Traditionally, standard Lagrangian-type finite elements, such as quads and triangles, have been the elements of choice in the field of topology optimization. However, finite element meshes with these elements exhibit the well-known "checkerboard" pathology in the solution of topology optimization problems. A feasible alternative to eliminate this long-standing problem consists of using hexagonal elements with Wachspress-type shape functions. The features of the hexagonal mesh include 2-node connections (i.e. 2 elements are either not connected or connected by 2 nodes), and 3 edge-based symmetry lines per element. In contrast, quads can display 1-node connection, which can lead to checkerboard; and only have 2 edge-based symmetry lines. We explore the Wachspress-type hexagonal elements and show their advantages in solving topology optimization problems. We also discuss extensions of the work to account for material gradient effects.