If ${\mathcal{X}}$ is toroidal, then ${\mathcal{X}}$ is lc, and ${\mathcal{X}}$ is dlt if and only if it is snc. Following [dFKX12, KNX15], we could say that an lc model ${\mathcal{X}}$ is qdlt (for quotient of dlt) if its lc centers are contained in a toroidal open subset ${\mathcal{U}}\subset{\mathcal{X}}$.