Another beauty, great job Carl!
I'd love to see a screen capture video overview of how you go about designing these. I have a very good idea of how to design more "traditional" shell-mech puzzles but the multi-origin aspect of these puzzles seems to complicate things.
To be honest I think this is easier then some of the shell-mech stuff out there but maybe that comes from me using POV-Ray and doing all this stuff manually before. Any suggestions of screen video capture software? I assume I'd need a mic to pick up sound too if I wanted to talk during the video. I'll look into it but basically you just design your basic cut. In this case its a sphere centered on the point of one corner. Add in the groves which become the feet on the edge pieces and apply this cut to all the corners. This gives you the core. To get the corner piece you could apply those same cuts to a cube (single-origin puzzle) and you'd have the corner. Go back to the original puzzle and take the piece which is the union of the cut of two corners which are 3 edges apart. Their overlap is just one edge so that gives you that part. The overlap of two corners which are two 2 edges apart is two of the above "outer" edges and one inner edge. The union of these 3 pieces is defined by these two cuts. Now just shift those two cuts outward by the width of an "outer" edge to cut off those two outer edge pieces and you are left with the inner edge. That's the basic process. Now while I do this I actually change the original cut slightly depending on where I use it to take into the account tolerances, etc. For example the feet on the edge pieces are NOT as wide as the groves they fit into, but this I believe is very similar to what is used in the traditional shell-mech method.