  It is well known that the lattice packing density and the lattice covering
density of a triangle are $\frac{2}{3}$ and $\frac{3}{2}$ respectively. We also
know that the lattices that attain these densities both are unique. Let
$\delta_{L}(K)$ and $\vartheta_{L}(K)$ denote the lattice packing density and
the lattice covering density of $K$, respectively. In this paper, I study the
lattice packings and coverings for a special class of convex disks, which
includes all triangles and convex quadrilaterals. In particular, I determine
the densities $\delta_{L}(Q)$ and $\vartheta_{L}(Q)$, where $Q$ is an arbitrary
convex quadrilateral. Furthermore, I also obtain all of lattices that attain
these densities. Finally, I show that $\delta_{L}(Q)\vartheta_{L}(Q)\geq 1$ and
$\frac{1}{\delta_{L}(Q)}+\frac{1}{\vartheta_{L}(Q)}\geq 2$, for each convex
quadrilateral $Q$.
