The three-triplet model of Han and Nambu is extended to a broken $\mathrm{SU}(18)$ symmetry. Quarks are assumed to be fermions (only antisymmetric states are allowed). The corresponding representations of $\mathrm{SU}(18)$ are reduced with respect to the subgroup $\mathrm{SU}(6)\ensuremath{\bigotimes}\mathrm{SU}{(3)}^{\ensuremath{'}}$, and only $\mathrm{SU}{(3)}^{\ensuremath{'}}$ singlets are retained. This selects the permissible representations of $\mathrm{SU}(6)$. If all quarks are in $s$ states, the $q\overline{q}$ (quark-antiquark) system corresponds to 1+35, and the $\mathrm{qqq}$ system to 56, as expected (20 and 70 do not appear). The next higher meson resonances consist of $\mathrm{qq}\overline{q}\overline{q}$ and come in three sets, corresponding to 1, 35, and (1+35+189+405). Their parity is always positive, and their charge-conjugation properties are tabulated. The negative-parity baryon resonances ($\mathrm{qqq}\overline{q}\overline{q}$) can be classified according to 56 and (70+1134), while 700 does not appear. Still higher resonances can easily be obtained by the same method, but the results then become rather dubious, because of the competition of states with nonzero orbital angular momentum, and because of relativistic effects. Finally, we mention the possibility of creating stable isobars with strangeness -6.
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