Dihedral-symmetry realization for generalized Penrose CASTs

Let $n$ be odd with $n\geq5$, and consider a CAST as described in the generalized Penrose CAST conjecture, with its prototiles and substitution rules. A CAST has individual dihedral symmetry $D_n$ when each relevant prototile or substitution-rule configuration has that dihedral symmetry. Dihedral-symmetry conjecture. For every odd $n\geq5$, the substitution rules of such a CAST can be modified so that the resulting CAST has individual dihedral symmetry $D_n$. The paper reports constructions by trial and error for $7\leq n\leq11$, but does not establish the assertion for every odd $n\geq5$.