  It is well-known that every graph with maximum degree 4 has an orthogonal
drawing with area at most $\frac{49}{64} n^2+O(n) \approx 0.76n^2$. In this
paper, we show that if the graph is 3-connected, then the area can be reduced
even further to $\frac{9}{16}n^2+O(n) \approx 0.56n^2$. The drawing uses the
3-canonical order for (not necessarily planar) 3-connected graphs, which is a
special Mondshein sequence and can hence be computed in linear time. To our
knowledge, this is the first application of a Mondshein sequence in graph
drawing.
