Just read an interesting article suggesting space-time may not be quantized. The quantization of space-time I think was first suggested by Heizenberg. Anyhow, the basic idea is that, from quantum probability, a fundamental particle's quantum state is undefined once you shrink it's available space down to below the Planck length (1x10**-34m). Well, this all sounds interesting but how do you prove it? What observation(s) would confirm it? No clue. Still......???
I am unable to imagine a shape no matter how tiny or ambiguous that would not create prefered directions. Pack spheres, squares, triangles or any other shape you can think of and as best I can tell, moving from one to the next will be easier in some directions than others I.e. prefered directions. We have not observed this.
Very interesting subject. There is still so much to be discovered and things we can not explain. I think it is obvious that there are "states" that we have not yet been able to define, that are not part of the quantum model. Maybe more research while using LSD would help.