Hexagons are widely observed as a packing or tiling geometry in nature, yet they appear to have been avoided in conventional halftone tiling. A goal of the present study is to understand the potential barriers that have prevented their use and present new halftone geometry options that overcome the issues while offering several potential benefits. While conventional halftone geometries often include the fourth screen (e.g., yellow) in a suboptimal manner, the hexagonal geometry presented here can include a clustered-dot fourth screen moire-free. Hexagonal screens can appear to have smoother texture. Due to differences in packing geometry and touch point geometry, hexagons have the potential to possess different tone reproduction characteristics, which may be favorable for some marking processes. We also present a parametrically controlled hexagonal halftone spot function that allows for optimization of dot touch points and provides compact growth. The controllable touch points can prevent a tone reproduction discontinuity, while the compact growth throughout the gray range ensures maximum stability. Additionally, we present a three-colorant dot-off-dot halftone configuration using hexagonal geometry. Examples are provided.