Mach Demonic

Too much time on my brain.

Trying to figure out how to create an actual fully functional Tesseract replica. The shape shifting aspect is where the problem stands. Mentally It seems possible if I created it with no corner points, But then it would look bootleg and stupid. Now being able to shift an Outer-Cube corner into an Inner-Cube corner without destroying the cube is the answer, How can I create a sphere-like mechanism which freely relocates it’s X, Y and Z attachments?