Network with six-fold symmetry under stress

An interesting behavior of the above network under compression is not captured by the assumption of a non-equilateral triangle and that is called network collapse. For example, in the above analysis we have minimized the energy w.r.t., which however may not be the global minima, because, we have not really considered shapes other than  equilateral triangle. Whereas, the term with negative drives the system towards smaller area, the equilateral triangle encloses largest area for a given perimeter. The relaxation of this assumption then leads to smaller area, in fact to zero area achieved by isosceles triangles with two short sides of length  and one long side of length . The spring energy of such a network can be estimated as,

(38.8)

Minimizing this energy with respect to  yields, the minimum energy as  which is achieved at . The enthalpy per vertex of the equilateral triangle increases with pressure (), until it exceeds the enthalpy of a zero area isosceles triangle , at collapse tension , or equivalently of a spring of length .