This is an announcement for the paper "The variance conjecture on some polytopes" by David Alonso-Gutierrez and Jesus Bastero. Abstract: We show that any random vector uniformly distributed on any hyperplane projection of $B_1^n$ or $B_\infty^n$ verifies the variance conjecture $$\text{Var }|X|^2\leq C\sup_{\xi\in S^{n-1}}\E\langle X,\xi\rangle^2\E|X|^2.$$ Furthermore, a random vector uniformly distributed on a hyperplane projection of $B_\infty^n$ verifies a negative square correlation property and consequently any of its linear images verifies the variance conjecture. Archive classification: math.FA Submitted from: bastero@unizar.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1209.4270 or http://arXiv.org/abs/1209.4270