  We introduce Dehn invariants as a useful tool in the study of the inflation
of quasiperiodic space tilings. The tilings by ``golden tetrahedra'' are
considered. We discuss how the Dehn invariants can be applied to the study of
inflation properties of the six golden tetrahedra. We also use geometry of the
faces of the golden tetrahedra to analyze their inflation properties. We give
the inflation rules for decorated Mosseri-Sadoc tiles in the projection class
of tilings ${\cal T}^{(MS)}$. The Dehn invariants of the Mosseri-Sadoc tiles
provide two eigenvectors of the inflation matrix with eigenvalues equal to
$\tau = \frac{1+\sqrt{5}}{2}$ and $-\frac{1}{\tau}$, and allow to reconstruct
the inflation matrix uniquely.
