3-DIMENSIONAL FOLDING OF THE TRIANGULAR LATTICE

We study the folding of the regular triangular lattice in three-dimens ional embedding space, a model for the crumpling of polymerised membra nes, We consider a discrete model, where folds are either planar or fo rm the angles of a regular octahedron. These ''octahedral'' folding ru les 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 t riangle In q(3d) is evaluated numerically to be q(3d) = 1.43(1). Vario us exact bounds on q(3d) are derived.