We present an analysis of extensive large-scale Monte Carlo simulations of
self-avoiding fixed-connectivity membranes for sizes (number of faces) rang
ing from 512 to. 17672 (triangular) plaquettes. Self-avoidance is implement
ed via impenetrable plaquettes. T;Ve simulate the impenetrable plaquette mo
del in both three and four bulk dimensions. In both cases we find the membr
ane 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 i
n three dimensions is xi = 0.63(4). This suggests that there is a unique un
iversality class for flat fixed-connectivity membranes without attractive i
nteractions. Finally, we address some theoretical and experimental implicat
ions of our work.