  This paper studies the first passage percolation (FPP) model: each edge in
the cubic lattice is assigned a random passage time, and consideration is given
to the behavior of the percolation region $B(t)$, which consists of those
vertices that can be reached from the origin within a time $t > 0$. Cox and
Durrett showed the shape theorem for the percolation region, saying that the
normalized region $B(t)/t$ converges to some limit shape $\mathcal{B}$. This
paper introduces a general FPP model defined on crystal lattices, and shows the
monotonicity of the limit shapes under covering maps, thereby providing insight
into the limit shape of the cubic FPP model.
