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