  We study a family of 3-dimensional Lorentz manifolds. Some members of the
family are 0-curvature homogeneous, 1-affine curvature homogeneous, but not
1-curvature homogeneous. Some are 1-curvature homogeneous but not 2-curvature
homogeneous. All are 0-modeled on indecomposible local symmetric spaces. Some
of the members of the family are geodesically complete, others are not. All
have vanishing scalar invariants.
