This is an announcement for the paper "Sufficient enlargements of minimal volume for finite dimensional normed linear spaces" by M.I. Ostrovskii. Abstract: Let $B_Y$ denote the unit ball of a normed linear space $Y$. A symmetric, bounded, closed, convex set $A$ in a finite dimensional normed linear space $X$ is called a {\it sufficient enlargement} for $X$ if, for an arbitrary isometric embedding of $X$ into a Banach space $Y$, there exists a linear projection $P:Y\to X$ such that $P(B_Y)\subset A$. The main results of the paper: {\bf (1)} Each minimal-volume sufficient enlargement is linearly equivalent to a zonotope spanned by multiples of columns of a totally unimodular matrix. {\bf (2)} If a finite dimensional normed linear space has a minimal-volume sufficient enlargement which is not a parallelepiped, then it contains a two-dimensional subspace whose unit ball is linearly equivalent to a regular hexagon. Archive classification: math.FA Mathematics Subject Classification: 46B07, 52A21 Citation: J. Funct. Anal. 255 (2008), no. 3, 589-619 The source file(s), ost.tex: 97543 bytes, is(are) stored in gzipped form as 0811.1701.gz with size 28kb. The corresponding postcript file has gzipped size 173kb. Submitted from: ostrovsm@stjohns.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0811.1701 or http://arXiv.org/abs/0811.1701 or by email in unzipped form by transmitting an empty message with subject line uget 0811.1701 or in gzipped form by using subject line get 0811.1701 to: math@arXiv.org.