Two-dimensional hexagonally ordered honeycomb surfaces have been created by solvent casting polybutadiene films under controlled humidity. Subsequent CF4 plasmachemical fluorination introduces cross-linking and surface texturing, leading to hierarchical surfaces with roughness on both the 10 pm (honeycomb) and micrometer (texturing) length scales. For microliter droplets, these display high water contact angle values (>170 degrees) in combination with low contact angle hysteresis (i.e., superhydrophobicity) while displaying bouncing of picoliter water droplets. In the case of picoliter droplets, it is found that surfaces which exhibit similar static contact angles can give rise to different droplet impact dynamics, governed by the underlying surface topography. These studies are of relevance to technological processes such as rapid cooling, delayed freezing, crop spraying, and inkjet printing.