  We study geometric properties of coordinate projections. Among other results,
we show that if a body K in R^n has an "almost extremal" volume ratio, then it
has a projection of proportional dimension which is close to the cube. We
compare type 2 and infratype 2 constant of a Banach space. This follows from a
comparison lemma for Rademacher and Gaussian averages. We also establish a
sharp estimate on the shattering dimension of the convex hull of a class of
functions in terms of the shattering dimension of the class itself.
