  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.
