  This paper classifies Hermitian structures on 6-dimensional nilmanifolds
M=G/L for which the fundamental 2-form is d d-bar closed, a condition that is
shown to depend only on the underlying complex structure J of M. The space of
such J is described when G is the complex Heisenberg group, and explicit
solutions are obtained from a limacon-shaped curve in the complex plane.
Related theory provides examples of various types of Ricci-flat structures.
