We derive bounds on the regularity of the algebra C^α(P) of mixed splines over a central polytopal complex P⊂R^3. As a consequence we bound the largest integer d (the postulation number) for which the Hilbert polynomial HP(C^α(P),d) disagrees with the Hilbert function HF(C^α(P),d)= C^α(P)_d. The polynomial HP(C^α(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

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... e correct dimension of the spline space C^α(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].