The Kagome structure has been shown to be a highly suited micro-architecture for adaptive lattice materials, in which selected lattice members are replaced by actuators aiming to create shape morphing structures. It is the combination of in-plane isotropy, high stiffness and low energy requirement for actuation that makes the planar Kagome structure the best performing micro-architecture known to date. Recently, Pronk et al. (2017) have proposed a set of topological criteria to identify other micro-architectures suitable for actuation. In the present paper, four novel lattice topologies are presented which were contrived in light of these criteria. Matrix analysis is performed to reveal the static and kinematic properties of the pin-jointed versions of these four structures. The finite element method is used to determine their stiffness and actuation characteristics. One of the proposed designs is found to match the optimal elastic properties of the Kagome structure, while it requires less energy for (single member) actuation. However, the displacement field induced by actuation attenuates faster than in a Kagome lattice. The presented results also show that the criteria proposed by Pronk et al. (2017) should be refined in two regards: (i) statically indeterminate lattice materials do not necessarily result in high actuation energy and thus should not be ruled out, and (ii) as shown by counterexample, the criteria are not sufficient.