Rotating unit systems constitute one of the main classes of auxetic metamaterials. In this work, a new design procedure for lightweight auxetic systems based on this deformation mechanism is proposed through the implementation of a hierarchical triangular truss network in place of a full block of material for the rotating component of the system. Using numerical simulations in conjunction with experimental tests on 3D printed prototypes, the mechanical properties of six types of auxetic structures, which include a range of rotating polygons and chiral honeycombs, were analysed under the application of small tensile loads. The results obtained show that there is almost no difference in the Poisson’s ratios obtained from the regular, full structures and the ones made from triangular truss systems despite the latter, in some cases, being 80% lighter than the former. This indicates that these systems could be ideal candidates for implementation in applications requiring lightweight auxetic metamaterial systems such as in the aerospace industry.