Does a polymerized membrane crumple ?

Evidence for crumpled conformations of polymerized membranes is reported. This is based on Monte Carlo simulations of flexible self-avoiding plaquette surfaces. The radius of gyration $R$ scales with the surfaces area $A$ according to $R^{2} \sim A^{0.8}$. It is shown that the correlation function between plaquette normals $\langle{\bf n}(0)\cdot {\bf n}(x)\rangle$ decays rapidly to zero for plaquette membranes, in contrast to hard-sphere membranes exhibiting long ranged strong correlations. The probability distribution $P(\cos \theta)$ of enclosed angles between adjacent plaquettes is discussed with respect to differences between plaquette and hard-sphere membranes