  The hallmark of topological phases is their robust boundary signature whose
intriguing properties---such as the one-way transport on the chiral edge of a
Chern insulator and the sudden disappearance of surface states forming open
Fermi arcs on the surfaces of Weyl semimetals---are impossible to realize on
the surface alone. Yet, despite the glaring simplicity of non-interacting
topological bulk Hamiltonians and their concomitant energy spectrum, the
detailed study of the corresponding surface states has essentially been
restricted to numerical simulation. In this work, however, we show that exact
analytical solutions of both topological and trivial surface states can be
obtained for generic tight-binding models on a large class of geometrically
frustrated lattices in any dimension without the need for fine-tuning of
hopping amplitudes. Our solutions derive from local constraints tantamount to
destructive interference between neighboring layer lattices perpendicular to
the surface and provide microscopic insights into the structure of the surface
states that enable analytical calculation of many desired properties. We
illustrate our general findings on a large number of examples in two and three
spatial dimensions. Notably, we derive exact chiral Chern insulator edge states
on the spin orbit-coupled kagome lattice, and Fermi arcs relevant for various
recently synthesized pyrochlore iridate slabs. Remarkably, each of the
pyrochlore slabs exhibit Fermi arcs although only the ones with a magnetic
one-in-three-out configuration feature bulk Weyl nodes in realistic parameter
regimes. Our approach furthermore signal the absence of topological surface
states, which we illustrate for a class of models akin to the trivial surface
of Hourglass materials KHg$X$.
