<p>Optimal elastic structures often exhibit a multiscale nature, combining global material distribution with locally optimized microstructures. In two-dimensional elasticity, theory predicts that rank-3 laminates achieve the optimal mean energy for multiple-load scenarios. However, the practical use of rank-3 laminates is limited by manufacturing complexity. This motivates the search for single-scale alternative microstructures with near-optimal performance. This work investigates a simple class of single-scale periodic microstructures consisting of a star-shaped void within a convex unit cell (triangular, square, or hexagonal). An efficient parameterization of the void geometry in terms of Fourier coefficients is introduced. A gradient-based optimization procedure is developed to tune both the cell shape and the void geometry so as to minimize the mean effective stress energy under prescribed loading scenarios, without any need for an external length-scale parameter. The resulting optimized microstructures achieve energies within 0.5–3.7% of the theoretical optimum, with an average deviation of 1.8%. Their performance compares favorably with that of other single-scale microstructure families reported in the literature, while offering simplicity, practical manufacturability, and strong geometric compatibility across unit cells of varying densities.</p>