  Folding of the triangular lattice in a discrete three-dimensional space is
investigated by means of the transfer-matrix method. This model was introduced
by Bowick and co-workers as a discretized version of the polymerized membrane
in thermal equilibrium. The folding rule (constraint) is incompatible with the
periodic-boundary condition, and the simulation has been made under the
open-boundary condition. In this paper, we propose a modified constraint, which
is compatible with the periodic-boundary condition; technically, the
restoration of translational invariance leads to a substantial reduction of the
transfer-matrix size. Treating the cluster sizes L \le 7, we analyze the
singularities of the crumpling transitions for a wide range of the bending
rigidity K. We observe a series of the crumpling transitions at K=0.206(2),
-0.32(1), and -0.76(10). At each transition point, we estimate the latent heat
as Q=0.356(30), 0.08(3), and 0.05(5), respectively.
