  Methods were developed in Ref. [1] for constructing reference metrics (and
from them differentiable structures) on three-dimensional manifolds with
topologies specified by suitable triangulations. This note generalizes those
methods by expanding the class of suitable triangulations, significantly
increasing the number of manifolds to which these methods apply. These new
results show that this expanded class of triangulations is still a small subset
of all possible triangulations. This demonstrates that fundamental changes to
these methods are needed to further expand the collection of manifolds on which
differentiable structures can be constructed numerically.
