## Physics

Article

10-4-2011

English

Physics

#### Description/Abstract

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.

55 pages, uuencoded, uses harvmac (l mode) and epsf, 19+2 figures included More information at http://arxiv.org/abs/cond-mat/9502063

#### Source

Harvested from Arxiv.org