= Solution
Choose the orientation relation $(0001)_{\rm hcp}\parallel(111)_{\rm ccp}$ with aligned close-packed rows, for example $[11\bar20]_{\rm hcp}\parallel[1\bar10]_{\rm ccp}$. The two phases then share matching triangular layers at the broad faces. The stacking changes from $ABCABC\ldots$ to $ABAB\ldots$ 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 \b[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.
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