Polytope of Type {22,44}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,44}*1936b
if this polytope has a 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 : 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}*968b
   4-fold quotients : {22,11}*484
   11-fold quotients : {2,44}*176
   22-fold quotients : {2,22}*88
   44-fold quotients : {2,11}*44
   121-fold quotients : {2,4}*16
   242-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   None.

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)( 12,354)( 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);;
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*s0*s1*s0*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, 
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)( 12,354)( 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);
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*s0*s1*s0*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, 
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

Twisty Puzzle