We find families of integrable n-leg spin-1/2 ladders and tubes with general isotropic exchange interactions between spins. These models are equivalent to su(N) spin chains with N=2^n. Arbitrary rung interactions in the spin tubes and ladders induce chemical potentials in the equivalent spin chains. The potentials are n-dependent and differ for the tube and ladder models. The models are solvable by means of nested Bethe Ansatz.
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