Polytope of Type {12,5}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,5}*1920f
if this polytope has a name.
Group : SmallGroup(1920,241004)
Rank : 3
Schlafli Type : {12,5}
Number of vertices, edges, etc : 192, 480, 80
Order of s₀s₁s₂ : 10
Order of s₀s₁s₂s₁ : 5
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-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 : {6,5}*960
   32-fold quotients : {3,5}*60
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2> of order 2.
      40 facets:
         40 of {12}*24
      96 vertex figures:
         96 of {5}*10
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 3.
      28 facets:
         26 of {12}*24
         2 of {4}*8
      64 vertex figures:
         64 of {5}*10

Permutation Representation (GAP) :

s0 := ( 3, 4)( 5,15)( 7, 8)( 9,30)(11,16)(12,17)(13,25)(14,19)(18,29)(20,31)(21,28)(22,27)(23,32)(24,26);;
s1 := ( 1, 3)( 2,17)( 4, 7)( 5,27)( 6,14)( 8,24)( 9,20)(10,12)(11,19)(13,32)(15,21)(16,26)(23,29)(25,28);;
s2 := ( 1, 6)( 2,10)( 3,32)( 4,23)( 5,19)( 7,31)( 8,20)( 9,16)(11,30)(12,26)(13,25)(14,15)(17,24)(21,28);;
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, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(32)!( 3, 4)( 5,15)( 7, 8)( 9,30)(11,16)(12,17)(13,25)(14,19)(18,29)(20,31)(21,28)(22,27)(23,32)(24,26);
s1 := Sym(32)!( 1, 3)( 2,17)( 4, 7)( 5,27)( 6,14)( 8,24)( 9,20)(10,12)(11,19)(13,32)(15,21)(16,26)(23,29)(25,28);
s2 := Sym(32)!( 1, 6)( 2,10)( 3,32)( 4,23)( 5,19)( 7,31)( 8,20)( 9,16)(11,30)(12,26)(13,25)(14,15)(17,24)(21,28);
poly := sub<Sym(32)|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, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1 >;

References : None.
to this polytope

Polytope of Type {12,5}

Twisty Puzzle