  We derive the analytical solutions of surface states in a series of lattice
models for three-dimensional topological insulators and their nontopological
counterparts based on an ansatz. A restriction on the spin-flip matrices in
nearest-neighbor hopping characterizes the series. This restriction affords the
ansatz and favors analytical solvability of surface-state eigenvectors. Despite
the restriction, the series retains sufficient designability to describe
various types of surface states. We also describe how it can serve as a
tractable tool for elucidating unique phenomena on topological surfaces.
