  A two-parameter family of quantum spin ladders with local bilinear and
biquadratic interactions is shown to be solvable by a mapping onto fragments of
integrable spin 1 chains. The phase diagram, consisting of four phases, and the
ground state properties are discussed. In one novel phase, the ground state is
made up of plaquette singlets and rung singlets, alternating with a three-rung
periodicity.
