In reaction diffusion based pattern formation (or other types of pattern formation too, really), it seems that the absence of an inversion symmetry (i.e., if the field $u(x,t)$ is a stable solution/steady state, then $-u(x,t)$ is not) leads to hexagonal pattern formation (rather than stripes or squares). This can be seen, for example, in the references 1, 2, 3, 4,5 and several other sources.
However, I am unable to come up with a simple mathematical explanation, or intuitive reason for this; and the explanations in the above references seem to be quite detailed or scenario specific. Why does a lack of inversion symmetry generally lead to hexagons in pattern formation?