  The purpose of this work is to collect in one place available information on
line arrangements known in the literature as braid, monomial, Ceva or Fermat
arrangement. They have been studied for a long time and appeared recently in
connection with highly interesting problems, namely: the containment problem
between symbolic and ordinary powers of ideals and the existence of unexpected
hypersurfaces. We also study also derived configurations of points (or more
general: linear flats) which arise by intersecting hyperplanes in Fermat
arrangements or by taking duals of these hyperplanes. Furthermore we discuss
briefly higher dimensional generalizations and present results arising by
applying this approach to problems mentioned above. Some of our results are
original and appear for the first time in print.
