Polytope of Type {44,22}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {44,22}*1936b
if this polytope has a name.
Group : SmallGroup(1936,124)
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
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}*968c
   4-fold quotients : {11,22}*484
   11-fold quotients : {44,2}*176
   22-fold quotients : {22,2}*88
   44-fold quotients : {11,2}*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 := (  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)
(243,364)(244,374)(245,373)(246,372)(247,371)(248,370)(249,369)(250,368)
(251,367)(252,366)(253,365)(254,474)(255,484)(256,483)(257,482)(258,481)
(259,480)(260,479)(261,478)(262,477)(263,476)(264,475)(265,463)(266,473)
(267,472)(268,471)(269,470)(270,469)(271,468)(272,467)(273,466)(274,465)
(275,464)(276,452)(277,462)(278,461)(279,460)(280,459)(281,458)(282,457)
(283,456)(284,455)(285,454)(286,453)(287,441)(288,451)(289,450)(290,449)
(291,448)(292,447)(293,446)(294,445)(295,444)(296,443)(297,442)(298,430)
(299,440)(300,439)(301,438)(302,437)(303,436)(304,435)(305,434)(306,433)
(307,432)(308,431)(309,419)(310,429)(311,428)(312,427)(313,426)(314,425)
(315,424)(316,423)(317,422)(318,421)(319,420)(320,408)(321,418)(322,417)
(323,416)(324,415)(325,414)(326,413)(327,412)(328,411)(329,410)(330,409)
(331,397)(332,407)(333,406)(334,405)(335,404)(336,403)(337,402)(338,401)
(339,400)(340,399)(341,398)(342,386)(343,396)(344,395)(345,394)(346,393)
(347,392)(348,391)(349,390)(350,389)(351,388)(352,387)(353,375)(354,385)
(355,384)(356,383)(357,382)(358,381)(359,380)(360,379)(361,378)(362,377)
(363,376);;
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)(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);;
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*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*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(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)(243,364)(244,374)(245,373)(246,372)(247,371)(248,370)(249,369)
(250,368)(251,367)(252,366)(253,365)(254,474)(255,484)(256,483)(257,482)
(258,481)(259,480)(260,479)(261,478)(262,477)(263,476)(264,475)(265,463)
(266,473)(267,472)(268,471)(269,470)(270,469)(271,468)(272,467)(273,466)
(274,465)(275,464)(276,452)(277,462)(278,461)(279,460)(280,459)(281,458)
(282,457)(283,456)(284,455)(285,454)(286,453)(287,441)(288,451)(289,450)
(290,449)(291,448)(292,447)(293,446)(294,445)(295,444)(296,443)(297,442)
(298,430)(299,440)(300,439)(301,438)(302,437)(303,436)(304,435)(305,434)
(306,433)(307,432)(308,431)(309,419)(310,429)(311,428)(312,427)(313,426)
(314,425)(315,424)(316,423)(317,422)(318,421)(319,420)(320,408)(321,418)
(322,417)(323,416)(324,415)(325,414)(326,413)(327,412)(328,411)(329,410)
(330,409)(331,397)(332,407)(333,406)(334,405)(335,404)(336,403)(337,402)
(338,401)(339,400)(340,399)(341,398)(342,386)(343,396)(344,395)(345,394)
(346,393)(347,392)(348,391)(349,390)(350,389)(351,388)(352,387)(353,375)
(354,385)(355,384)(356,383)(357,382)(358,381)(359,380)(360,379)(361,378)
(362,377)(363,376);
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)(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);
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*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*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