  We examine the metrics that arise when a finite set of points is embedded in
the real line, in such a way that the distance between each pair of points is
at least 1. These metrics are closely related to some other known metrics in
the literature, and also to a class of combinatorial optimization problems
known as graph layout problems. We prove several results about the structure of
these metrics. In particular, it is shown that their convex hull is not closed
in general. We then show that certain linear inequalities define facets of the
closure of the convex hull. Finally, we characterise the unbounded edges of the
convex hull and of its closure.
