  A census is presented of all closed non-orientable 3-manifold triangulations
formed from at most seven tetrahedra satisfying the additional constraints of
minimality and P^2-irreducibility. The eight different 3-manifolds represented
by these 41 different triangulations are identified and described in detail,
with particular attention paid to the recurring combinatorial structures that
are shared amongst the different triangulations. Using these recurring
structures, the resulting triangulations are generalised to infinite families
that allow similar triangulations of additional 3-manifolds to be formed.
Algorithms and techniques used in constructing the census are included.
