  We present a unification model based on the well-known but mysterious
cubic-structure grouping of quarks and leptons that suggests an underlying
symmetry connection deemed explainable by a unified theory. It results in an
extension of the Pati-Salam model that consolidates the fermions into two
sixteen-dimensional chiral representations of the gauge group. Moreover, the
discrete cubic flavor symmetry arbitrarily conjectured in the literature is
found here to be implied by the gauge symmetry. Furthermore, the gauge algebra
also describes an eleven-dimensional spacetime decomposed into the usual
spacetime and the seven-sphere, which is the manifold of unit octonions. This
suggests such a spacetime is apt for embracing all elementary particles and
their interactions.
