Photonic graphene is a two-dimensional photonic crystal structure that is analogous to graphene. We use 5 mm diameter Al2O3 rods placed on a triangular lattice with a lattice constant a=8 mm to create an isolated conical singularity in the photonic band structure at a microwave frequency of 17.6 GHz. At this frequency, the measured transmission of microwaves through a perfectly ordered structure enters a pseudodiffusive regime where the transmission scales inversely with the thickness L of the crystal (L/a greater than or approximately 5). The transmission depends critically on the configuration of the edges: distinct oscillations with an amplitude comparable to the transmission are observed for structures terminated with zigzag edges, while these oscillations are absent for samples with a straight edge configuration.