This is an announcement for the paper "On approximations by projections of polytopes with few facets" by Alexander E. Litvak, Mark Rudelson, and Nicole Tomczak-Jaegermann. Abstract: We provide an affirmative answer to a problem posed by Barvinok and Veomett, showing that in general an n-dimensional convex body cannot be approximated by a projection of a section of a simplex of a sub-exponential dimension. Moreover, we establish a lower bound of the Banach-Mazur distance between n-dimensional projections of sections of an N-dimensional simplex and a certain convex symmetric body, which is sharp up to a logarithmic factor for all N>n. Archive classification: math.FA math.MG Mathematics Subject Classification: Primary: 52A23, 52A27, Secondary: 52B55, 46B09 Remarks: 22 pages Submitted from: rudelson@umich.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1209.6281 or http://arXiv.org/abs/1209.6281