  The intrinsic volumes are measures of the content of a convex body. This
paper uses probabilistic and information-theoretic methods to study the
sequence of intrinsic volumes of a convex body. The main result states that the
intrinsic volume sequence concentrates sharply around a specific index, called
the central intrinsic volume. Furthermore, among all convex bodies whose
central intrinsic volume is fixed, an appropriately scaled cube has the
intrinsic volume sequence with maximum entropy.
