We calculate the lattice thermal conductivity ($kappa$) for cubic (zinc-blende) and hexagonal (wurtzite) phases for 8 semiconductors using $textit{ab initio}$ calculations and solving the Phonon Boltzmann Transport Equation, explaining the different behavior of the ratio $kappa_{rm hex}/kappa_{rm cub}$ between the two phases. We show that this behavior depends on the relative importance of two antagonistic factors: anharmonicity, which we find to be always higher in the cubic phase; and the accessible phase space, which is higher for the less symmetric hexagonal phase. Based on that, we develop a method that predicts the most conducting phase---cubic or hexagonal---where other more heuristic approaches fail. We also present results for nanowires made of the same materials, showing the possibility to tune $kappa_{rm hex}/kappa_{rm cub}$ over a wide range by modifying their diameter, thus making them attractive materials for complex phononic and thermoelectric applications/systems.
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