We introduce and analyze an efficient reconstruction algorithm for FCC-sampled data. The reconstruction is based on the 6-direction box spline that is naturally associated with the FCC lattice and shares the continuity and approximation order of the triquadratic B-spline. We observe less aliasing for generic level sets and derive special techniques to attain the higher evaluation efficiency promised by the lower degree and smaller stencil-size of the C1 6-direction box spline over the triquadratic B-spline.