  In this paper we define a generalization of the pentagram map to a map on
twisted polygons in the Grassmannian space Gr(n;mn). We define invariants of
Grassmannian twisted polygons under the natural action of SL(nm), invariants
that define coordinates in the moduli space of twisted polygons. We then prove
that when written in terms of the moduli space coordinates, the pentagram map
is preserved by a certain scaling. The scaling is then used to construct a Lax
representation for the map that can be used for integration.
