Polytope of Type {40,22}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,22}*1760
Also Known As : {40,22|2}. if this polytope has another name.
Group : SmallGroup(1760,474)
Rank : 3
Schlafli Type : {40,22}
Number of vertices, edges, etc : 40, 440, 22
Order of s0s1s2 : 440
Order of s0s1s2s1 : 2
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 : {20,22}*880
   4-fold quotients : {10,22}*440
   5-fold quotients : {8,22}*352
   10-fold quotients : {4,22}*176
   11-fold quotients : {40,2}*160
   20-fold quotients : {2,22}*88
   22-fold quotients : {20,2}*80
   40-fold quotients : {2,11}*44
   44-fold quotients : {10,2}*40
   55-fold quotients : {8,2}*32
   88-fold quotients : {5,2}*20
   110-fold quotients : {4,2}*16
   220-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, 45)( 13, 46)( 14, 47)( 15, 48)( 16, 49)( 17, 50)( 18, 51)( 19, 52)( 20, 53)( 21, 54)( 22, 55)( 23, 34)( 24, 35)( 25, 36)( 26, 37)( 27, 38)( 28, 39)( 29, 40)( 30, 41)( 31, 42)( 32, 43)( 33, 44)( 67,100)( 68,101)( 69,102)( 70,103)( 71,104)( 72,105)( 73,106)( 74,107)( 75,108)( 76,109)( 77,110)( 78, 89)( 79, 90)( 80, 91)( 81, 92)( 82, 93)( 83, 94)( 84, 95)( 85, 96)( 86, 97)( 87, 98)( 88, 99)(111,166)(112,167)(113,168)(114,169)(115,170)(116,171)(117,172)(118,173)(119,174)(120,175)(121,176)(122,210)(123,211)(124,212)(125,213)(126,214)(127,215)(128,216)(129,217)(130,218)(131,219)(132,220)(133,199)(134,200)(135,201)(136,202)(137,203)(138,204)(139,205)(140,206)(141,207)(142,208)(143,209)(144,188)(145,189)(146,190)(147,191)(148,192)(149,193)(150,194)(151,195)(152,196)(153,197)(154,198)(155,177)(156,178)(157,179)(158,180)(159,181)(160,182)(161,183)(162,184)(163,185)(164,186)(165,187)(221,331)(222,332)(223,333)(224,334)(225,335)(226,336)(227,337)(228,338)(229,339)(230,340)(231,341)(232,375)(233,376)(234,377)(235,378)(236,379)(237,380)(238,381)(239,382)(240,383)(241,384)(242,385)(243,364)(244,365)(245,366)(246,367)(247,368)(248,369)(249,370)(250,371)(251,372)(252,373)(253,374)(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)(276,386)(277,387)(278,388)(279,389)(280,390)(281,391)(282,392)(283,393)(284,394)(285,395)(286,396)(287,430)(288,431)(289,432)(290,433)(291,434)(292,435)(293,436)(294,437)(295,438)(296,439)(297,440)(298,419)(299,420)(300,421)(301,422)(302,423)(303,424)(304,425)(305,426)(306,427)(307,428)(308,429)(309,408)(310,409)(311,410)(312,411)(313,412)(314,413)(315,414)(316,415)(317,416)(318,417)(319,418)(320,397)(321,398)(322,399)(323,400)(324,401)(325,402)(326,403)(327,404)(328,405)(329,406)(330,407);;
s1 := (  1,232)(  2,242)(  3,241)(  4,240)(  5,239)(  6,238)(  7,237)(  8,236)(  9,235)( 10,234)( 11,233)( 12,221)( 13,231)( 14,230)( 15,229)( 16,228)( 17,227)( 18,226)( 19,225)( 20,224)( 21,223)( 22,222)( 23,265)( 24,275)( 25,274)( 26,273)( 27,272)( 28,271)( 29,270)( 30,269)( 31,268)( 32,267)( 33,266)( 34,254)( 35,264)( 36,263)( 37,262)( 38,261)( 39,260)( 40,259)( 41,258)( 42,257)( 43,256)( 44,255)( 45,243)( 46,253)( 47,252)( 48,251)( 49,250)( 50,249)( 51,248)( 52,247)( 53,246)( 54,245)( 55,244)( 56,287)( 57,297)( 58,296)( 59,295)( 60,294)( 61,293)( 62,292)( 63,291)( 64,290)( 65,289)( 66,288)( 67,276)( 68,286)( 69,285)( 70,284)( 71,283)( 72,282)( 73,281)( 74,280)( 75,279)( 76,278)( 77,277)( 78,320)( 79,330)( 80,329)( 81,328)( 82,327)( 83,326)( 84,325)( 85,324)( 86,323)( 87,322)( 88,321)( 89,309)( 90,319)( 91,318)( 92,317)( 93,316)( 94,315)( 95,314)( 96,313)( 97,312)( 98,311)( 99,310)(100,298)(101,308)(102,307)(103,306)(104,305)(105,304)(106,303)(107,302)(108,301)(109,300)(110,299)(111,397)(112,407)(113,406)(114,405)(115,404)(116,403)(117,402)(118,401)(119,400)(120,399)(121,398)(122,386)(123,396)(124,395)(125,394)(126,393)(127,392)(128,391)(129,390)(130,389)(131,388)(132,387)(133,430)(134,440)(135,439)(136,438)(137,437)(138,436)(139,435)(140,434)(141,433)(142,432)(143,431)(144,419)(145,429)(146,428)(147,427)(148,426)(149,425)(150,424)(151,423)(152,422)(153,421)(154,420)(155,408)(156,418)(157,417)(158,416)(159,415)(160,414)(161,413)(162,412)(163,411)(164,410)(165,409)(166,342)(167,352)(168,351)(169,350)(170,349)(171,348)(172,347)(173,346)(174,345)(175,344)(176,343)(177,331)(178,341)(179,340)(180,339)(181,338)(182,337)(183,336)(184,335)(185,334)(186,333)(187,332)(188,375)(189,385)(190,384)(191,383)(192,382)(193,381)(194,380)(195,379)(196,378)(197,377)(198,376)(199,364)(200,374)(201,373)(202,372)(203,371)(204,370)(205,369)(206,368)(207,367)(208,366)(209,365)(210,353)(211,363)(212,362)(213,361)(214,360)(215,359)(216,358)(217,357)(218,356)(219,355)(220,354);;
s2 := (  1,  2)(  3, 11)(  4, 10)(  5,  9)(  6,  8)( 12, 13)( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 23, 24)( 25, 33)( 26, 32)( 27, 31)( 28, 30)( 34, 35)( 36, 44)( 37, 43)( 38, 42)( 39, 41)( 45, 46)( 47, 55)( 48, 54)( 49, 53)( 50, 52)( 56, 57)( 58, 66)( 59, 65)( 60, 64)( 61, 63)( 67, 68)( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 78, 79)( 80, 88)( 81, 87)( 82, 86)( 83, 85)( 89, 90)( 91, 99)( 92, 98)( 93, 97)( 94, 96)(100,101)(102,110)(103,109)(104,108)(105,107)(111,112)(113,121)(114,120)(115,119)(116,118)(122,123)(124,132)(125,131)(126,130)(127,129)(133,134)(135,143)(136,142)(137,141)(138,140)(144,145)(146,154)(147,153)(148,152)(149,151)(155,156)(157,165)(158,164)(159,163)(160,162)(166,167)(168,176)(169,175)(170,174)(171,173)(177,178)(179,187)(180,186)(181,185)(182,184)(188,189)(190,198)(191,197)(192,196)(193,195)(199,200)(201,209)(202,208)(203,207)(204,206)(210,211)(212,220)(213,219)(214,218)(215,217)(221,222)(223,231)(224,230)(225,229)(226,228)(232,233)(234,242)(235,241)(236,240)(237,239)(243,244)(245,253)(246,252)(247,251)(248,250)(254,255)(256,264)(257,263)(258,262)(259,261)(265,266)(267,275)(268,274)(269,273)(270,272)(276,277)(278,286)(279,285)(280,284)(281,283)(287,288)(289,297)(290,296)(291,295)(292,294)(298,299)(300,308)(301,307)(302,306)(303,305)(309,310)(311,319)(312,318)(313,317)(314,316)(320,321)(322,330)(323,329)(324,328)(325,327)(331,332)(333,341)(334,340)(335,339)(336,338)(342,343)(344,352)(345,351)(346,350)(347,349)(353,354)(355,363)(356,362)(357,361)(358,360)(364,365)(366,374)(367,373)(368,372)(369,371)(375,376)(377,385)(378,384)(379,383)(380,382)(386,387)(388,396)(389,395)(390,394)(391,393)(397,398)(399,407)(400,406)(401,405)(402,404)(408,409)(410,418)(411,417)(412,416)(413,415)(419,420)(421,429)(422,428)(423,427)(424,426)(430,431)(432,440)(433,439)(434,438)(435,437);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(440)!( 12, 45)( 13, 46)( 14, 47)( 15, 48)( 16, 49)( 17, 50)( 18, 51)( 19, 52)( 20, 53)( 21, 54)( 22, 55)( 23, 34)( 24, 35)( 25, 36)( 26, 37)( 27, 38)( 28, 39)( 29, 40)( 30, 41)( 31, 42)( 32, 43)( 33, 44)( 67,100)( 68,101)( 69,102)( 70,103)( 71,104)( 72,105)( 73,106)( 74,107)( 75,108)( 76,109)( 77,110)( 78, 89)( 79, 90)( 80, 91)( 81, 92)( 82, 93)( 83, 94)( 84, 95)( 85, 96)( 86, 97)( 87, 98)( 88, 99)(111,166)(112,167)(113,168)(114,169)(115,170)(116,171)(117,172)(118,173)(119,174)(120,175)(121,176)(122,210)(123,211)(124,212)(125,213)(126,214)(127,215)(128,216)(129,217)(130,218)(131,219)(132,220)(133,199)(134,200)(135,201)(136,202)(137,203)(138,204)(139,205)(140,206)(141,207)(142,208)(143,209)(144,188)(145,189)(146,190)(147,191)(148,192)(149,193)(150,194)(151,195)(152,196)(153,197)(154,198)(155,177)(156,178)(157,179)(158,180)(159,181)(160,182)(161,183)(162,184)(163,185)(164,186)(165,187)(221,331)(222,332)(223,333)(224,334)(225,335)(226,336)(227,337)(228,338)(229,339)(230,340)(231,341)(232,375)(233,376)(234,377)(235,378)(236,379)(237,380)(238,381)(239,382)(240,383)(241,384)(242,385)(243,364)(244,365)(245,366)(246,367)(247,368)(248,369)(249,370)(250,371)(251,372)(252,373)(253,374)(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)(276,386)(277,387)(278,388)(279,389)(280,390)(281,391)(282,392)(283,393)(284,394)(285,395)(286,396)(287,430)(288,431)(289,432)(290,433)(291,434)(292,435)(293,436)(294,437)(295,438)(296,439)(297,440)(298,419)(299,420)(300,421)(301,422)(302,423)(303,424)(304,425)(305,426)(306,427)(307,428)(308,429)(309,408)(310,409)(311,410)(312,411)(313,412)(314,413)(315,414)(316,415)(317,416)(318,417)(319,418)(320,397)(321,398)(322,399)(323,400)(324,401)(325,402)(326,403)(327,404)(328,405)(329,406)(330,407);
s1 := Sym(440)!(  1,232)(  2,242)(  3,241)(  4,240)(  5,239)(  6,238)(  7,237)(  8,236)(  9,235)( 10,234)( 11,233)( 12,221)( 13,231)( 14,230)( 15,229)( 16,228)( 17,227)( 18,226)( 19,225)( 20,224)( 21,223)( 22,222)( 23,265)( 24,275)( 25,274)( 26,273)( 27,272)( 28,271)( 29,270)( 30,269)( 31,268)( 32,267)( 33,266)( 34,254)( 35,264)( 36,263)( 37,262)( 38,261)( 39,260)( 40,259)( 41,258)( 42,257)( 43,256)( 44,255)( 45,243)( 46,253)( 47,252)( 48,251)( 49,250)( 50,249)( 51,248)( 52,247)( 53,246)( 54,245)( 55,244)( 56,287)( 57,297)( 58,296)( 59,295)( 60,294)( 61,293)( 62,292)( 63,291)( 64,290)( 65,289)( 66,288)( 67,276)( 68,286)( 69,285)( 70,284)( 71,283)( 72,282)( 73,281)( 74,280)( 75,279)( 76,278)( 77,277)( 78,320)( 79,330)( 80,329)( 81,328)( 82,327)( 83,326)( 84,325)( 85,324)( 86,323)( 87,322)( 88,321)( 89,309)( 90,319)( 91,318)( 92,317)( 93,316)( 94,315)( 95,314)( 96,313)( 97,312)( 98,311)( 99,310)(100,298)(101,308)(102,307)(103,306)(104,305)(105,304)(106,303)(107,302)(108,301)(109,300)(110,299)(111,397)(112,407)(113,406)(114,405)(115,404)(116,403)(117,402)(118,401)(119,400)(120,399)(121,398)(122,386)(123,396)(124,395)(125,394)(126,393)(127,392)(128,391)(129,390)(130,389)(131,388)(132,387)(133,430)(134,440)(135,439)(136,438)(137,437)(138,436)(139,435)(140,434)(141,433)(142,432)(143,431)(144,419)(145,429)(146,428)(147,427)(148,426)(149,425)(150,424)(151,423)(152,422)(153,421)(154,420)(155,408)(156,418)(157,417)(158,416)(159,415)(160,414)(161,413)(162,412)(163,411)(164,410)(165,409)(166,342)(167,352)(168,351)(169,350)(170,349)(171,348)(172,347)(173,346)(174,345)(175,344)(176,343)(177,331)(178,341)(179,340)(180,339)(181,338)(182,337)(183,336)(184,335)(185,334)(186,333)(187,332)(188,375)(189,385)(190,384)(191,383)(192,382)(193,381)(194,380)(195,379)(196,378)(197,377)(198,376)(199,364)(200,374)(201,373)(202,372)(203,371)(204,370)(205,369)(206,368)(207,367)(208,366)(209,365)(210,353)(211,363)(212,362)(213,361)(214,360)(215,359)(216,358)(217,357)(218,356)(219,355)(220,354);
s2 := Sym(440)!(  1,  2)(  3, 11)(  4, 10)(  5,  9)(  6,  8)( 12, 13)( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 23, 24)( 25, 33)( 26, 32)( 27, 31)( 28, 30)( 34, 35)( 36, 44)( 37, 43)( 38, 42)( 39, 41)( 45, 46)( 47, 55)( 48, 54)( 49, 53)( 50, 52)( 56, 57)( 58, 66)( 59, 65)( 60, 64)( 61, 63)( 67, 68)( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 78, 79)( 80, 88)( 81, 87)( 82, 86)( 83, 85)( 89, 90)( 91, 99)( 92, 98)( 93, 97)( 94, 96)(100,101)(102,110)(103,109)(104,108)(105,107)(111,112)(113,121)(114,120)(115,119)(116,118)(122,123)(124,132)(125,131)(126,130)(127,129)(133,134)(135,143)(136,142)(137,141)(138,140)(144,145)(146,154)(147,153)(148,152)(149,151)(155,156)(157,165)(158,164)(159,163)(160,162)(166,167)(168,176)(169,175)(170,174)(171,173)(177,178)(179,187)(180,186)(181,185)(182,184)(188,189)(190,198)(191,197)(192,196)(193,195)(199,200)(201,209)(202,208)(203,207)(204,206)(210,211)(212,220)(213,219)(214,218)(215,217)(221,222)(223,231)(224,230)(225,229)(226,228)(232,233)(234,242)(235,241)(236,240)(237,239)(243,244)(245,253)(246,252)(247,251)(248,250)(254,255)(256,264)(257,263)(258,262)(259,261)(265,266)(267,275)(268,274)(269,273)(270,272)(276,277)(278,286)(279,285)(280,284)(281,283)(287,288)(289,297)(290,296)(291,295)(292,294)(298,299)(300,308)(301,307)(302,306)(303,305)(309,310)(311,319)(312,318)(313,317)(314,316)(320,321)(322,330)(323,329)(324,328)(325,327)(331,332)(333,341)(334,340)(335,339)(336,338)(342,343)(344,352)(345,351)(346,350)(347,349)(353,354)(355,363)(356,362)(357,361)(358,360)(364,365)(366,374)(367,373)(368,372)(369,371)(375,376)(377,385)(378,384)(379,383)(380,382)(386,387)(388,396)(389,395)(390,394)(391,393)(397,398)(399,407)(400,406)(401,405)(402,404)(408,409)(410,418)(411,417)(412,416)(413,415)(419,420)(421,429)(422,428)(423,427)(424,426)(430,431)(432,440)(433,439)(434,438)(435,437);
poly := sub<Sym(440)|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 >;
References : None.
to this polytope

Twisty Puzzle