In premixed flame propagation of lean hydrogen or hydrogen-enriched blends, both hydrodynamic and thermo-diffusive instabilities are governing the flame front shape and affect its propagation velocity. As a result, different types of cellular patterns can occur along the flame front in a laminar scenario. In this context, an interesting phenomenon is the formation of polyhedral flames which can be observed in a Bunsen burner. It is the objective of this work to systematically characterize the polyhedral structures of premixed methane/hydrogen Bunsen flames in a combined experimental and numerical study. A series of lean flames with hydrogen content varying between 20 and 85% at two equivalence ratios is investigated. The experiments encompass chemiluminescence imaging together with Planar Laser-induced Fluorescence (PLIF) measurements of the OH radical. Characteristic cell sizes are quantified from the experiments and related to the characteristic length scales obtained from a linear stability analysis. In the experiments, it is observed that the cell sizes at the base of the polyhedral Bunsen flames decrease almost linearly with hydrogen addition and only a weak dependence on the equivalence ratio is noted. These trends are well reflected in the numerical results and the length scale comparison further shows that the wavelength with the maximum growth rate predicted by the linear stability analysis is comparable to the cell size obtained from the experiment. The correlation between the experimental findings and the linear stability analysis is discussed from multiple perspectives considering the governing time and length scales, furthermore drawing relations to previous studies on cellular flames.