  We show that the topological states inherent in the two-dimensional vertex
transitive fes lattice, also referred to as square-octagon lattice, can be
tailored by modifying the interactions between the knots. Contrary to other
lattices formed of light-weight atoms, such as in graphene, where the
spin-orbit interactions are too weak for opening a band gap of sufficient size
to access the topological states at temperatures above the boiling point of
helium, the second-neighbor interactions in the fes lattice open a sizable band
gap that allows accessing the topological states at room temperature. However,
these interactions need to be carefully selected in order to maintain the
topological character of the network. We explore the topological feature space
of the fes net using tight-binding theory, where we vary the interaction
strength (first and second neighbors) between the knots and then implement this
net in atomistic two-dimensional polymer structures. There, we demonstrate that
these novel crystalline materials offer a playground to explore exotic
topological states at ambient conditions in experiments.
