  The triple point numbers and the triple point spectrum of a closed 3-manifold
were defined in (R. Vigara, Representaci\'on de 3-variedades por esferas de
Dehn rellenantes, PhD Thesis, UNED 2006). They are topological invariants that
give a measure of the complexity of a 3-manifold using the number of triple
points of minimal filling Dehn surfaces. Basic properties of these invariants
are presented, and the triple point spectra of $\mathbb{S}^2\times
\mathbb{S}^1$ and $\mathbb{S}^3$ are computed.
