Reply to: An explanation for the Rule of Four in Inorganic Materials

The Rule of Four captures the observation that in experimentally known inorganic stoichiometric compounds the number of atoms in the primitive cell shows an unusual abundance of cases where that number is a multiple of four. The previous comment provides some insightful and appealing explanations of this abundance, some of which we had already considered, and in response we provide further data and analysis. We do not find confirmations of these explanations in our data, despite structural and compositional modulations, and suggest that the origins of the Rule of Four remain elusive, and open for further investigation.