  One measure of the complexity of a 3-manifold is its triangulation
complexity: the minimal number of tetrahedra in a triangulation of it. A
natural question is whether we can relate this quantity to its topology. We
determine the triangulation complexity of Seifert fibered spaces with non-empty
boundary in terms of their Seifert data, up to a multiplicative constant. We
also show that all singular fibres of such a Seifert fibered space (aside from
those of multiplicity two) can be made simplicial in the 79th barycentric
subdivision of any triangulation of it.
