Two discoveries allow fundamentally diverse structural systems with hexagon-type lattice to be offered for the synthesis of minimum mass and maximum stiffness constructions. The highest efficiency of both properties could be achieved using hexagon-type spatial rigid bar structures with tetrapod-shaped joints, referred to as superelements. Geometric parameterization, required for shape optimization as the chosen means for realising the task set, will be considered. The main tasks for defining the parameterization include exact definition of the geometry to be parameterized, choosing the most appropriate independent shape parameters and determination of the parameter constraints to adhere.