  We consider arrangements of axis-aligned rectangles in the plane. A geometric
arrangement specifies the coordinates of all rectangles, while a combinatorial
arrangement specifies only the respective intersection type in which each pair
of rectangles intersects. First, we investigate combinatorial contact
arrangements, i.e., arrangements of interior-disjoint rectangles, with a
triangle-free intersection graph. We show that such rectangle arrangements are
in bijection with the 4-orientations of an underlying planar multigraph and
prove that there is a corresponding geometric rectangle contact arrangement.
Moreover, we prove that every triangle-free planar graph is the contact graph
of such an arrangement. Secondly, we introduce the question whether a given
rectangle arrangement has a combinatorially equivalent square arrangement. In
addition to some necessary conditions and counterexamples, we show that
rectangle arrangements pierced by a horizontal line are squarable under certain
sufficient conditions.
