Polytope of Type {12,82}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,82}*1968
Also Known As : {12,82|2}. if this polytope has another name.
Group : SmallGroup(1968,132)
Rank : 3
Schlafli Type : {12,82}
Number of vertices, edges, etc : 12, 492, 82
Order of s0s1s2 : 492
Order of s0s1s2s1 : 2
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) :
2-fold quotients : {6,82}*984
3-fold quotients : {4,82}*656
6-fold quotients : {2,82}*328
12-fold quotients : {2,41}*164
41-fold quotients : {12,2}*48
82-fold quotients : {6,2}*24
123-fold quotients : {4,2}*16
164-fold quotients : {3,2}*12
246-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 42, 83)( 43, 84)( 44, 85)( 45, 86)( 46, 87)( 47, 88)( 48, 89)( 49, 90)
( 50, 91)( 51, 92)( 52, 93)( 53, 94)( 54, 95)( 55, 96)( 56, 97)( 57, 98)
( 58, 99)( 59,100)( 60,101)( 61,102)( 62,103)( 63,104)( 64,105)( 65,106)
( 66,107)( 67,108)( 68,109)( 69,110)( 70,111)( 71,112)( 72,113)( 73,114)
( 74,115)( 75,116)( 76,117)( 77,118)( 78,119)( 79,120)( 80,121)( 81,122)
( 82,123)(165,206)(166,207)(167,208)(168,209)(169,210)(170,211)(171,212)
(172,213)(173,214)(174,215)(175,216)(176,217)(177,218)(178,219)(179,220)
(180,221)(181,222)(182,223)(183,224)(184,225)(185,226)(186,227)(187,228)
(188,229)(189,230)(190,231)(191,232)(192,233)(193,234)(194,235)(195,236)
(196,237)(197,238)(198,239)(199,240)(200,241)(201,242)(202,243)(203,244)
(204,245)(205,246)(247,370)(248,371)(249,372)(250,373)(251,374)(252,375)
(253,376)(254,377)(255,378)(256,379)(257,380)(258,381)(259,382)(260,383)
(261,384)(262,385)(263,386)(264,387)(265,388)(266,389)(267,390)(268,391)
(269,392)(270,393)(271,394)(272,395)(273,396)(274,397)(275,398)(276,399)
(277,400)(278,401)(279,402)(280,403)(281,404)(282,405)(283,406)(284,407)
(285,408)(286,409)(287,410)(288,452)(289,453)(290,454)(291,455)(292,456)
(293,457)(294,458)(295,459)(296,460)(297,461)(298,462)(299,463)(300,464)
(301,465)(302,466)(303,467)(304,468)(305,469)(306,470)(307,471)(308,472)
(309,473)(310,474)(311,475)(312,476)(313,477)(314,478)(315,479)(316,480)
(317,481)(318,482)(319,483)(320,484)(321,485)(322,486)(323,487)(324,488)
(325,489)(326,490)(327,491)(328,492)(329,411)(330,412)(331,413)(332,414)
(333,415)(334,416)(335,417)(336,418)(337,419)(338,420)(339,421)(340,422)
(341,423)(342,424)(343,425)(344,426)(345,427)(346,428)(347,429)(348,430)
(349,431)(350,432)(351,433)(352,434)(353,435)(354,436)(355,437)(356,438)
(357,439)(358,440)(359,441)(360,442)(361,443)(362,444)(363,445)(364,446)
(365,447)(366,448)(367,449)(368,450)(369,451);;
s1 := ( 1,288)( 2,328)( 3,327)( 4,326)( 5,325)( 6,324)( 7,323)( 8,322)
( 9,321)( 10,320)( 11,319)( 12,318)( 13,317)( 14,316)( 15,315)( 16,314)
( 17,313)( 18,312)( 19,311)( 20,310)( 21,309)( 22,308)( 23,307)( 24,306)
( 25,305)( 26,304)( 27,303)( 28,302)( 29,301)( 30,300)( 31,299)( 32,298)
( 33,297)( 34,296)( 35,295)( 36,294)( 37,293)( 38,292)( 39,291)( 40,290)
( 41,289)( 42,247)( 43,287)( 44,286)( 45,285)( 46,284)( 47,283)( 48,282)
( 49,281)( 50,280)( 51,279)( 52,278)( 53,277)( 54,276)( 55,275)( 56,274)
( 57,273)( 58,272)( 59,271)( 60,270)( 61,269)( 62,268)( 63,267)( 64,266)
( 65,265)( 66,264)( 67,263)( 68,262)( 69,261)( 70,260)( 71,259)( 72,258)
( 73,257)( 74,256)( 75,255)( 76,254)( 77,253)( 78,252)( 79,251)( 80,250)
( 81,249)( 82,248)( 83,329)( 84,369)( 85,368)( 86,367)( 87,366)( 88,365)
( 89,364)( 90,363)( 91,362)( 92,361)( 93,360)( 94,359)( 95,358)( 96,357)
( 97,356)( 98,355)( 99,354)(100,353)(101,352)(102,351)(103,350)(104,349)
(105,348)(106,347)(107,346)(108,345)(109,344)(110,343)(111,342)(112,341)
(113,340)(114,339)(115,338)(116,337)(117,336)(118,335)(119,334)(120,333)
(121,332)(122,331)(123,330)(124,411)(125,451)(126,450)(127,449)(128,448)
(129,447)(130,446)(131,445)(132,444)(133,443)(134,442)(135,441)(136,440)
(137,439)(138,438)(139,437)(140,436)(141,435)(142,434)(143,433)(144,432)
(145,431)(146,430)(147,429)(148,428)(149,427)(150,426)(151,425)(152,424)
(153,423)(154,422)(155,421)(156,420)(157,419)(158,418)(159,417)(160,416)
(161,415)(162,414)(163,413)(164,412)(165,370)(166,410)(167,409)(168,408)
(169,407)(170,406)(171,405)(172,404)(173,403)(174,402)(175,401)(176,400)
(177,399)(178,398)(179,397)(180,396)(181,395)(182,394)(183,393)(184,392)
(185,391)(186,390)(187,389)(188,388)(189,387)(190,386)(191,385)(192,384)
(193,383)(194,382)(195,381)(196,380)(197,379)(198,378)(199,377)(200,376)
(201,375)(202,374)(203,373)(204,372)(205,371)(206,452)(207,492)(208,491)
(209,490)(210,489)(211,488)(212,487)(213,486)(214,485)(215,484)(216,483)
(217,482)(218,481)(219,480)(220,479)(221,478)(222,477)(223,476)(224,475)
(225,474)(226,473)(227,472)(228,471)(229,470)(230,469)(231,468)(232,467)
(233,466)(234,465)(235,464)(236,463)(237,462)(238,461)(239,460)(240,459)
(241,458)(242,457)(243,456)(244,455)(245,454)(246,453);;
s2 := ( 1, 2)( 3, 41)( 4, 40)( 5, 39)( 6, 38)( 7, 37)( 8, 36)( 9, 35)
( 10, 34)( 11, 33)( 12, 32)( 13, 31)( 14, 30)( 15, 29)( 16, 28)( 17, 27)
( 18, 26)( 19, 25)( 20, 24)( 21, 23)( 42, 43)( 44, 82)( 45, 81)( 46, 80)
( 47, 79)( 48, 78)( 49, 77)( 50, 76)( 51, 75)( 52, 74)( 53, 73)( 54, 72)
( 55, 71)( 56, 70)( 57, 69)( 58, 68)( 59, 67)( 60, 66)( 61, 65)( 62, 64)
( 83, 84)( 85,123)( 86,122)( 87,121)( 88,120)( 89,119)( 90,118)( 91,117)
( 92,116)( 93,115)( 94,114)( 95,113)( 96,112)( 97,111)( 98,110)( 99,109)
(100,108)(101,107)(102,106)(103,105)(124,125)(126,164)(127,163)(128,162)
(129,161)(130,160)(131,159)(132,158)(133,157)(134,156)(135,155)(136,154)
(137,153)(138,152)(139,151)(140,150)(141,149)(142,148)(143,147)(144,146)
(165,166)(167,205)(168,204)(169,203)(170,202)(171,201)(172,200)(173,199)
(174,198)(175,197)(176,196)(177,195)(178,194)(179,193)(180,192)(181,191)
(182,190)(183,189)(184,188)(185,187)(206,207)(208,246)(209,245)(210,244)
(211,243)(212,242)(213,241)(214,240)(215,239)(216,238)(217,237)(218,236)
(219,235)(220,234)(221,233)(222,232)(223,231)(224,230)(225,229)(226,228)
(247,248)(249,287)(250,286)(251,285)(252,284)(253,283)(254,282)(255,281)
(256,280)(257,279)(258,278)(259,277)(260,276)(261,275)(262,274)(263,273)
(264,272)(265,271)(266,270)(267,269)(288,289)(290,328)(291,327)(292,326)
(293,325)(294,324)(295,323)(296,322)(297,321)(298,320)(299,319)(300,318)
(301,317)(302,316)(303,315)(304,314)(305,313)(306,312)(307,311)(308,310)
(329,330)(331,369)(332,368)(333,367)(334,366)(335,365)(336,364)(337,363)
(338,362)(339,361)(340,360)(341,359)(342,358)(343,357)(344,356)(345,355)
(346,354)(347,353)(348,352)(349,351)(370,371)(372,410)(373,409)(374,408)
(375,407)(376,406)(377,405)(378,404)(379,403)(380,402)(381,401)(382,400)
(383,399)(384,398)(385,397)(386,396)(387,395)(388,394)(389,393)(390,392)
(411,412)(413,451)(414,450)(415,449)(416,448)(417,447)(418,446)(419,445)
(420,444)(421,443)(422,442)(423,441)(424,440)(425,439)(426,438)(427,437)
(428,436)(429,435)(430,434)(431,433)(452,453)(454,492)(455,491)(456,490)
(457,489)(458,488)(459,487)(460,486)(461,485)(462,484)(463,483)(464,482)
(465,481)(466,480)(467,479)(468,478)(469,477)(470,476)(471,475)(472,474);;
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*s2*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,
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*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(492)!( 42, 83)( 43, 84)( 44, 85)( 45, 86)( 46, 87)( 47, 88)( 48, 89)
( 49, 90)( 50, 91)( 51, 92)( 52, 93)( 53, 94)( 54, 95)( 55, 96)( 56, 97)
( 57, 98)( 58, 99)( 59,100)( 60,101)( 61,102)( 62,103)( 63,104)( 64,105)
( 65,106)( 66,107)( 67,108)( 68,109)( 69,110)( 70,111)( 71,112)( 72,113)
( 73,114)( 74,115)( 75,116)( 76,117)( 77,118)( 78,119)( 79,120)( 80,121)
( 81,122)( 82,123)(165,206)(166,207)(167,208)(168,209)(169,210)(170,211)
(171,212)(172,213)(173,214)(174,215)(175,216)(176,217)(177,218)(178,219)
(179,220)(180,221)(181,222)(182,223)(183,224)(184,225)(185,226)(186,227)
(187,228)(188,229)(189,230)(190,231)(191,232)(192,233)(193,234)(194,235)
(195,236)(196,237)(197,238)(198,239)(199,240)(200,241)(201,242)(202,243)
(203,244)(204,245)(205,246)(247,370)(248,371)(249,372)(250,373)(251,374)
(252,375)(253,376)(254,377)(255,378)(256,379)(257,380)(258,381)(259,382)
(260,383)(261,384)(262,385)(263,386)(264,387)(265,388)(266,389)(267,390)
(268,391)(269,392)(270,393)(271,394)(272,395)(273,396)(274,397)(275,398)
(276,399)(277,400)(278,401)(279,402)(280,403)(281,404)(282,405)(283,406)
(284,407)(285,408)(286,409)(287,410)(288,452)(289,453)(290,454)(291,455)
(292,456)(293,457)(294,458)(295,459)(296,460)(297,461)(298,462)(299,463)
(300,464)(301,465)(302,466)(303,467)(304,468)(305,469)(306,470)(307,471)
(308,472)(309,473)(310,474)(311,475)(312,476)(313,477)(314,478)(315,479)
(316,480)(317,481)(318,482)(319,483)(320,484)(321,485)(322,486)(323,487)
(324,488)(325,489)(326,490)(327,491)(328,492)(329,411)(330,412)(331,413)
(332,414)(333,415)(334,416)(335,417)(336,418)(337,419)(338,420)(339,421)
(340,422)(341,423)(342,424)(343,425)(344,426)(345,427)(346,428)(347,429)
(348,430)(349,431)(350,432)(351,433)(352,434)(353,435)(354,436)(355,437)
(356,438)(357,439)(358,440)(359,441)(360,442)(361,443)(362,444)(363,445)
(364,446)(365,447)(366,448)(367,449)(368,450)(369,451);
s1 := Sym(492)!( 1,288)( 2,328)( 3,327)( 4,326)( 5,325)( 6,324)( 7,323)
( 8,322)( 9,321)( 10,320)( 11,319)( 12,318)( 13,317)( 14,316)( 15,315)
( 16,314)( 17,313)( 18,312)( 19,311)( 20,310)( 21,309)( 22,308)( 23,307)
( 24,306)( 25,305)( 26,304)( 27,303)( 28,302)( 29,301)( 30,300)( 31,299)
( 32,298)( 33,297)( 34,296)( 35,295)( 36,294)( 37,293)( 38,292)( 39,291)
( 40,290)( 41,289)( 42,247)( 43,287)( 44,286)( 45,285)( 46,284)( 47,283)
( 48,282)( 49,281)( 50,280)( 51,279)( 52,278)( 53,277)( 54,276)( 55,275)
( 56,274)( 57,273)( 58,272)( 59,271)( 60,270)( 61,269)( 62,268)( 63,267)
( 64,266)( 65,265)( 66,264)( 67,263)( 68,262)( 69,261)( 70,260)( 71,259)
( 72,258)( 73,257)( 74,256)( 75,255)( 76,254)( 77,253)( 78,252)( 79,251)
( 80,250)( 81,249)( 82,248)( 83,329)( 84,369)( 85,368)( 86,367)( 87,366)
( 88,365)( 89,364)( 90,363)( 91,362)( 92,361)( 93,360)( 94,359)( 95,358)
( 96,357)( 97,356)( 98,355)( 99,354)(100,353)(101,352)(102,351)(103,350)
(104,349)(105,348)(106,347)(107,346)(108,345)(109,344)(110,343)(111,342)
(112,341)(113,340)(114,339)(115,338)(116,337)(117,336)(118,335)(119,334)
(120,333)(121,332)(122,331)(123,330)(124,411)(125,451)(126,450)(127,449)
(128,448)(129,447)(130,446)(131,445)(132,444)(133,443)(134,442)(135,441)
(136,440)(137,439)(138,438)(139,437)(140,436)(141,435)(142,434)(143,433)
(144,432)(145,431)(146,430)(147,429)(148,428)(149,427)(150,426)(151,425)
(152,424)(153,423)(154,422)(155,421)(156,420)(157,419)(158,418)(159,417)
(160,416)(161,415)(162,414)(163,413)(164,412)(165,370)(166,410)(167,409)
(168,408)(169,407)(170,406)(171,405)(172,404)(173,403)(174,402)(175,401)
(176,400)(177,399)(178,398)(179,397)(180,396)(181,395)(182,394)(183,393)
(184,392)(185,391)(186,390)(187,389)(188,388)(189,387)(190,386)(191,385)
(192,384)(193,383)(194,382)(195,381)(196,380)(197,379)(198,378)(199,377)
(200,376)(201,375)(202,374)(203,373)(204,372)(205,371)(206,452)(207,492)
(208,491)(209,490)(210,489)(211,488)(212,487)(213,486)(214,485)(215,484)
(216,483)(217,482)(218,481)(219,480)(220,479)(221,478)(222,477)(223,476)
(224,475)(225,474)(226,473)(227,472)(228,471)(229,470)(230,469)(231,468)
(232,467)(233,466)(234,465)(235,464)(236,463)(237,462)(238,461)(239,460)
(240,459)(241,458)(242,457)(243,456)(244,455)(245,454)(246,453);
s2 := Sym(492)!( 1, 2)( 3, 41)( 4, 40)( 5, 39)( 6, 38)( 7, 37)( 8, 36)
( 9, 35)( 10, 34)( 11, 33)( 12, 32)( 13, 31)( 14, 30)( 15, 29)( 16, 28)
( 17, 27)( 18, 26)( 19, 25)( 20, 24)( 21, 23)( 42, 43)( 44, 82)( 45, 81)
( 46, 80)( 47, 79)( 48, 78)( 49, 77)( 50, 76)( 51, 75)( 52, 74)( 53, 73)
( 54, 72)( 55, 71)( 56, 70)( 57, 69)( 58, 68)( 59, 67)( 60, 66)( 61, 65)
( 62, 64)( 83, 84)( 85,123)( 86,122)( 87,121)( 88,120)( 89,119)( 90,118)
( 91,117)( 92,116)( 93,115)( 94,114)( 95,113)( 96,112)( 97,111)( 98,110)
( 99,109)(100,108)(101,107)(102,106)(103,105)(124,125)(126,164)(127,163)
(128,162)(129,161)(130,160)(131,159)(132,158)(133,157)(134,156)(135,155)
(136,154)(137,153)(138,152)(139,151)(140,150)(141,149)(142,148)(143,147)
(144,146)(165,166)(167,205)(168,204)(169,203)(170,202)(171,201)(172,200)
(173,199)(174,198)(175,197)(176,196)(177,195)(178,194)(179,193)(180,192)
(181,191)(182,190)(183,189)(184,188)(185,187)(206,207)(208,246)(209,245)
(210,244)(211,243)(212,242)(213,241)(214,240)(215,239)(216,238)(217,237)
(218,236)(219,235)(220,234)(221,233)(222,232)(223,231)(224,230)(225,229)
(226,228)(247,248)(249,287)(250,286)(251,285)(252,284)(253,283)(254,282)
(255,281)(256,280)(257,279)(258,278)(259,277)(260,276)(261,275)(262,274)
(263,273)(264,272)(265,271)(266,270)(267,269)(288,289)(290,328)(291,327)
(292,326)(293,325)(294,324)(295,323)(296,322)(297,321)(298,320)(299,319)
(300,318)(301,317)(302,316)(303,315)(304,314)(305,313)(306,312)(307,311)
(308,310)(329,330)(331,369)(332,368)(333,367)(334,366)(335,365)(336,364)
(337,363)(338,362)(339,361)(340,360)(341,359)(342,358)(343,357)(344,356)
(345,355)(346,354)(347,353)(348,352)(349,351)(370,371)(372,410)(373,409)
(374,408)(375,407)(376,406)(377,405)(378,404)(379,403)(380,402)(381,401)
(382,400)(383,399)(384,398)(385,397)(386,396)(387,395)(388,394)(389,393)
(390,392)(411,412)(413,451)(414,450)(415,449)(416,448)(417,447)(418,446)
(419,445)(420,444)(421,443)(422,442)(423,441)(424,440)(425,439)(426,438)
(427,437)(428,436)(429,435)(430,434)(431,433)(452,453)(454,492)(455,491)
(456,490)(457,489)(458,488)(459,487)(460,486)(461,485)(462,484)(463,483)
(464,482)(465,481)(466,480)(467,479)(468,478)(469,477)(470,476)(471,475)
(472,474);
poly := sub<Sym(492)|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*s2*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,
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*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