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