  An early result in the theory of Natural Dualities is that an algebra with a
near unanimity (NU) term is dualizable. A converse to this is also true: if
V(A) is congruence distributive and A is dualizable, then A has an NU term. An
important generalization of the NU term for congruence distributive varieties
is the cube term for congruence modular (CM) varieties, and it has been thought
that a similar characterization of dualizability for algebras in a CM variety
would also hold. We prove that if A omits tame congruence types 1 and 5 (all
locally finite CM varieties omit these types) and is dualizable, then A has a
cube term.
