We study the transmission of narrow electromagnetic beams associated to different K valleys, from both the armchair and zigzag edges, in a graphenelike triangular metallic photonic crystal. Due to the metallic nature of the structure, the propagation of an electromagnetic wave, with the wave vector close to the quasitriangular isofrequency contours of the Dirac cones resulting from the band trigonal warping, can be considered as being based on a series of bonding or antibonding states, formed by the local resonance modes in the unit cells. The transmission of a narrow incident beam, of the width of the crystal period size, depends on the local structure configurations in the beam impact zone that determine the distribution of the excited local resonance modes as well as the coupling between the latter and the incident field, thus the beam propagation in different directions. This investigation allows us to understand the interaction between an incident field and the resonance states associated to the Dirac cones at elementary structure scales reaching the size of these states. It can find application in valley photonics for transport tuning and optimization.