Polytope of Type {3,16}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,16}*1344b
if this polytope has a name.
Group : SmallGroup(1344,11291)
Rank : 3
Schlafli Type : {3,16}
Number of vertices, edges, etc : 42, 336, 224
Order of s₀s₁s₂ : 16
Order of s₀s₁s₂s₁ : 16
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 : {3,8}*672b
   4-fold quotients : {3,8}*336b
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1> of order 7.
      32 facets:
         32 of {3}*6
      6 vertex figures:
         6 of {16}*32

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {3,16}

Twisty Puzzle