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