  On the reference tetrahedron $\widehat K$, we define three projection-based
interpolation operators on $H^2(\widehat K)$, ${\mathbf H}^1(\widehat
K,\operatorname{\mathbf{curl}})$, and ${\mathbf H}^1(\widehat
K,\operatorname{div})$. These operators are projections onto space of
polynomials, they have the commuting diagram property and feature the optimal
convergence rate as the polynomial degree increases in $H^{1-s}(\widehat K)$,
${\mathbf H}^{-s}(\widehat K,\operatorname{\mathbf{curl}})$, ${\mathbf
H}^{-s}(\widehat K,\operatorname{div})$ for $0 \leq s \leq 1$.
