Polyhedral Bunsen flames, induced by hydrodynamic and thermo-diffusive instabilities, are characterized by periodic trough and cusp cellular structures along the conical flame front. In this study, the effects of flow velocity, hydrogen content, and equivalence ratio on the internal cellular structure of premixed fuel-lean hydrogen/methane/air polyhedral flames are experimentally investigated. A high-spatial-resolution one-dimensional Raman/Rayleigh scattering system is employed to measure the internal scalar structures of polyhedral flames in troughs and cusps. Planar laser-induced fluorescence of hydroxyl radicals and chemiluminescence imaging measurements are used to quantify the flame front morphology. In the experiments, stationary polyhedral flames with varying flow velocities from 1.65 to 2.50 m/s, hydrogen contents from 50 to 83%, and equivalence ratios from 0.53 to 0.64 are selected and measured. The results indicate that the positively curved troughs exhibit significantly higher hydrogen mole fractions and local equivalence ratios compared to the negatively curved cusps, due to the respective focusing/defocusing effect of trough/cusp structure on highly diffusive hydrogen. The hydrogen mole fraction and local equivalence ratio differences between troughs and cusps are first increased and then decreased with increasing measurement height from 5 to 13 mm, due to the three-dimensional effect of the flame front. With increasing flow velocity from 1.65 to 2.50 m/s, the hydrogen mole fraction and local equivalence ratio differences between troughs and cusps decrease, which is attributed to the overall decreasing curvatures in troughs and cusps due to the decreased residence time and increased velocity-induced strain. With increasing hydrogen content from 50 to 83%, the hydrogen mole fraction and local equivalence ratio differences between troughs and cusps are amplified, due to the enhanced effects of the flame front curvature and the differential diffusion of hydrogen. With increasing equivalence ratio from 0.53 to 0.64, a clear increasing trend in hydrogen mole fraction and equivalence ratio differences between troughs and cusps is observed at constant flow velocity condition, which is a trade-off result between increasing effective Lewis number and increasing curvatures in troughs and cusps.