Polytope of Type {22,44}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,44}*1936c
if this polytope has a name.
Group : SmallGroup(1936,134)
Rank : 3
Schlafli Type : {22,44}
Number of vertices, edges, etc : 22, 484, 44
Order of s0s1s2 : 44
Order of s0s1s2s1 : 22
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}*968c
4-fold quotients : {11,22}*484
11-fold quotients : {22,4}*176
22-fold quotients : {22,2}*88
44-fold quotients : {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 := ( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 12,111)( 13,121)( 14,120)
( 15,119)( 16,118)( 17,117)( 18,116)( 19,115)( 20,114)( 21,113)( 22,112)
( 23,100)( 24,110)( 25,109)( 26,108)( 27,107)( 28,106)( 29,105)( 30,104)
( 31,103)( 32,102)( 33,101)( 34, 89)( 35, 99)( 36, 98)( 37, 97)( 38, 96)
( 39, 95)( 40, 94)( 41, 93)( 42, 92)( 43, 91)( 44, 90)( 45, 78)( 46, 88)
( 47, 87)( 48, 86)( 49, 85)( 50, 84)( 51, 83)( 52, 82)( 53, 81)( 54, 80)
( 55, 79)( 56, 67)( 57, 77)( 58, 76)( 59, 75)( 60, 74)( 61, 73)( 62, 72)
( 63, 71)( 64, 70)( 65, 69)( 66, 68)(123,132)(124,131)(125,130)(126,129)
(127,128)(133,232)(134,242)(135,241)(136,240)(137,239)(138,238)(139,237)
(140,236)(141,235)(142,234)(143,233)(144,221)(145,231)(146,230)(147,229)
(148,228)(149,227)(150,226)(151,225)(152,224)(153,223)(154,222)(155,210)
(156,220)(157,219)(158,218)(159,217)(160,216)(161,215)(162,214)(163,213)
(164,212)(165,211)(166,199)(167,209)(168,208)(169,207)(170,206)(171,205)
(172,204)(173,203)(174,202)(175,201)(176,200)(177,188)(178,198)(179,197)
(180,196)(181,195)(182,194)(183,193)(184,192)(185,191)(186,190)(187,189)
(244,253)(245,252)(246,251)(247,250)(248,249)(254,353)(255,363)(256,362)
(257,361)(258,360)(259,359)(260,358)(261,357)(262,356)(263,355)(264,354)
(265,342)(266,352)(267,351)(268,350)(269,349)(270,348)(271,347)(272,346)
(273,345)(274,344)(275,343)(276,331)(277,341)(278,340)(279,339)(280,338)
(281,337)(282,336)(283,335)(284,334)(285,333)(286,332)(287,320)(288,330)
(289,329)(290,328)(291,327)(292,326)(293,325)(294,324)(295,323)(296,322)
(297,321)(298,309)(299,319)(300,318)(301,317)(302,316)(303,315)(304,314)
(305,313)(306,312)(307,311)(308,310)(365,374)(366,373)(367,372)(368,371)
(369,370)(375,474)(376,484)(377,483)(378,482)(379,481)(380,480)(381,479)
(382,478)(383,477)(384,476)(385,475)(386,463)(387,473)(388,472)(389,471)
(390,470)(391,469)(392,468)(393,467)(394,466)(395,465)(396,464)(397,452)
(398,462)(399,461)(400,460)(401,459)(402,458)(403,457)(404,456)(405,455)
(406,454)(407,453)(408,441)(409,451)(410,450)(411,449)(412,448)(413,447)
(414,446)(415,445)(416,444)(417,443)(418,442)(419,430)(420,440)(421,439)
(422,438)(423,437)(424,436)(425,435)(426,434)(427,433)(428,432)(429,431);;
s1 := ( 1,255)( 2,254)( 3,264)( 4,263)( 5,262)( 6,261)( 7,260)( 8,259)
( 9,258)( 10,257)( 11,256)( 12,244)( 13,243)( 14,253)( 15,252)( 16,251)
( 17,250)( 18,249)( 19,248)( 20,247)( 21,246)( 22,245)( 23,354)( 24,353)
( 25,363)( 26,362)( 27,361)( 28,360)( 29,359)( 30,358)( 31,357)( 32,356)
( 33,355)( 34,343)( 35,342)( 36,352)( 37,351)( 38,350)( 39,349)( 40,348)
( 41,347)( 42,346)( 43,345)( 44,344)( 45,332)( 46,331)( 47,341)( 48,340)
( 49,339)( 50,338)( 51,337)( 52,336)( 53,335)( 54,334)( 55,333)( 56,321)
( 57,320)( 58,330)( 59,329)( 60,328)( 61,327)( 62,326)( 63,325)( 64,324)
( 65,323)( 66,322)( 67,310)( 68,309)( 69,319)( 70,318)( 71,317)( 72,316)
( 73,315)( 74,314)( 75,313)( 76,312)( 77,311)( 78,299)( 79,298)( 80,308)
( 81,307)( 82,306)( 83,305)( 84,304)( 85,303)( 86,302)( 87,301)( 88,300)
( 89,288)( 90,287)( 91,297)( 92,296)( 93,295)( 94,294)( 95,293)( 96,292)
( 97,291)( 98,290)( 99,289)(100,277)(101,276)(102,286)(103,285)(104,284)
(105,283)(106,282)(107,281)(108,280)(109,279)(110,278)(111,266)(112,265)
(113,275)(114,274)(115,273)(116,272)(117,271)(118,270)(119,269)(120,268)
(121,267)(122,376)(123,375)(124,385)(125,384)(126,383)(127,382)(128,381)
(129,380)(130,379)(131,378)(132,377)(133,365)(134,364)(135,374)(136,373)
(137,372)(138,371)(139,370)(140,369)(141,368)(142,367)(143,366)(144,475)
(145,474)(146,484)(147,483)(148,482)(149,481)(150,480)(151,479)(152,478)
(153,477)(154,476)(155,464)(156,463)(157,473)(158,472)(159,471)(160,470)
(161,469)(162,468)(163,467)(164,466)(165,465)(166,453)(167,452)(168,462)
(169,461)(170,460)(171,459)(172,458)(173,457)(174,456)(175,455)(176,454)
(177,442)(178,441)(179,451)(180,450)(181,449)(182,448)(183,447)(184,446)
(185,445)(186,444)(187,443)(188,431)(189,430)(190,440)(191,439)(192,438)
(193,437)(194,436)(195,435)(196,434)(197,433)(198,432)(199,420)(200,419)
(201,429)(202,428)(203,427)(204,426)(205,425)(206,424)(207,423)(208,422)
(209,421)(210,409)(211,408)(212,418)(213,417)(214,416)(215,415)(216,414)
(217,413)(218,412)(219,411)(220,410)(221,398)(222,397)(223,407)(224,406)
(225,405)(226,404)(227,403)(228,402)(229,401)(230,400)(231,399)(232,387)
(233,386)(234,396)(235,395)(236,394)(237,393)(238,392)(239,391)(240,390)
(241,389)(242,388);;
s2 := ( 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)(243,364)(244,365)
(245,366)(246,367)(247,368)(248,369)(249,370)(250,371)(251,372)(252,373)
(253,374)(254,474)(255,475)(256,476)(257,477)(258,478)(259,479)(260,480)
(261,481)(262,482)(263,483)(264,484)(265,463)(266,464)(267,465)(268,466)
(269,467)(270,468)(271,469)(272,470)(273,471)(274,472)(275,473)(276,452)
(277,453)(278,454)(279,455)(280,456)(281,457)(282,458)(283,459)(284,460)
(285,461)(286,462)(287,441)(288,442)(289,443)(290,444)(291,445)(292,446)
(293,447)(294,448)(295,449)(296,450)(297,451)(298,430)(299,431)(300,432)
(301,433)(302,434)(303,435)(304,436)(305,437)(306,438)(307,439)(308,440)
(309,419)(310,420)(311,421)(312,422)(313,423)(314,424)(315,425)(316,426)
(317,427)(318,428)(319,429)(320,408)(321,409)(322,410)(323,411)(324,412)
(325,413)(326,414)(327,415)(328,416)(329,417)(330,418)(331,397)(332,398)
(333,399)(334,400)(335,401)(336,402)(337,403)(338,404)(339,405)(340,406)
(341,407)(342,386)(343,387)(344,388)(345,389)(346,390)(347,391)(348,392)
(349,393)(350,394)(351,395)(352,396)(353,375)(354,376)(355,377)(356,378)
(357,379)(358,380)(359,381)(360,382)(361,383)(362,384)(363,385);;
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, s2*s0*s1*s2*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(484)!( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 12,111)( 13,121)
( 14,120)( 15,119)( 16,118)( 17,117)( 18,116)( 19,115)( 20,114)( 21,113)
( 22,112)( 23,100)( 24,110)( 25,109)( 26,108)( 27,107)( 28,106)( 29,105)
( 30,104)( 31,103)( 32,102)( 33,101)( 34, 89)( 35, 99)( 36, 98)( 37, 97)
( 38, 96)( 39, 95)( 40, 94)( 41, 93)( 42, 92)( 43, 91)( 44, 90)( 45, 78)
( 46, 88)( 47, 87)( 48, 86)( 49, 85)( 50, 84)( 51, 83)( 52, 82)( 53, 81)
( 54, 80)( 55, 79)( 56, 67)( 57, 77)( 58, 76)( 59, 75)( 60, 74)( 61, 73)
( 62, 72)( 63, 71)( 64, 70)( 65, 69)( 66, 68)(123,132)(124,131)(125,130)
(126,129)(127,128)(133,232)(134,242)(135,241)(136,240)(137,239)(138,238)
(139,237)(140,236)(141,235)(142,234)(143,233)(144,221)(145,231)(146,230)
(147,229)(148,228)(149,227)(150,226)(151,225)(152,224)(153,223)(154,222)
(155,210)(156,220)(157,219)(158,218)(159,217)(160,216)(161,215)(162,214)
(163,213)(164,212)(165,211)(166,199)(167,209)(168,208)(169,207)(170,206)
(171,205)(172,204)(173,203)(174,202)(175,201)(176,200)(177,188)(178,198)
(179,197)(180,196)(181,195)(182,194)(183,193)(184,192)(185,191)(186,190)
(187,189)(244,253)(245,252)(246,251)(247,250)(248,249)(254,353)(255,363)
(256,362)(257,361)(258,360)(259,359)(260,358)(261,357)(262,356)(263,355)
(264,354)(265,342)(266,352)(267,351)(268,350)(269,349)(270,348)(271,347)
(272,346)(273,345)(274,344)(275,343)(276,331)(277,341)(278,340)(279,339)
(280,338)(281,337)(282,336)(283,335)(284,334)(285,333)(286,332)(287,320)
(288,330)(289,329)(290,328)(291,327)(292,326)(293,325)(294,324)(295,323)
(296,322)(297,321)(298,309)(299,319)(300,318)(301,317)(302,316)(303,315)
(304,314)(305,313)(306,312)(307,311)(308,310)(365,374)(366,373)(367,372)
(368,371)(369,370)(375,474)(376,484)(377,483)(378,482)(379,481)(380,480)
(381,479)(382,478)(383,477)(384,476)(385,475)(386,463)(387,473)(388,472)
(389,471)(390,470)(391,469)(392,468)(393,467)(394,466)(395,465)(396,464)
(397,452)(398,462)(399,461)(400,460)(401,459)(402,458)(403,457)(404,456)
(405,455)(406,454)(407,453)(408,441)(409,451)(410,450)(411,449)(412,448)
(413,447)(414,446)(415,445)(416,444)(417,443)(418,442)(419,430)(420,440)
(421,439)(422,438)(423,437)(424,436)(425,435)(426,434)(427,433)(428,432)
(429,431);
s1 := Sym(484)!( 1,255)( 2,254)( 3,264)( 4,263)( 5,262)( 6,261)( 7,260)
( 8,259)( 9,258)( 10,257)( 11,256)( 12,244)( 13,243)( 14,253)( 15,252)
( 16,251)( 17,250)( 18,249)( 19,248)( 20,247)( 21,246)( 22,245)( 23,354)
( 24,353)( 25,363)( 26,362)( 27,361)( 28,360)( 29,359)( 30,358)( 31,357)
( 32,356)( 33,355)( 34,343)( 35,342)( 36,352)( 37,351)( 38,350)( 39,349)
( 40,348)( 41,347)( 42,346)( 43,345)( 44,344)( 45,332)( 46,331)( 47,341)
( 48,340)( 49,339)( 50,338)( 51,337)( 52,336)( 53,335)( 54,334)( 55,333)
( 56,321)( 57,320)( 58,330)( 59,329)( 60,328)( 61,327)( 62,326)( 63,325)
( 64,324)( 65,323)( 66,322)( 67,310)( 68,309)( 69,319)( 70,318)( 71,317)
( 72,316)( 73,315)( 74,314)( 75,313)( 76,312)( 77,311)( 78,299)( 79,298)
( 80,308)( 81,307)( 82,306)( 83,305)( 84,304)( 85,303)( 86,302)( 87,301)
( 88,300)( 89,288)( 90,287)( 91,297)( 92,296)( 93,295)( 94,294)( 95,293)
( 96,292)( 97,291)( 98,290)( 99,289)(100,277)(101,276)(102,286)(103,285)
(104,284)(105,283)(106,282)(107,281)(108,280)(109,279)(110,278)(111,266)
(112,265)(113,275)(114,274)(115,273)(116,272)(117,271)(118,270)(119,269)
(120,268)(121,267)(122,376)(123,375)(124,385)(125,384)(126,383)(127,382)
(128,381)(129,380)(130,379)(131,378)(132,377)(133,365)(134,364)(135,374)
(136,373)(137,372)(138,371)(139,370)(140,369)(141,368)(142,367)(143,366)
(144,475)(145,474)(146,484)(147,483)(148,482)(149,481)(150,480)(151,479)
(152,478)(153,477)(154,476)(155,464)(156,463)(157,473)(158,472)(159,471)
(160,470)(161,469)(162,468)(163,467)(164,466)(165,465)(166,453)(167,452)
(168,462)(169,461)(170,460)(171,459)(172,458)(173,457)(174,456)(175,455)
(176,454)(177,442)(178,441)(179,451)(180,450)(181,449)(182,448)(183,447)
(184,446)(185,445)(186,444)(187,443)(188,431)(189,430)(190,440)(191,439)
(192,438)(193,437)(194,436)(195,435)(196,434)(197,433)(198,432)(199,420)
(200,419)(201,429)(202,428)(203,427)(204,426)(205,425)(206,424)(207,423)
(208,422)(209,421)(210,409)(211,408)(212,418)(213,417)(214,416)(215,415)
(216,414)(217,413)(218,412)(219,411)(220,410)(221,398)(222,397)(223,407)
(224,406)(225,405)(226,404)(227,403)(228,402)(229,401)(230,400)(231,399)
(232,387)(233,386)(234,396)(235,395)(236,394)(237,393)(238,392)(239,391)
(240,390)(241,389)(242,388);
s2 := 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)(243,364)
(244,365)(245,366)(246,367)(247,368)(248,369)(249,370)(250,371)(251,372)
(252,373)(253,374)(254,474)(255,475)(256,476)(257,477)(258,478)(259,479)
(260,480)(261,481)(262,482)(263,483)(264,484)(265,463)(266,464)(267,465)
(268,466)(269,467)(270,468)(271,469)(272,470)(273,471)(274,472)(275,473)
(276,452)(277,453)(278,454)(279,455)(280,456)(281,457)(282,458)(283,459)
(284,460)(285,461)(286,462)(287,441)(288,442)(289,443)(290,444)(291,445)
(292,446)(293,447)(294,448)(295,449)(296,450)(297,451)(298,430)(299,431)
(300,432)(301,433)(302,434)(303,435)(304,436)(305,437)(306,438)(307,439)
(308,440)(309,419)(310,420)(311,421)(312,422)(313,423)(314,424)(315,425)
(316,426)(317,427)(318,428)(319,429)(320,408)(321,409)(322,410)(323,411)
(324,412)(325,413)(326,414)(327,415)(328,416)(329,417)(330,418)(331,397)
(332,398)(333,399)(334,400)(335,401)(336,402)(337,403)(338,404)(339,405)
(340,406)(341,407)(342,386)(343,387)(344,388)(345,389)(346,390)(347,391)
(348,392)(349,393)(350,394)(351,395)(352,396)(353,375)(354,376)(355,377)
(356,378)(357,379)(358,380)(359,381)(360,382)(361,383)(362,384)(363,385);
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, s2*s0*s1*s2*s1*s2*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 >;
References : None.
to this polytope