  Soft topological surface phonons in idealized ball-and-spring lattices with
coordination number $z=2d$ in $d$ dimensions become finite-frequency surface
phonons in physically realizable superisostatic lattices with $z>2d$. We study
these finite-frequency modes in model lattices with added next-nearest-neighbor
springs or bending forces at nodes with an eye to signatures of the topological
surface modes that are retained in the physical lattices. Our results apply to
metamaterial lattices, prepared with modern printing techniques, that closely
approach isostaticity.
