  I propose monoradical nanographenes without C3 symmetry as building blocks to
design two-dimensional (2D) carbon crystals. As representative examples I study
the honeycomb and Kagome lattices, showing that by replacing the sites with
olympicene radicals the band dispersion near the Fermi energy corresponds,
respectively, to that of Kekul\'e/anti-Kekul\'e graphene and breathing Kagome
tight-binding models. As a consequence, finite islands of these new crystals
present corner states close to the Fermi energy, just like the parent models.
In the case of Kekul\'e/anti-Kekul\'e graphene, such states are topologically
protected, standing as examples of second-order topological insulators with a
non-zero Z2- or Z6-Berry phase. Differently, those of the breathing Kagome
lattice are of trivial nature, but the ground state has been predicted to be a
spin liquid in the antiferromagnetic Heisenberg model. Hence, 2D systems made
of low-symmetric nanographenes may be convenient platforms to explore exotic
physics in carbon materials.
