Crystalline frameworks (nets) are a standard model of three-dimensional periodic structure in materials. To first order, the allowed motions of framework structures can be modelled as perfectly stiff beams joined at freely-pivoting junctions. Recent work by Power et al, has shown that the low-energy (soft) deformation modes of such a crystalline framework are characterized by a matrix function and its points of rank degeneracy. The associated geometric flex spectrum helps us determine the possible existence of surface modes: a mechanical analogue of topological insulator materials. 
 
This project will compute the first-order geometric flexes of a suite of crystalline frameworks in the EPINET and RCSR databases.  We will look for signatures of different categories of motions such as rigidity, one-degree-of-freedom structures, auxetic deformations, and surface modes. 

This project involves advanced applied mathematics (e.g. linear algebra, tangent spaces) and requires computations and coding in a high-level scripting language such as python.