  Finite pieces of locally isostatic networks have a large number of floppy
modes because of missing constraints at the surface. Here we show that by
imposing suitable boundary conditions at the surface, the network can be
rendered effectively isostatic. We refer to these as anchored boundary
conditions. An important example is formed by a two-dimensional network of
corner sharing triangles, which is the focus of this paper. Another way of
rendering such networks isostatic, is by adding an external wire along which
all unpinned vertices can slide (sliding boundary conditions). This approach
also allows for the incorporation of boundaries associated with internal holes
and complex sample geometries, which are illustrated with examples. The recent
synthesis of bilayers of vitreous silica has provided impetus for this work.
Experimental results from the imaging of finite pieces at the atomic level
needs such boundary conditions, if the observed structure is to be
computer-refined so that the interior atoms have the perception of being in an
infinite isostatic environment.
