Polytope of Type {60,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {60,6}*1440c
if this polytope has a name.
Group : SmallGroup(1440,5871)
Rank : 3
Schlafli Type : {60,6}
Number of vertices, edges, etc : 120, 360, 12
Order of s₀s₁s₂ : 30
Order of s₀s₁s₂s₁ : 12
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) :
   3-fold quotients : {20,6}*480c
   4-fold quotients : {30,6}*360a
   5-fold quotients : {12,6}*288b
   6-fold quotients : {20,6}*240b
   10-fold quotients : {12,3}*144
   12-fold quotients : {10,6}*120
   15-fold quotients : {4,6}*96
   20-fold quotients : {6,6}*72b
   30-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   36-fold quotients : {10,2}*40
   40-fold quotients : {6,3}*36
   60-fold quotients : {4,3}*24, {2,6}*24
   72-fold quotients : {5,2}*20
   120-fold quotients : {2,3}*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*s0*s2*s1*s2*s1*s0*s1*s2> of order 2.
      8 facets:
         4 of {30}*60
         4 of {60}*120
      60 vertex figures:
         60 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1> of order 2.
      6 facets:
         6 of {60}*120
      60 vertex figures:
         60 of {6}*12
   P/N, where N=<s1*s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1> of order 2.
      6 facets:
         6 of {60}*120
      60 vertex figures:
         60 of {6}*12

Permutation Representation (GAP) :

s0 := ( 1, 3)( 2, 4)( 5,19)( 6,20)( 7,17)( 8,18)( 9,15)(10,16)(11,13)(12,14)(21,43)(22,44)(23,41)(24,42)(25,59)(26,60)(27,57)(28,58)(29,55)(30,56)(31,53)(32,54)(33,51)(34,52)(35,49)(36,50)(37,47)(38,48)(39,45)(40,46);;
s1 := ( 1,25)( 2,26)( 3,28)( 4,27)( 5,21)( 6,22)( 7,24)( 8,23)( 9,37)(10,38)(11,40)(12,39)(13,33)(14,34)(15,36)(16,35)(17,29)(18,30)(19,32)(20,31)(41,45)(42,46)(43,48)(44,47)(49,57)(50,58)(51,60)(52,59)(55,56);;
s2 := ( 2, 4)( 6, 8)(10,12)(14,16)(18,20)(21,41)(22,44)(23,43)(24,42)(25,45)(26,48)(27,47)(28,46)(29,49)(30,52)(31,51)(32,50)(33,53)(34,56)(35,55)(36,54)(37,57)(38,60)(39,59)(40,58);;
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*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(60)!( 1, 3)( 2, 4)( 5,19)( 6,20)( 7,17)( 8,18)( 9,15)(10,16)(11,13)(12,14)(21,43)(22,44)(23,41)(24,42)(25,59)(26,60)(27,57)(28,58)(29,55)(30,56)(31,53)(32,54)(33,51)(34,52)(35,49)(36,50)(37,47)(38,48)(39,45)(40,46);
s1 := Sym(60)!( 1,25)( 2,26)( 3,28)( 4,27)( 5,21)( 6,22)( 7,24)( 8,23)( 9,37)(10,38)(11,40)(12,39)(13,33)(14,34)(15,36)(16,35)(17,29)(18,30)(19,32)(20,31)(41,45)(42,46)(43,48)(44,47)(49,57)(50,58)(51,60)(52,59)(55,56);
s2 := Sym(60)!( 2, 4)( 6, 8)(10,12)(14,16)(18,20)(21,41)(22,44)(23,43)(24,42)(25,45)(26,48)(27,47)(28,46)(29,49)(30,52)(31,51)(32,50)(33,53)(34,56)(35,55)(36,54)(37,57)(38,60)(39,59)(40,58);
poly := sub<Sym(60)|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*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope

Polytope of Type {60,6}

Twisty Puzzle