  We study the periodic homogenization of first order front propagations. Based
on PDE methods, we provide a simple proof that for $n \geq 3$, the class of
centrally symmetric polytopes with rational coordinates and nonempty interior
is admissible as effective fronts, which was also established in [1,10] in the
form of stable norms as an extension of Hedlund's classical result [7].
Besides, we obtain the optimal convergence rate of the homogenization problem
for this class.
