Polytope of Type {40,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,6}*1920b
if this polytope has a name.
Group : SmallGroup(1920,238596)
Rank : 3
Schlafli Type : {40,6}
Number of vertices, edges, etc : 160, 480, 24
Order of s0s1s2 : 60
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {20,6}*960e, {40,6}*960d, {40,6}*960e
   4-fold quotients : {20,6}*480c
   5-fold quotients : {8,6}*384f
   8-fold quotients : {20,6}*240a, {20,6}*240b
   10-fold quotients : {4,6}*192b, {8,6}*192b, {8,6}*192c
   16-fold quotients : {10,6}*120
   20-fold quotients : {8,3}*96, {4,6}*96
   24-fold quotients : {20,2}*80
   40-fold quotients : {4,6}*48a, {4,3}*48, {4,6}*48b, {4,6}*48c
   48-fold quotients : {10,2}*40
   80-fold quotients : {4,3}*24, {2,6}*24
   96-fold quotients : {5,2}*20
   120-fold quotients : {4,2}*16
   160-fold quotients : {2,3}*12
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s1*s2*s1*s2> of order 3.
      8 facets:
         8 of {40}*80
      80 vertex figures:
         40 of {2}*4
         40 of {6}*12

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

Twisty Puzzle