Polytope of Type {22,44}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,44}*1936a
Also Known As : {22,44|2}. if this polytope has another name.
Group : SmallGroup(1936,124)
Rank : 3
Schlafli Type : {22,44}
Number of vertices, edges, etc : 22, 484, 44
Order of s0s1s2 : 44
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 : {22,22}*968a
11-fold quotients : {2,44}*176, {22,4}*176
22-fold quotients : {2,22}*88, {22,2}*88
44-fold quotients : {2,11}*44, {11,2}*44
121-fold quotients : {2,4}*16
242-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 12,111)( 13,112)( 14,113)( 15,114)( 16,115)( 17,116)( 18,117)( 19,118)
( 20,119)( 21,120)( 22,121)( 23,100)( 24,101)( 25,102)( 26,103)( 27,104)
( 28,105)( 29,106)( 30,107)( 31,108)( 32,109)( 33,110)( 34, 89)( 35, 90)
( 36, 91)( 37, 92)( 38, 93)( 39, 94)( 40, 95)( 41, 96)( 42, 97)( 43, 98)
( 44, 99)( 45, 78)( 46, 79)( 47, 80)( 48, 81)( 49, 82)( 50, 83)( 51, 84)
( 52, 85)( 53, 86)( 54, 87)( 55, 88)( 56, 67)( 57, 68)( 58, 69)( 59, 70)
( 60, 71)( 61, 72)( 62, 73)( 63, 74)( 64, 75)( 65, 76)( 66, 77)(133,232)
(134,233)(135,234)(136,235)(137,236)(138,237)(139,238)(140,239)(141,240)
(142,241)(143,242)(144,221)(145,222)(146,223)(147,224)(148,225)(149,226)
(150,227)(151,228)(152,229)(153,230)(154,231)(155,210)(156,211)(157,212)
(158,213)(159,214)(160,215)(161,216)(162,217)(163,218)(164,219)(165,220)
(166,199)(167,200)(168,201)(169,202)(170,203)(171,204)(172,205)(173,206)
(174,207)(175,208)(176,209)(177,188)(178,189)(179,190)(180,191)(181,192)
(182,193)(183,194)(184,195)(185,196)(186,197)(187,198)(254,353)(255,354)
(256,355)(257,356)(258,357)(259,358)(260,359)(261,360)(262,361)(263,362)
(264,363)(265,342)(266,343)(267,344)(268,345)(269,346)(270,347)(271,348)
(272,349)(273,350)(274,351)(275,352)(276,331)(277,332)(278,333)(279,334)
(280,335)(281,336)(282,337)(283,338)(284,339)(285,340)(286,341)(287,320)
(288,321)(289,322)(290,323)(291,324)(292,325)(293,326)(294,327)(295,328)
(296,329)(297,330)(298,309)(299,310)(300,311)(301,312)(302,313)(303,314)
(304,315)(305,316)(306,317)(307,318)(308,319)(375,474)(376,475)(377,476)
(378,477)(379,478)(380,479)(381,480)(382,481)(383,482)(384,483)(385,484)
(386,463)(387,464)(388,465)(389,466)(390,467)(391,468)(392,469)(393,470)
(394,471)(395,472)(396,473)(397,452)(398,453)(399,454)(400,455)(401,456)
(402,457)(403,458)(404,459)(405,460)(406,461)(407,462)(408,441)(409,442)
(410,443)(411,444)(412,445)(413,446)(414,447)(415,448)(416,449)(417,450)
(418,451)(419,430)(420,431)(421,432)(422,433)(423,434)(424,435)(425,436)
(426,437)(427,438)(428,439)(429,440);;
s1 := ( 1, 12)( 2, 22)( 3, 21)( 4, 20)( 5, 19)( 6, 18)( 7, 17)( 8, 16)
( 9, 15)( 10, 14)( 11, 13)( 23,111)( 24,121)( 25,120)( 26,119)( 27,118)
( 28,117)( 29,116)( 30,115)( 31,114)( 32,113)( 33,112)( 34,100)( 35,110)
( 36,109)( 37,108)( 38,107)( 39,106)( 40,105)( 41,104)( 42,103)( 43,102)
( 44,101)( 45, 89)( 46, 99)( 47, 98)( 48, 97)( 49, 96)( 50, 95)( 51, 94)
( 52, 93)( 53, 92)( 54, 91)( 55, 90)( 56, 78)( 57, 88)( 58, 87)( 59, 86)
( 60, 85)( 61, 84)( 62, 83)( 63, 82)( 64, 81)( 65, 80)( 66, 79)( 68, 77)
( 69, 76)( 70, 75)( 71, 74)( 72, 73)(122,133)(123,143)(124,142)(125,141)
(126,140)(127,139)(128,138)(129,137)(130,136)(131,135)(132,134)(144,232)
(145,242)(146,241)(147,240)(148,239)(149,238)(150,237)(151,236)(152,235)
(153,234)(154,233)(155,221)(156,231)(157,230)(158,229)(159,228)(160,227)
(161,226)(162,225)(163,224)(164,223)(165,222)(166,210)(167,220)(168,219)
(169,218)(170,217)(171,216)(172,215)(173,214)(174,213)(175,212)(176,211)
(177,199)(178,209)(179,208)(180,207)(181,206)(182,205)(183,204)(184,203)
(185,202)(186,201)(187,200)(189,198)(190,197)(191,196)(192,195)(193,194)
(243,375)(244,385)(245,384)(246,383)(247,382)(248,381)(249,380)(250,379)
(251,378)(252,377)(253,376)(254,364)(255,374)(256,373)(257,372)(258,371)
(259,370)(260,369)(261,368)(262,367)(263,366)(264,365)(265,474)(266,484)
(267,483)(268,482)(269,481)(270,480)(271,479)(272,478)(273,477)(274,476)
(275,475)(276,463)(277,473)(278,472)(279,471)(280,470)(281,469)(282,468)
(283,467)(284,466)(285,465)(286,464)(287,452)(288,462)(289,461)(290,460)
(291,459)(292,458)(293,457)(294,456)(295,455)(296,454)(297,453)(298,441)
(299,451)(300,450)(301,449)(302,448)(303,447)(304,446)(305,445)(306,444)
(307,443)(308,442)(309,430)(310,440)(311,439)(312,438)(313,437)(314,436)
(315,435)(316,434)(317,433)(318,432)(319,431)(320,419)(321,429)(322,428)
(323,427)(324,426)(325,425)(326,424)(327,423)(328,422)(329,421)(330,420)
(331,408)(332,418)(333,417)(334,416)(335,415)(336,414)(337,413)(338,412)
(339,411)(340,410)(341,409)(342,397)(343,407)(344,406)(345,405)(346,404)
(347,403)(348,402)(349,401)(350,400)(351,399)(352,398)(353,386)(354,396)
(355,395)(356,394)(357,393)(358,392)(359,391)(360,390)(361,389)(362,388)
(363,387);;
s2 := ( 1,244)( 2,243)( 3,253)( 4,252)( 5,251)( 6,250)( 7,249)( 8,248)
( 9,247)( 10,246)( 11,245)( 12,255)( 13,254)( 14,264)( 15,263)( 16,262)
( 17,261)( 18,260)( 19,259)( 20,258)( 21,257)( 22,256)( 23,266)( 24,265)
( 25,275)( 26,274)( 27,273)( 28,272)( 29,271)( 30,270)( 31,269)( 32,268)
( 33,267)( 34,277)( 35,276)( 36,286)( 37,285)( 38,284)( 39,283)( 40,282)
( 41,281)( 42,280)( 43,279)( 44,278)( 45,288)( 46,287)( 47,297)( 48,296)
( 49,295)( 50,294)( 51,293)( 52,292)( 53,291)( 54,290)( 55,289)( 56,299)
( 57,298)( 58,308)( 59,307)( 60,306)( 61,305)( 62,304)( 63,303)( 64,302)
( 65,301)( 66,300)( 67,310)( 68,309)( 69,319)( 70,318)( 71,317)( 72,316)
( 73,315)( 74,314)( 75,313)( 76,312)( 77,311)( 78,321)( 79,320)( 80,330)
( 81,329)( 82,328)( 83,327)( 84,326)( 85,325)( 86,324)( 87,323)( 88,322)
( 89,332)( 90,331)( 91,341)( 92,340)( 93,339)( 94,338)( 95,337)( 96,336)
( 97,335)( 98,334)( 99,333)(100,343)(101,342)(102,352)(103,351)(104,350)
(105,349)(106,348)(107,347)(108,346)(109,345)(110,344)(111,354)(112,353)
(113,363)(114,362)(115,361)(116,360)(117,359)(118,358)(119,357)(120,356)
(121,355)(122,365)(123,364)(124,374)(125,373)(126,372)(127,371)(128,370)
(129,369)(130,368)(131,367)(132,366)(133,376)(134,375)(135,385)(136,384)
(137,383)(138,382)(139,381)(140,380)(141,379)(142,378)(143,377)(144,387)
(145,386)(146,396)(147,395)(148,394)(149,393)(150,392)(151,391)(152,390)
(153,389)(154,388)(155,398)(156,397)(157,407)(158,406)(159,405)(160,404)
(161,403)(162,402)(163,401)(164,400)(165,399)(166,409)(167,408)(168,418)
(169,417)(170,416)(171,415)(172,414)(173,413)(174,412)(175,411)(176,410)
(177,420)(178,419)(179,429)(180,428)(181,427)(182,426)(183,425)(184,424)
(185,423)(186,422)(187,421)(188,431)(189,430)(190,440)(191,439)(192,438)
(193,437)(194,436)(195,435)(196,434)(197,433)(198,432)(199,442)(200,441)
(201,451)(202,450)(203,449)(204,448)(205,447)(206,446)(207,445)(208,444)
(209,443)(210,453)(211,452)(212,462)(213,461)(214,460)(215,459)(216,458)
(217,457)(218,456)(219,455)(220,454)(221,464)(222,463)(223,473)(224,472)
(225,471)(226,470)(227,469)(228,468)(229,467)(230,466)(231,465)(232,475)
(233,474)(234,484)(235,483)(236,482)(237,481)(238,480)(239,479)(240,478)
(241,477)(242,476);;
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*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*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(484)!( 12,111)( 13,112)( 14,113)( 15,114)( 16,115)( 17,116)( 18,117)
( 19,118)( 20,119)( 21,120)( 22,121)( 23,100)( 24,101)( 25,102)( 26,103)
( 27,104)( 28,105)( 29,106)( 30,107)( 31,108)( 32,109)( 33,110)( 34, 89)
( 35, 90)( 36, 91)( 37, 92)( 38, 93)( 39, 94)( 40, 95)( 41, 96)( 42, 97)
( 43, 98)( 44, 99)( 45, 78)( 46, 79)( 47, 80)( 48, 81)( 49, 82)( 50, 83)
( 51, 84)( 52, 85)( 53, 86)( 54, 87)( 55, 88)( 56, 67)( 57, 68)( 58, 69)
( 59, 70)( 60, 71)( 61, 72)( 62, 73)( 63, 74)( 64, 75)( 65, 76)( 66, 77)
(133,232)(134,233)(135,234)(136,235)(137,236)(138,237)(139,238)(140,239)
(141,240)(142,241)(143,242)(144,221)(145,222)(146,223)(147,224)(148,225)
(149,226)(150,227)(151,228)(152,229)(153,230)(154,231)(155,210)(156,211)
(157,212)(158,213)(159,214)(160,215)(161,216)(162,217)(163,218)(164,219)
(165,220)(166,199)(167,200)(168,201)(169,202)(170,203)(171,204)(172,205)
(173,206)(174,207)(175,208)(176,209)(177,188)(178,189)(179,190)(180,191)
(181,192)(182,193)(183,194)(184,195)(185,196)(186,197)(187,198)(254,353)
(255,354)(256,355)(257,356)(258,357)(259,358)(260,359)(261,360)(262,361)
(263,362)(264,363)(265,342)(266,343)(267,344)(268,345)(269,346)(270,347)
(271,348)(272,349)(273,350)(274,351)(275,352)(276,331)(277,332)(278,333)
(279,334)(280,335)(281,336)(282,337)(283,338)(284,339)(285,340)(286,341)
(287,320)(288,321)(289,322)(290,323)(291,324)(292,325)(293,326)(294,327)
(295,328)(296,329)(297,330)(298,309)(299,310)(300,311)(301,312)(302,313)
(303,314)(304,315)(305,316)(306,317)(307,318)(308,319)(375,474)(376,475)
(377,476)(378,477)(379,478)(380,479)(381,480)(382,481)(383,482)(384,483)
(385,484)(386,463)(387,464)(388,465)(389,466)(390,467)(391,468)(392,469)
(393,470)(394,471)(395,472)(396,473)(397,452)(398,453)(399,454)(400,455)
(401,456)(402,457)(403,458)(404,459)(405,460)(406,461)(407,462)(408,441)
(409,442)(410,443)(411,444)(412,445)(413,446)(414,447)(415,448)(416,449)
(417,450)(418,451)(419,430)(420,431)(421,432)(422,433)(423,434)(424,435)
(425,436)(426,437)(427,438)(428,439)(429,440);
s1 := Sym(484)!( 1, 12)( 2, 22)( 3, 21)( 4, 20)( 5, 19)( 6, 18)( 7, 17)
( 8, 16)( 9, 15)( 10, 14)( 11, 13)( 23,111)( 24,121)( 25,120)( 26,119)
( 27,118)( 28,117)( 29,116)( 30,115)( 31,114)( 32,113)( 33,112)( 34,100)
( 35,110)( 36,109)( 37,108)( 38,107)( 39,106)( 40,105)( 41,104)( 42,103)
( 43,102)( 44,101)( 45, 89)( 46, 99)( 47, 98)( 48, 97)( 49, 96)( 50, 95)
( 51, 94)( 52, 93)( 53, 92)( 54, 91)( 55, 90)( 56, 78)( 57, 88)( 58, 87)
( 59, 86)( 60, 85)( 61, 84)( 62, 83)( 63, 82)( 64, 81)( 65, 80)( 66, 79)
( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)(122,133)(123,143)(124,142)
(125,141)(126,140)(127,139)(128,138)(129,137)(130,136)(131,135)(132,134)
(144,232)(145,242)(146,241)(147,240)(148,239)(149,238)(150,237)(151,236)
(152,235)(153,234)(154,233)(155,221)(156,231)(157,230)(158,229)(159,228)
(160,227)(161,226)(162,225)(163,224)(164,223)(165,222)(166,210)(167,220)
(168,219)(169,218)(170,217)(171,216)(172,215)(173,214)(174,213)(175,212)
(176,211)(177,199)(178,209)(179,208)(180,207)(181,206)(182,205)(183,204)
(184,203)(185,202)(186,201)(187,200)(189,198)(190,197)(191,196)(192,195)
(193,194)(243,375)(244,385)(245,384)(246,383)(247,382)(248,381)(249,380)
(250,379)(251,378)(252,377)(253,376)(254,364)(255,374)(256,373)(257,372)
(258,371)(259,370)(260,369)(261,368)(262,367)(263,366)(264,365)(265,474)
(266,484)(267,483)(268,482)(269,481)(270,480)(271,479)(272,478)(273,477)
(274,476)(275,475)(276,463)(277,473)(278,472)(279,471)(280,470)(281,469)
(282,468)(283,467)(284,466)(285,465)(286,464)(287,452)(288,462)(289,461)
(290,460)(291,459)(292,458)(293,457)(294,456)(295,455)(296,454)(297,453)
(298,441)(299,451)(300,450)(301,449)(302,448)(303,447)(304,446)(305,445)
(306,444)(307,443)(308,442)(309,430)(310,440)(311,439)(312,438)(313,437)
(314,436)(315,435)(316,434)(317,433)(318,432)(319,431)(320,419)(321,429)
(322,428)(323,427)(324,426)(325,425)(326,424)(327,423)(328,422)(329,421)
(330,420)(331,408)(332,418)(333,417)(334,416)(335,415)(336,414)(337,413)
(338,412)(339,411)(340,410)(341,409)(342,397)(343,407)(344,406)(345,405)
(346,404)(347,403)(348,402)(349,401)(350,400)(351,399)(352,398)(353,386)
(354,396)(355,395)(356,394)(357,393)(358,392)(359,391)(360,390)(361,389)
(362,388)(363,387);
s2 := Sym(484)!( 1,244)( 2,243)( 3,253)( 4,252)( 5,251)( 6,250)( 7,249)
( 8,248)( 9,247)( 10,246)( 11,245)( 12,255)( 13,254)( 14,264)( 15,263)
( 16,262)( 17,261)( 18,260)( 19,259)( 20,258)( 21,257)( 22,256)( 23,266)
( 24,265)( 25,275)( 26,274)( 27,273)( 28,272)( 29,271)( 30,270)( 31,269)
( 32,268)( 33,267)( 34,277)( 35,276)( 36,286)( 37,285)( 38,284)( 39,283)
( 40,282)( 41,281)( 42,280)( 43,279)( 44,278)( 45,288)( 46,287)( 47,297)
( 48,296)( 49,295)( 50,294)( 51,293)( 52,292)( 53,291)( 54,290)( 55,289)
( 56,299)( 57,298)( 58,308)( 59,307)( 60,306)( 61,305)( 62,304)( 63,303)
( 64,302)( 65,301)( 66,300)( 67,310)( 68,309)( 69,319)( 70,318)( 71,317)
( 72,316)( 73,315)( 74,314)( 75,313)( 76,312)( 77,311)( 78,321)( 79,320)
( 80,330)( 81,329)( 82,328)( 83,327)( 84,326)( 85,325)( 86,324)( 87,323)
( 88,322)( 89,332)( 90,331)( 91,341)( 92,340)( 93,339)( 94,338)( 95,337)
( 96,336)( 97,335)( 98,334)( 99,333)(100,343)(101,342)(102,352)(103,351)
(104,350)(105,349)(106,348)(107,347)(108,346)(109,345)(110,344)(111,354)
(112,353)(113,363)(114,362)(115,361)(116,360)(117,359)(118,358)(119,357)
(120,356)(121,355)(122,365)(123,364)(124,374)(125,373)(126,372)(127,371)
(128,370)(129,369)(130,368)(131,367)(132,366)(133,376)(134,375)(135,385)
(136,384)(137,383)(138,382)(139,381)(140,380)(141,379)(142,378)(143,377)
(144,387)(145,386)(146,396)(147,395)(148,394)(149,393)(150,392)(151,391)
(152,390)(153,389)(154,388)(155,398)(156,397)(157,407)(158,406)(159,405)
(160,404)(161,403)(162,402)(163,401)(164,400)(165,399)(166,409)(167,408)
(168,418)(169,417)(170,416)(171,415)(172,414)(173,413)(174,412)(175,411)
(176,410)(177,420)(178,419)(179,429)(180,428)(181,427)(182,426)(183,425)
(184,424)(185,423)(186,422)(187,421)(188,431)(189,430)(190,440)(191,439)
(192,438)(193,437)(194,436)(195,435)(196,434)(197,433)(198,432)(199,442)
(200,441)(201,451)(202,450)(203,449)(204,448)(205,447)(206,446)(207,445)
(208,444)(209,443)(210,453)(211,452)(212,462)(213,461)(214,460)(215,459)
(216,458)(217,457)(218,456)(219,455)(220,454)(221,464)(222,463)(223,473)
(224,472)(225,471)(226,470)(227,469)(228,468)(229,467)(230,466)(231,465)
(232,475)(233,474)(234,484)(235,483)(236,482)(237,481)(238,480)(239,479)
(240,478)(241,477)(242,476);
poly := sub<Sym(484)|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*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 >;
References : None.
to this polytope