Let 
be the maximum face degree of a graph and 
its cyclic chromatic
number. It is conjectured that 
for polyhedral
graphs (Plummer and Toft 1987).
A number of infinite families satisfying 
are known, including the stacked 3-prism graphs and
two other families noted by Plummer and Toft (1987). The first of these are known
in this work as Plummer-Toft graphs, and the first few are illustrated above in three
different types of embeddings.
