We describe the challenges involved with extending the limited lateral size of two-dimensional polymers (2DPs). An amphiphilic monomer with three-fold symmetry is chosen to form an ideally tessellated monolayer at the air/water interface. Anthracene [4+4] photo-dimerization is chosen as the growth reaction. Formation of covalent net-points upon anthracene dimerization has an influence on the mechanical coherence of the resulting sheets which could be investigated qualitatively and quantitatively by means of AFM nano-indentation.