This is an announcement for the paper "On a Loomnis-Whitney type inequality for permutationally invariant unconditional convex bodies" by Piotr Nayar and Tomasz Tkocz. Abstract: For a permutationally invariant unconditional convex body K in R^n we define a finite sequence (K_j), j = 1, ..., n of projections of the body K to the space spanned by first j vectors of the standard basis of R^n. We prove that the sequence of volumes (|K_1|, ..., |K_n|) is log-concave. Archive classification: math.FA Mathematics Subject Classification: 52A20 (Primary), 52A40 (Secondary) Remarks: 5 pages Submitted from: t.tkocz@students.mimuw.edu.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1103.6232 or http://arXiv.org/abs/1103.6232