  We examine the local geometry of a simulated glass-forming polymer melt.
Using the Voronoi construction, we find that the distributions of Voronoi
volume $P(v_V)$ and asphericity $P(a)$ appear to be universal properties of
dense liquids, supporting the use of packing approaches to understand liquid
properties. We also calculate the average free volume $<v_f>$ along a path of
constant density and find that $<v_f>$ extrapolates to zero at the same
temperature $T_0$ that the extrapolated relaxation time diverges. We relate
$<v_f>$ to the Debye-Waller factor.
