  We propose a method to efficiently compute the Minkowski sum, denoted by
binary operator $\oplus$ in the paper, of convex polytopes in $\Re^d$ using
their face lattice structures as input. In plane, the Minkowski sum of convex
polygons can be computed in linear time of the total number of vertices of the
polygons. In $\Re^d$, we first show how to compute the Minkowski sum, $P \oplus
Q$, of two convex polytopes $P$ and $Q$ of input size $n$ and $m$ respectively
in time $O(nm)$. Then we generalize the method to compute the Minkowski sum of
$n$ convex polytopes, $P_1 \oplus P_2 \oplus \cdots \oplus P_n$, in $\Re^d$ in
time $O(\prod_{i}^{n}N_i)$, where $P_1$, $P_2$, $\dots$, $P_n$ are $n$ input
convex polytopes and for each $i$, $N_i$ is size of the face lattice structure
of $P_i$. Our algorithm for Minkowski sum of two convex polytopes is optimal in
the worst case since the output face lattice structure of $P\oplus Q$ for
convex polytopes in $\Re^d$ can be $O(nm)$ in worst case.
