Polytope of Type {6,60}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,60}*1440d
if this polytope has a name.
Group : SmallGroup(1440,5901)
Rank : 3
Schlafli Type : {6,60}
Number of vertices, edges, etc : 12, 360, 120
Order of s0s1s2 : 30
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {6,60}*720d
   3-fold quotients : {6,20}*480c
   4-fold quotients : {6,30}*360b
   5-fold quotients : {6,12}*288a
   6-fold quotients : {6,20}*240b
   10-fold quotients : {6,12}*144d
   12-fold quotients : {6,10}*120, {2,30}*120
   15-fold quotients : {6,4}*96
   20-fold quotients : {6,6}*72a
   24-fold quotients : {2,15}*60
   30-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
   36-fold quotients : {2,10}*40
   60-fold quotients : {3,4}*24, {2,6}*24, {6,2}*24
   72-fold quotients : {2,5}*20
   120-fold quotients : {2,3}*12, {3,2}*12
   180-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*s2*s1*s0*s1*s2*s1> of order 2.
      60 facets:
         60 of {6}*12
      8 vertex figures:
         4 of {60}*120
         4 of {30}*60
   P/N, where N=<s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 2.
      60 facets:
         60 of {6}*12
      6 vertex figures:
         6 of {60}*120

Permutation Representation (GAP) : 
s0 := (  3,  4)(  7,  8)( 11, 12)( 15, 16)( 19, 20)( 23, 24)( 27, 28)( 31, 32)( 35, 36)( 39, 40)( 43, 44)( 47, 48)( 51, 52)( 55, 56)( 59, 60)( 61,121)( 62,122)( 63,124)( 64,123)( 65,125)( 66,126)( 67,128)( 68,127)( 69,129)( 70,130)( 71,132)( 72,131)( 73,133)( 74,134)( 75,136)( 76,135)( 77,137)( 78,138)( 79,140)( 80,139)( 81,141)( 82,142)( 83,144)( 84,143)( 85,145)( 86,146)( 87,148)( 88,147)( 89,149)( 90,150)( 91,152)( 92,151)( 93,153)( 94,154)( 95,156)( 96,155)( 97,157)( 98,158)( 99,160)(100,159)(101,161)(102,162)(103,164)(104,163)(105,165)(106,166)(107,168)(108,167)(109,169)(110,170)(111,172)(112,171)(113,173)(114,174)(115,176)(116,175)(117,177)(118,178)(119,180)(120,179)(183,184)(187,188)(191,192)(195,196)(199,200)(203,204)(207,208)(211,212)(215,216)(219,220)(223,224)(227,228)(231,232)(235,236)(239,240)(241,301)(242,302)(243,304)(244,303)(245,305)(246,306)(247,308)(248,307)(249,309)(250,310)(251,312)(252,311)(253,313)(254,314)(255,316)(256,315)(257,317)(258,318)(259,320)(260,319)(261,321)(262,322)(263,324)(264,323)(265,325)(266,326)(267,328)(268,327)(269,329)(270,330)(271,332)(272,331)(273,333)(274,334)(275,336)(276,335)(277,337)(278,338)(279,340)(280,339)(281,341)(282,342)(283,344)(284,343)(285,345)(286,346)(287,348)(288,347)(289,349)(290,350)(291,352)(292,351)(293,353)(294,354)(295,356)(296,355)(297,357)(298,358)(299,360)(300,359);;
s1 := (  1, 61)(  2, 64)(  3, 63)(  4, 62)(  5, 77)(  6, 80)(  7, 79)(  8, 78)(  9, 73)( 10, 76)( 11, 75)( 12, 74)( 13, 69)( 14, 72)( 15, 71)( 16, 70)( 17, 65)( 18, 68)( 19, 67)( 20, 66)( 21,101)( 22,104)( 23,103)( 24,102)( 25,117)( 26,120)( 27,119)( 28,118)( 29,113)( 30,116)( 31,115)( 32,114)( 33,109)( 34,112)( 35,111)( 36,110)( 37,105)( 38,108)( 39,107)( 40,106)( 41, 81)( 42, 84)( 43, 83)( 44, 82)( 45, 97)( 46,100)( 47, 99)( 48, 98)( 49, 93)( 50, 96)( 51, 95)( 52, 94)( 53, 89)( 54, 92)( 55, 91)( 56, 90)( 57, 85)( 58, 88)( 59, 87)( 60, 86)(122,124)(125,137)(126,140)(127,139)(128,138)(129,133)(130,136)(131,135)(132,134)(141,161)(142,164)(143,163)(144,162)(145,177)(146,180)(147,179)(148,178)(149,173)(150,176)(151,175)(152,174)(153,169)(154,172)(155,171)(156,170)(157,165)(158,168)(159,167)(160,166)(181,241)(182,244)(183,243)(184,242)(185,257)(186,260)(187,259)(188,258)(189,253)(190,256)(191,255)(192,254)(193,249)(194,252)(195,251)(196,250)(197,245)(198,248)(199,247)(200,246)(201,281)(202,284)(203,283)(204,282)(205,297)(206,300)(207,299)(208,298)(209,293)(210,296)(211,295)(212,294)(213,289)(214,292)(215,291)(216,290)(217,285)(218,288)(219,287)(220,286)(221,261)(222,264)(223,263)(224,262)(225,277)(226,280)(227,279)(228,278)(229,273)(230,276)(231,275)(232,274)(233,269)(234,272)(235,271)(236,270)(237,265)(238,268)(239,267)(240,266)(302,304)(305,317)(306,320)(307,319)(308,318)(309,313)(310,316)(311,315)(312,314)(321,341)(322,344)(323,343)(324,342)(325,357)(326,360)(327,359)(328,358)(329,353)(330,356)(331,355)(332,354)(333,349)(334,352)(335,351)(336,350)(337,345)(338,348)(339,347)(340,346);;
s2 := (  1,206)(  2,205)(  3,208)(  4,207)(  5,202)(  6,201)(  7,204)(  8,203)(  9,218)( 10,217)( 11,220)( 12,219)( 13,214)( 14,213)( 15,216)( 16,215)( 17,210)( 18,209)( 19,212)( 20,211)( 21,186)( 22,185)( 23,188)( 24,187)( 25,182)( 26,181)( 27,184)( 28,183)( 29,198)( 30,197)( 31,200)( 32,199)( 33,194)( 34,193)( 35,196)( 36,195)( 37,190)( 38,189)( 39,192)( 40,191)( 41,226)( 42,225)( 43,228)( 44,227)( 45,222)( 46,221)( 47,224)( 48,223)( 49,238)( 50,237)( 51,240)( 52,239)( 53,234)( 54,233)( 55,236)( 56,235)( 57,230)( 58,229)( 59,232)( 60,231)( 61,266)( 62,265)( 63,268)( 64,267)( 65,262)( 66,261)( 67,264)( 68,263)( 69,278)( 70,277)( 71,280)( 72,279)( 73,274)( 74,273)( 75,276)( 76,275)( 77,270)( 78,269)( 79,272)( 80,271)( 81,246)( 82,245)( 83,248)( 84,247)( 85,242)( 86,241)( 87,244)( 88,243)( 89,258)( 90,257)( 91,260)( 92,259)( 93,254)( 94,253)( 95,256)( 96,255)( 97,250)( 98,249)( 99,252)(100,251)(101,286)(102,285)(103,288)(104,287)(105,282)(106,281)(107,284)(108,283)(109,298)(110,297)(111,300)(112,299)(113,294)(114,293)(115,296)(116,295)(117,290)(118,289)(119,292)(120,291)(121,326)(122,325)(123,328)(124,327)(125,322)(126,321)(127,324)(128,323)(129,338)(130,337)(131,340)(132,339)(133,334)(134,333)(135,336)(136,335)(137,330)(138,329)(139,332)(140,331)(141,306)(142,305)(143,308)(144,307)(145,302)(146,301)(147,304)(148,303)(149,318)(150,317)(151,320)(152,319)(153,314)(154,313)(155,316)(156,315)(157,310)(158,309)(159,312)(160,311)(161,346)(162,345)(163,348)(164,347)(165,342)(166,341)(167,344)(168,343)(169,358)(170,357)(171,360)(172,359)(173,354)(174,353)(175,356)(176,355)(177,350)(178,349)(179,352)(180,351);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s0*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*s0*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(360)!(  3,  4)(  7,  8)( 11, 12)( 15, 16)( 19, 20)( 23, 24)( 27, 28)( 31, 32)( 35, 36)( 39, 40)( 43, 44)( 47, 48)( 51, 52)( 55, 56)( 59, 60)( 61,121)( 62,122)( 63,124)( 64,123)( 65,125)( 66,126)( 67,128)( 68,127)( 69,129)( 70,130)( 71,132)( 72,131)( 73,133)( 74,134)( 75,136)( 76,135)( 77,137)( 78,138)( 79,140)( 80,139)( 81,141)( 82,142)( 83,144)( 84,143)( 85,145)( 86,146)( 87,148)( 88,147)( 89,149)( 90,150)( 91,152)( 92,151)( 93,153)( 94,154)( 95,156)( 96,155)( 97,157)( 98,158)( 99,160)(100,159)(101,161)(102,162)(103,164)(104,163)(105,165)(106,166)(107,168)(108,167)(109,169)(110,170)(111,172)(112,171)(113,173)(114,174)(115,176)(116,175)(117,177)(118,178)(119,180)(120,179)(183,184)(187,188)(191,192)(195,196)(199,200)(203,204)(207,208)(211,212)(215,216)(219,220)(223,224)(227,228)(231,232)(235,236)(239,240)(241,301)(242,302)(243,304)(244,303)(245,305)(246,306)(247,308)(248,307)(249,309)(250,310)(251,312)(252,311)(253,313)(254,314)(255,316)(256,315)(257,317)(258,318)(259,320)(260,319)(261,321)(262,322)(263,324)(264,323)(265,325)(266,326)(267,328)(268,327)(269,329)(270,330)(271,332)(272,331)(273,333)(274,334)(275,336)(276,335)(277,337)(278,338)(279,340)(280,339)(281,341)(282,342)(283,344)(284,343)(285,345)(286,346)(287,348)(288,347)(289,349)(290,350)(291,352)(292,351)(293,353)(294,354)(295,356)(296,355)(297,357)(298,358)(299,360)(300,359);
s1 := Sym(360)!(  1, 61)(  2, 64)(  3, 63)(  4, 62)(  5, 77)(  6, 80)(  7, 79)(  8, 78)(  9, 73)( 10, 76)( 11, 75)( 12, 74)( 13, 69)( 14, 72)( 15, 71)( 16, 70)( 17, 65)( 18, 68)( 19, 67)( 20, 66)( 21,101)( 22,104)( 23,103)( 24,102)( 25,117)( 26,120)( 27,119)( 28,118)( 29,113)( 30,116)( 31,115)( 32,114)( 33,109)( 34,112)( 35,111)( 36,110)( 37,105)( 38,108)( 39,107)( 40,106)( 41, 81)( 42, 84)( 43, 83)( 44, 82)( 45, 97)( 46,100)( 47, 99)( 48, 98)( 49, 93)( 50, 96)( 51, 95)( 52, 94)( 53, 89)( 54, 92)( 55, 91)( 56, 90)( 57, 85)( 58, 88)( 59, 87)( 60, 86)(122,124)(125,137)(126,140)(127,139)(128,138)(129,133)(130,136)(131,135)(132,134)(141,161)(142,164)(143,163)(144,162)(145,177)(146,180)(147,179)(148,178)(149,173)(150,176)(151,175)(152,174)(153,169)(154,172)(155,171)(156,170)(157,165)(158,168)(159,167)(160,166)(181,241)(182,244)(183,243)(184,242)(185,257)(186,260)(187,259)(188,258)(189,253)(190,256)(191,255)(192,254)(193,249)(194,252)(195,251)(196,250)(197,245)(198,248)(199,247)(200,246)(201,281)(202,284)(203,283)(204,282)(205,297)(206,300)(207,299)(208,298)(209,293)(210,296)(211,295)(212,294)(213,289)(214,292)(215,291)(216,290)(217,285)(218,288)(219,287)(220,286)(221,261)(222,264)(223,263)(224,262)(225,277)(226,280)(227,279)(228,278)(229,273)(230,276)(231,275)(232,274)(233,269)(234,272)(235,271)(236,270)(237,265)(238,268)(239,267)(240,266)(302,304)(305,317)(306,320)(307,319)(308,318)(309,313)(310,316)(311,315)(312,314)(321,341)(322,344)(323,343)(324,342)(325,357)(326,360)(327,359)(328,358)(329,353)(330,356)(331,355)(332,354)(333,349)(334,352)(335,351)(336,350)(337,345)(338,348)(339,347)(340,346);
s2 := Sym(360)!(  1,206)(  2,205)(  3,208)(  4,207)(  5,202)(  6,201)(  7,204)(  8,203)(  9,218)( 10,217)( 11,220)( 12,219)( 13,214)( 14,213)( 15,216)( 16,215)( 17,210)( 18,209)( 19,212)( 20,211)( 21,186)( 22,185)( 23,188)( 24,187)( 25,182)( 26,181)( 27,184)( 28,183)( 29,198)( 30,197)( 31,200)( 32,199)( 33,194)( 34,193)( 35,196)( 36,195)( 37,190)( 38,189)( 39,192)( 40,191)( 41,226)( 42,225)( 43,228)( 44,227)( 45,222)( 46,221)( 47,224)( 48,223)( 49,238)( 50,237)( 51,240)( 52,239)( 53,234)( 54,233)( 55,236)( 56,235)( 57,230)( 58,229)( 59,232)( 60,231)( 61,266)( 62,265)( 63,268)( 64,267)( 65,262)( 66,261)( 67,264)( 68,263)( 69,278)( 70,277)( 71,280)( 72,279)( 73,274)( 74,273)( 75,276)( 76,275)( 77,270)( 78,269)( 79,272)( 80,271)( 81,246)( 82,245)( 83,248)( 84,247)( 85,242)( 86,241)( 87,244)( 88,243)( 89,258)( 90,257)( 91,260)( 92,259)( 93,254)( 94,253)( 95,256)( 96,255)( 97,250)( 98,249)( 99,252)(100,251)(101,286)(102,285)(103,288)(104,287)(105,282)(106,281)(107,284)(108,283)(109,298)(110,297)(111,300)(112,299)(113,294)(114,293)(115,296)(116,295)(117,290)(118,289)(119,292)(120,291)(121,326)(122,325)(123,328)(124,327)(125,322)(126,321)(127,324)(128,323)(129,338)(130,337)(131,340)(132,339)(133,334)(134,333)(135,336)(136,335)(137,330)(138,329)(139,332)(140,331)(141,306)(142,305)(143,308)(144,307)(145,302)(146,301)(147,304)(148,303)(149,318)(150,317)(151,320)(152,319)(153,314)(154,313)(155,316)(156,315)(157,310)(158,309)(159,312)(160,311)(161,346)(162,345)(163,348)(164,347)(165,342)(166,341)(167,344)(168,343)(169,358)(170,357)(171,360)(172,359)(173,354)(174,353)(175,356)(176,355)(177,350)(178,349)(179,352)(180,351);
poly := sub<Sym(360)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s0*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*s0*s1*s2*s0*s1*s2*s1 >;
References : None.
to this polytope

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