Polytope of Type {20,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,6}*1920b
if this polytope has a name.
Group : SmallGroup(1920,238657)
Rank : 3
Schlafli Type : {20,6}
Number of vertices, edges, etc : 160, 480, 48
Order of s0s1s2 : 120
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
   4-fold quotients : {20,6}*480c
   5-fold quotients : {4,6}*384b
   8-fold quotients : {20,6}*240a, {20,6}*240b
   10-fold quotients : {4,6}*192b
   16-fold quotients : {10,6}*120
   20-fold quotients : {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=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 2.
      28 facets:
         20 of {20}*40
         8 of {10}*20
      80 vertex figures:
         80 of {6}*12
   P/N, where N=<s1*s2*s1*s2> of order 3.
      16 facets:
         16 of {20}*40
      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)(121,366)(122,365)(123,367)(124,368)(125,361)(126,362)(127,364)(128,363)(129,398)(130,397)(131,399)(132,400)(133,393)(134,394)(135,396)(136,395)(137,390)(138,389)(139,391)(140,392)(141,385)(142,386)(143,388)(144,387)(145,382)(146,381)(147,383)(148,384)(149,377)(150,378)(151,380)(152,379)(153,374)(154,373)(155,375)(156,376)(157,369)(158,370)(159,372)(160,371)(161,406)(162,405)(163,407)(164,408)(165,401)(166,402)(167,404)(168,403)(169,438)(170,437)(171,439)(172,440)(173,433)(174,434)(175,436)(176,435)(177,430)(178,429)(179,431)(180,432)(181,425)(182,426)(183,428)(184,427)(185,422)(186,421)(187,423)(188,424)(189,417)(190,418)(191,420)(192,419)(193,414)(194,413)(195,415)(196,416)(197,409)(198,410)(199,412)(200,411)(201,446)(202,445)(203,447)(204,448)(205,441)(206,442)(207,444)(208,443)(209,478)(210,477)(211,479)(212,480)(213,473)(214,474)(215,476)(216,475)(217,470)(218,469)(219,471)(220,472)(221,465)(222,466)(223,468)(224,467)(225,462)(226,461)(227,463)(228,464)(229,457)(230,458)(231,460)(232,459)(233,454)(234,453)(235,455)(236,456)(237,449)(238,450)(239,452)(240,451);;
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)(121,130)(122,129)(123,131)(124,132)(125,136)(126,135)(127,134)(128,133)(137,154)(138,153)(139,155)(140,156)(141,160)(142,159)(143,158)(144,157)(145,146)(149,152)(150,151)(161,210)(162,209)(163,211)(164,212)(165,216)(166,215)(167,214)(168,213)(169,202)(170,201)(171,203)(172,204)(173,208)(174,207)(175,206)(176,205)(177,234)(178,233)(179,235)(180,236)(181,240)(182,239)(183,238)(184,237)(185,226)(186,225)(187,227)(188,228)(189,232)(190,231)(191,230)(192,229)(193,218)(194,217)(195,219)(196,220)(197,224)(198,223)(199,222)(200,221)(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, 
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(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)(121,366)(122,365)(123,367)(124,368)(125,361)(126,362)(127,364)(128,363)(129,398)(130,397)(131,399)(132,400)(133,393)(134,394)(135,396)(136,395)(137,390)(138,389)(139,391)(140,392)(141,385)(142,386)(143,388)(144,387)(145,382)(146,381)(147,383)(148,384)(149,377)(150,378)(151,380)(152,379)(153,374)(154,373)(155,375)(156,376)(157,369)(158,370)(159,372)(160,371)(161,406)(162,405)(163,407)(164,408)(165,401)(166,402)(167,404)(168,403)(169,438)(170,437)(171,439)(172,440)(173,433)(174,434)(175,436)(176,435)(177,430)(178,429)(179,431)(180,432)(181,425)(182,426)(183,428)(184,427)(185,422)(186,421)(187,423)(188,424)(189,417)(190,418)(191,420)(192,419)(193,414)(194,413)(195,415)(196,416)(197,409)(198,410)(199,412)(200,411)(201,446)(202,445)(203,447)(204,448)(205,441)(206,442)(207,444)(208,443)(209,478)(210,477)(211,479)(212,480)(213,473)(214,474)(215,476)(216,475)(217,470)(218,469)(219,471)(220,472)(221,465)(222,466)(223,468)(224,467)(225,462)(226,461)(227,463)(228,464)(229,457)(230,458)(231,460)(232,459)(233,454)(234,453)(235,455)(236,456)(237,449)(238,450)(239,452)(240,451);
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)(121,130)(122,129)(123,131)(124,132)(125,136)(126,135)(127,134)(128,133)(137,154)(138,153)(139,155)(140,156)(141,160)(142,159)(143,158)(144,157)(145,146)(149,152)(150,151)(161,210)(162,209)(163,211)(164,212)(165,216)(166,215)(167,214)(168,213)(169,202)(170,201)(171,203)(172,204)(173,208)(174,207)(175,206)(176,205)(177,234)(178,233)(179,235)(180,236)(181,240)(182,239)(183,238)(184,237)(185,226)(186,225)(187,227)(188,228)(189,232)(190,231)(191,230)(192,229)(193,218)(194,217)(195,219)(196,220)(197,224)(198,223)(199,222)(200,221)(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, 
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