Thank you Gianluca. My objective though is not visualization but instead cropping these lattices for follow-on computations. One approach to cropping I'm exploring is iteration through each surface and discarding lattice points outside the bounds of the 4 complementary surfaces. A second approach is to create a Polygon surface from each of the 6 surface lattices, then for each polygonalized surface find the Built-in intersection of the 4 compliment surfaces, and use these intersections for boundaries of each surface lattice. Either way, once completed I can take the union of the surfaces and begin computation of the unusual voxels within the volume.
