Quartic surfaces up to volume preserving equivalence

We study log Calabi–Yau pairs of the form $({\mathbb{P}}^3,\mathrm{\Delta })$, where $\mathrm{\Delta }$ is a quartic surface, and classify all such pairs of coregularity less than or equal to one, up to volume preserving equivalence. In particular, if $({\mathbb{P}}^3,\mathrm{\Delta })$ is a maximal log Calabi–Yau pair then we show that it has a toric model.