# Layering two different sized hexagonal planes periodically

I have two planes stacked on top of each other. Each plane looks like this:

Each plane, however, has a different hexagonal side length (the first plane has hexagons with side length $a$ and the second plane has length $b$).

I am trying to figure out what angle I most rotate the $a$ plane in order to make each "unit cell" periodic. In other words, each ring in each plane should correspond to a ring below it, just with a different rotation.

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Don't know if it helps, but $(x,y)$ is a period of the lattice iff $(x,y)=(\frac{3n}2 a,\frac{m\sqrt 3}{2}a)$ where $n\equiv m\pmod 2$. It looks like you ant to find such a period for $a$ and another for $b$ of the same length ... –  Hagen von Eitzen Jun 27 '13 at 17:14