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We describe a compactification by stable pairs (also known as KSBAcompactification) of the $4$-dimensional family of Enriques surfaces whicharise as the $\mathbb{Z}_2^2$-covers of the blow up of $\mathbb{P}^2$ at threegeneral points branched along a configuration of three pairs of lines. Up to afinite group action, we show that this compactification is isomorphic to thetoric variety associated to the secondary polytope of the unit cube. We relatethe KSBA compactification considered to the Baily-Borel compactification of thesame family of Enriques surfaces. Part of the KSBA boundary has a toroidalbehavior, another part is isomorphic to the Baily-Borel compactification, andwhat remains is a mixture of these two. We relate the stable paircompactification studied here with Looijenga's semitoric compactifications.

The KSBA compactification of the moduli space of $D_{1,6}$-polarized Enriques surfaces