As a clear signature of modern urban design concepts, urban street networks in dense populated zones are evolving nowadays towards grid-like layouts with rectangular shapes, and most studies on traffic flow assume street networks as square lattices. However, ideas from forgotten design schools bring unexplored alternatives that might improve traffic flow in many circumstances. Inspired on an old and almost in oblivion urban plan, we report the behavior of the Biham-Middleton-Levine model (BML) \-- a paradigm for studying phase transitions of traffic flow \-- on a hypothetical city with a perfect honeycomb street network. In contrast with the original BML model on a square lattice, the same model on a honeycomb does not show any anisotropy or intermediate states, but a single continuous phase transition between free and totally congested flow, a transition that can be completely characterized by the tools of classical percolation. Although the transition occurs at a lower density than for the conventional BML, simple modifications, like randomly stopping the cars with a very small probability or increasing the traffic light periods, drives the model to perform better on honeycomb lattices. As traffic lights and disordered perturbations are inherent to real traffic, these results question the actual role of the square grid-like designs and suggests the honeycombs as an interesting alternative for urban planning in real cities.