Rhombic CAST existence with prescribed edge configurations and dihedral symmetry

Let $n$ be the polygon-order parameter, let the cases be those listed in Table~, and let $\eta_{\min}$ and the edge configurations be the quantities specified in Tables~--. A rhombic CAST is a CAST whose prototiles are rhombs. Rhombic CAST conjecture. For every case in the listed table and for every $n$, there exist rhombic CASTs with the specified edge configuration and inflation multiplier $\eta_{\min}$ that yield individual dihedral symmetry $D_n$ or $D_{2n}$. The claim summarizes the paper's proposed existence pattern across all eight cases; examples are given, but the universal assertion for all $n$ and all cases remains unproved.