SHARYGIN 2013 Problem 23

Two convex polytopes $A$ and $B$ do not intersect. The polytope $A$ has exactly $2012$ planes of symmetry. What is the maximal number of symmetry planes of the union of $A$ and $B$ , if $B$ has a) $2012$ , b) $2013$ symmetry planes?

c) What is the answer to the question of p.b), if the symmetry planes are replaced by the symmetry axes?