  We describe left-invariant half-flat SU(3)-structures on S^3xS^3 using the
representation theory of SO(4) and matrix algebra. This leads to a systematic
study of the associated cohomogeneity one Ricci-flat metrics with holonomy G_2
obtained on 7-manifolds with equidistant S^3xS^3 hypersurfaces. The generic
case is analysed numerically.
