  Ammann bars are formed by segments (decorations) on the tiles of a tiling
such that forming straight lines with them while tiling forces non-periodicity.
Only a few cases are known, starting with Robert Ammann's observations on
Penrose tiles, but there is no general explanation or construction. In this
article we propose a general method for cut and project tilings based on the
notion of subperiods and we illustrate it with an aperiodic set of 36 decorated
prototiles related to what we called Cyrenaic tilings.
