  We study the Hobby-McKenzie varieties that constitute a major class
investigated thoroughly in the monograph The shape of congruence lattices by
Kearnes and Kiss. We obtain new characterizations of the Hobby-McKenzie
varieties via compatible reflexive ternary structures. Based on our findings,
we prove that in the lattice of interpretability types of varieties, the filter
of the interpretability types of Hobby-McKenzie varieties is prime.
