  We present an analysis of extensive large-scale Monte Carlo simulations of
self-avoiding fixed-connectivity membranes for sizes (number of faces) ranging
from 512 to 17672 (triangular) plaquettes. Self-avoidance is implemented via
impenetrable plaquettes. We simulate the impenetrable plaquette model in both
three and four bulk dimensions. In both cases we find the membrane to be flat
for all temperatures: the size exponent in three dimensions is nu=0.95(5)
(Hausdorff dimension d_H=2.1(1)). The single flat phase appears, furthermore,
to be equivalent to the large bending rigidity phase of non-self-avoiding
fixed-connectivity membranes - the roughness exponent in three dimensions is
xi=0.63(4). This suggests that there is a unique universality class for flat
fixed-connectivity membranes without attractive interactions. Finally we
address some theoretical and experimental implications of our work.
