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