Size-based separation of particles in microfluidic devices can be achieved using arrays of micro- or nanoscale posts using a technique known as deterministic lateral displacement (DLD). To date, DLD arrays have been limited to parallelogram or rotated-square arrangements of posts, with various post shapes having been explored in these two principal arrangements. This work examines a new DLD geometry based on patterning obtainable through self-assembly of single-layer nanospheres, which we call hexagonally arranged triangle (HAT) geometry. Finite element simulations are used to characterize the DLD separation properties of the HAT geometry. The relationship between the array angle, the gap spacing, and the critical diameter for separation is derived for the HAT geometry and expressed in a similar mathematical form as conventional parallelogram and rotated-square DLD arrays. At array angles <7°, HAT structures demonstrate smaller particle sorting capability (smaller critical diameter-to-gap spacing ratio) compared to published experimental results for parallelogram-type DLD arrays with circular posts. Experimental validation of DLD separation confirms the separation ability of the HAT array geometry. It is envisioned that this work will provide the first step toward future implementation of nanoscale DLD arrays fabricated by low-cost, bottom-up self-assembly approaches.