  We study the folding of the regular triangular lattice in three dimensional
embedding space, a model for the crumpling of polymerised membranes. We
consider a discrete model, where folds are either planar or form the angles of
a regular octahedron. These "octahedral" folding rules correspond simply to a
discretisation of the 3d embedding space as a Face Centred Cubic lattice. The
model is shown to be equivalent to a 96--vertex model on the triangular
lattice. The folding entropy per triangle ${\rm ln} q_{3d}$ is evaluated
numerically to be $q_{3d}=1.43(1)$. Various exact bounds on $q_{3d}$ are
derived.

Condensed Matter;High Energy Physics - Theory