390,462)(391,464)(392,463)(393,457)
(394,458)(395,460)(396,459)(397,453)(398,454)(399,456)(400,455)(401,449)
(402,450)(403,452)(404,451)(405,445)(406,446)(407,448)(408,447)(409,441)
(410,442)(411,444)(412,443)(413,437)(414,438)(415,440)(416,439)(417,433)
(418,434)(419,436)(420,435);
s1 := Sym(504)!( 1, 97)( 2,100)( 3, 99)( 4, 98)( 5,105)( 6,108)( 7,107)
( 8,106)( 9,101)( 10,104)( 11,103)( 12,102)( 13, 85)( 14, 88)( 15, 87)
( 16, 86)( 17, 93)( 18, 96)( 19, 95)( 20, 94)( 21, 89)( 22, 92)( 23, 91)
( 24, 90)( 25,157)( 26,160)( 27,159)( 28,158)( 29,165)( 30,168)( 31,167)
( 32,166)( 33,161)( 34,164)( 35,163)( 36,162)( 37,145)( 38,148)( 39,147)
( 40,146)( 41,153)( 42,156)( 43,155)( 44,154)( 45,149)( 46,152)( 47,151)
( 48,150)( 49,133)( 50,136)( 51,135)( 52,134)( 53,141)( 54,144)( 55,143)
( 56,142)( 57,137)( 58,140)( 59,139)( 60,138)( 61,121)( 62,124)( 63,123)
( 64,122)( 65,129)( 66,132)( 67,131)( 68,130)( 69,125)( 70,128)( 71,127)
( 72,126)( 73,109)( 74,112)( 75,111)( 76,110)( 77,117)( 78,120)( 79,119)
( 80,118)( 81,113)( 82,116)( 83,115)( 84,114)(169,189)(170,192)(171,191)
(172,190)(173,185)(174,188)(175,187)(176,186)(177,181)(178,184)(179,183)
(180,182)(193,249)(194,252)(195,251)(196,250)(197,245)(198,248)(199,247)
(200,246)(201,241)(202,244)(203,243)(204,242)(205,237)(206,240)(207,239)
(208,238)(209,233)(210,236)(211,235)(212,234)(213,229)(214,232)(215,231)
(216,230)(217,225)(218,228)(219,227)(220,226)(222,224)(253,349)(254,352)
(255,351)(256,350)(257,357)(258,360)(259,359)(260,358)(261,353)(262,356)
(263,355)(264,354)(265,337)(266,340)(267,339)(268,338)(269,345)(270,348)
(271,347)(272,346)(273,341)(274,344)(275,343)(276,342)(277,409)(278,412)
(279,411)(280,410)(281,417)(282,420)(283,419)(284,418)(285,413)(286,416)
(287,415)(288,414)(289,397)(290,400)(291,399)(292,398)(293,405)(294,408)
(295,407)(296,406)(297,401)(298,404)(299,403)(300,402)(301,385)(302,388)
(303,387)(304,386)(305,393)(306,396)(307,395)(308,394)(309,389)(310,392)
(311,391)(312,390)(313,373)(314,376)(315,375)(316,374)(317,381)(318,384)
(319,383)(320,382)(321,377)(322,380)(323,379)(324,378)(325,361)(326,364)
(327,363)(328,362)(329,369)(330,372)(331,371)(332,370)(333,365)(334,368)
(335,367)(336,366)(421,441)(422,444)(423,443)(424,442)(425,437)(426,440)
(427,439)(428,438)(429,433)(430,436)(431,435)(432,434)(445,501)(446,504)
(447,503)(448,502)(449,497)(450,500)(451,499)(452,498)(453,493)(454,496)
(455,495)(456,494)(457,489)(458,492)(459,491)(460,490)(461,485)(462,488)
(463,487)(464,486)(465,481)(466,484)(467,483)(468,482)(469,477)(470,480)
(471,479)(472,478)(474,476);
s2 := Sym(504)!( 1,254)( 2,253)( 3,256)( 4,255)( 5,258)( 6,257)( 7,260)
( 8,259)( 9,262)( 10,261)( 11,264)( 12,263)( 13,266)( 14,265)( 15,268)
( 16,267)( 17,270)( 18,269)( 19,272)( 20,271)( 21,274)( 22,273)( 23,276)
( 24,275)( 25,278)( 26,277)( 27,280)( 28,279)( 29,282)( 30,281)( 31,284)
( 32,283)( 33,286)( 34,285)( 35,288)( 36,287)( 37,290)( 38,289)( 39,292)
( 40,291)( 41,294)( 42,293)( 43,296)( 44,295)( 45,298)( 46,297)( 47,300)
( 48,299)( 49,302)( 50,301)( 51,304)( 52,303)( 53,306)( 54,305)( 55,308)
( 56,307)( 57,310)( 58,309)( 59,312)( 60,311)( 61,314)( 62,313)( 63,316)
( 64,315)( 65,318)( 66,317)( 67,320)( 68,319)( 69,322)( 70,321)( 71,324)
( 72,323)( 73,326)( 74,325)( 75,328)( 76,327)( 77,330)( 78,329)( 79,332)
( 80,331)( 81,334)( 82,333)( 83,336)( 84,335)( 85,338)( 86,337)( 87,340)
( 88,339)( 89,342)( 90,341)( 91,344)( 92,343)( 93,346)( 94,345)( 95,348)
( 96,347)( 97,350)( 98,349)( 99,352)(100,351)(101,354)(102,353)(103,356)
(104,355)(105,358)(106,357)(107,360)(108,359)(109,362)(110,361)(111,364)
(112,363)(113,366)(114,365)(115,368)(116,367)(117,370)(118,369)(119,372)
(120,371)(121,374)(122,373)(123,376)(124,375)(125,378)(126,377)(127,380)
(128,379)(129,382)(130,381)(131,384)(132,383)(133,386)(134,385)(135,388)
(136,387)(137,390)(138,389)(139,392)(140,391)(141,394)(142,393)(143,396)
(144,395)(145,398)(146,397)(147,400)(148,399)(149,402)(150,401)(151,404)
(152,403)(153,406)(154,405)(155,408)(156,407)(157,410)(158,409)(159,412)
(160,411)(161,414)(162,413)(163,416)(164,415)(165,418)(166,417)(167,420)
(168,419)(169,422)(170,421)(171,424)(172,423)(173,426)(174,425)(175,428)
(176,427)(177,430)(178,429)(179,432)(180,431)(181,434)(182,433)(183,436)
(184,435)(185,438)(186,437)(187,440)(188,439)(189,442)(190,441)(191,444)
(192,443)(193,446)(194,445)(195,448)(196,447)(197,450)(198,449)(199,452)
(200,451)(201,454)(202,453)(203,456)(204,455)(205,458)(206,457)(207,460)
(208,459)(209,462)(210,461)(211,464)(212,463)(213,466)(214,465)(215,468)
(216,467)(217,470)(218,469)(219,472)(220,471)(221,474)(222,473)(223,476)
(224,475)(225,478)(226,477)(227,480)(228,479)(229,482)(230,481)(231,484)
(232,483)(233,486)(234,485)(235,488)(236,487)(237,490)(238,489)(239,492)
(240,491)(241,494)(242,493)(243,496)(244,495)(245,498)(246,497)(247,500)
(248,499)(249,502)(250,501)(251,504)(252,503);
poly := sub<Sym(504)|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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*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 >;
References : None.
to this polytope