  We study the problem of folding of the regular triangular lattice in the
presence of bending rigidity K and magnetic field h (conjugate to the local
normal vectors to the triangles). A numerical study of the transfer matrix of
the problem shows the existence of three first order transition lines in the
(K,h) plane separating three phases: a folded phase, a phase frozen in the
completely flat configuration (with all normal vectors pointing up) and its
mirror image (all normal vectors pointing down). At zero magnetic field, a
first order folding transition is found at a positive value K_c=0.11(1) of the
bending rigidity, corresponding to a triple point in the phase diagram.
