Tensegrity systems combine antagonistic tensile and compressive members. The computational cost of synthesis and form-finding greatly increases with the complexity of a tensegrity structure. One solution, the use of modules which can be combined to create a more complex structure (tensegrity primitives), has been investigated using highly symmetric primitives of a few canonical types. This thesis determines the multistable region of an example planar tensegrity-adjacent mechanism, measures the feasibility of various parameters for shape control and demonstrates a method for stacking any number of such mechanisms, then develops a search method which exhaustively determines all possible tensegrities with a specified cable graph and with varying additional constraints. To demonstrate the viability of these methods, full catalogues of tensegrity primitives for a host of simple cable graphs are generated.