  We describe how one can explicitly obtain all atoms of an arbitrary
root-closed monoid, whose quotient group is isomorphic to $\mathbb{Z}^2$. For
this purpose, we solve this task for three special types of such monoids in
Theorems 5 and 6, and then transfer these results to the general case. It turns
out that all atoms can be obtained from the (regular) continued fraction
expansion of the slopes of the bounding rays of the cone, which is spanned by
the monoid.
