Real-world aperiodic tiling

Tiles which tile only aperiodically may have practical implications to crystallography.

I used to think the quest for shapes which tile only aperiodically, culminating in the discovery of Penrose tiles in 2D, was only a curiosity of recreational mathematics and was not relevant to real life. I realize now that aperiodic tilings may in fact theoretically be relevant for real life because of X-ray crystallography. Imagine there existed a molecule, perhaps an important protein in the human body or of a pathogen, whose shape is such that it only tiles aperiodically. (Can such a single three-dimensional aperiodic tile exist?) (Update: Schmitt-Conway biprism, einstein problem.) However, X-ray crystallography, the best way to determine the exact 3D structure of a molecule, only works for periodic tilings, and one cannot grow a crystal of this aperiodic molecule. Any attempt to grow a crystal yields an aperiodic amorphous mass which does not diffract properly. Thus, one could end up with an important molecule whose structure we want to know, but it is fundamentally impossible to discover it.