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Canonical threefold singularities in M-theory and Type IIB string theory giverise to superconformal field theories (SCFTs) in 5d and 4d, respectively. Inthis paper, we study canonical hypersurface singularities whose resolutionscontain residual terminal singularities and/or 3-cycles. We focus on a certainclass of `trinion' singularities which exhibit these properties. In Type IIB,they give rise to 4d $\mathcal{N}=2$ SCFTs that we call $D_p^b(G)$-trinions,which are marginal gaugings of three SCFTs with $G$ flavor symmetry. In orderto understand the 5d physics of these trinion singularities in M-theory, wereduce these 4d and 5d SCFTs to 3d $\mathcal{N}=4$ theories, thus determiningthe electric and magnetic quivers (or, more generally, quiverines). InM-theory, residual terminal singularities give rise to free sectors of masslesshypermultiplets, which often are discretely gauged. These free sectors appearas `ugly' components of the magnetic quiver of the 5d SCFT. The 3-cycles in thecrepant resolution also give rise to free hypermultiplets, but their physics ismore subtle, and their presence renders the magnetic quiver `bad'. We propose away to redeem the badness of these quivers using a class $\mathcal{S}$realization. We also discover new S-dualities between different$D_p^b(G)$-trinions. For instance, a certain $E_8$ gauging of the $E_8$Minahan-Nemeschansky theory is S-dual to an $E_8$-shaped Lagrangian quiverSCFT.

5d and 4d SCFTs: Canonical Singularities, Trinions and S-Dualities