Maxcliques (maximal complete subgraphs) and unit disks (closed 
neighborhoods of vertices) sometimes play almost interchangable roles in 
graph theory.  For instance, that interchange makes two existing 
characterizations of chordal graphs into two new characterizations of 
chordal graphs.  These lead to several new characterizations of strongly 
chordal graphs, each of which is a natural strengthening of a 
characterization of chordal graphs.