  For a polytope we define the {\em flag polynomial}, a polynomial in commuting
variables related to the well-known flag vector and describe how to express the
the flag polynomial of the Minkowski sum of $k$ standard simplices in a direct
and canonical way in terms of the {\em $k$-th master polytope} $P(k)$ where
$k\in\nats$. The flag polynomial facilitates many direct computations. To
demonstrate this we provide two examples; we first derive a formula for the
$f$-polynomial and the maximum number of $d$-dimensional faces of the Minkowski
sum of two simplices. We then compute the maximum discrepancy between the
number of $(0,d)$-chains of faces of a Minkowski sum of two simplices and the
number of such chains of faces of a simple polytope of the same dimension and
on the same number of vertices.
