The stereospecific interaction of polypeptides with biominerals and ice represents a unique phenomenon in nature. Here, using the theoretical geometric lattice matching algorithm, CHASM (abbreviation for chain alignment on the surface of materials), we explore the geometric complementarity of specific C-alpha polypeptide secondary structures (alpha-helix, beta-sheet, gamma-turn) with the [001] planes of the biominerals, aragonite and calcite, and the [001], [100], and [201] faces of hexagonal ice. We find that certain secondary structure-surface pairings exhibit a defined set of orientational minima that agree closely with published results. Moreover, no two secondary structures feature the exact same set of global and local orientational minima for a given surface. This suggests that the molecular complementarity of each secondary structure with a given surface is highly specific and cannot be mimicked by another secondary structure. These results suggest that the site and orientation of polypeptide adsorption onto biominerals or ice may be influenced by secondary structure type.