We describe pentagram maps on polygons in any dimension, which
extend R.Schwartz's definition of the 2D pentagram map.
Many of those maps turn out to be discrete integrable dynamical
systems, while the corresponding continuous limits of such maps
coincide with equations of the KdV hierarchy, generalizing
the Boussinesq equation in 2D. (This is a joint work with F.Soloviev
and A.Izosimov)