 Solution

Choose the orientation relation $(0001{)}_{\mathrm{hcp}}\parallel (111{)}_{\mathrm{ccp}}$ with aligned close-packed rows, for example $[11\bar{2}0{]}_{\mathrm{hcp}}\parallel [1\bar{1}0{]}_{\mathrm{ccp}}$. The two phases then share matching triangular layers at the broad faces. The stacking changes from $ABCABC\dots$ to $ABAB\dots$ across the phase region, so broad coherent crystal interfaces can be made by a local change of stacking, with small mismatch if the in-plane atomic spacings are similar.

At the cylindrical edge, different layer sequences terminate against one another. Registry cannot generally be maintained everywhere, so ledges, stacking defects and possibly misfit dislocations are needed; this interface is less coherent and often more costly. Thus a low-energy basal/$(111)$ face and a higher-energy edge favour a thin plate. An ideal same-element stacking change need not imply zero edge energy or exactly zero face energy.