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Experimental evidence for $I(J^P)=0(3^+)$ $\Delta\Delta$ dibaryon ${\calD}_{03}(2370)$ has been presented recently by the WASA-at-COSY Collaboration.Here I review new hadronic-basis Faddeev calculations of $L=0$ nonstrangepion-assisted $N\Delta$ and $\Delta\Delta$ dibaryon candidates. Thesecalculations are so far the only ones to reproduce the relatively small ${\calD}_{03}(2370)$ width of 70--80 MeV. Predictions are also given for the locationand width of ${\cal D}_{30}$, the $I(J^P)=3(0^+)$ exotic partner of ${\calD}_{03}(2370)$. Extensions to strangeness ${\cal S}=-1$ dibaryons are brieflydiscussed.

Pion-assisted $N\Delta$ and $\Delta\Delta$ dibaryons, and beyond