  Materials with designed properties arises in a synergy between theoretical
and experimental approaches. In this study we explore the set of Archimedean
lattices forming a guidance to its electronic properties and topological
phases. Within these lattices, rich electronic structure emerge forming type-I
and II Dirac fermions, topological flat bands and high-degeneracy points with
linear and flat dispersions. Employing a tight-binding model, with spin-orbit
coupling, we characterize a quantum spin Hall (QSH) phase in all Archimedean
lattices. Our discussion is validated within density functional theory
calculations, where we show the characteristic bands of the studied lattices
arising in 2D carbon allotropes.
