  We derive bounds on the regularity of the algebra $C^\alpha(\mathcal{P})$ of
mixed splines over a central polytopal complex
$\mathcal{P}\subset\mathbb{R}^3$. As a consequence we bound the largest integer
$d$ (the postulation number) for which the Hilbert polynomial
$HP(C^\alpha(\mathcal{P}),d)$ disagrees with the Hilbert function
$HF(C^\alpha(\mathcal{P}),d)=\dim C^\alpha(\mathcal{P})_d$. The polynomial
$HP(C^\alpha(\mathcal{P}),d)$ has been computed in [DiPasquale 2014], building
on [McDonald-Schenck 09] and [Geramita-Schenck 98]. Hence the regularity bounds
obtained indicate when a known polynomial gives the correct dimension of the
spline space $C^\alpha(\mathcal{P})_d$. In the simplicial case with all
smoothness parameters equal, we recover a bound originally due to [Hong 91] and
[Ibrahim and Schumaker 91].
