Here's an example of penrose tiles:

https://dglittle.github.io/cdn/penrose002.html

It's an infinite plane of tiles, procedurally generated, that never repeats no matter how far you go.

Just to close the loop here, Penrose is also famous (to his readers, anyway) for his beautiful hand-drawn diagrams and illustrations. So it’s a terrific name for this project.

And has five-fold symmetry, which is impossible for wallpaper groups.

The discovery of Penrose tilings is partially tangled up with the discovery of quasicrystals, where researchers found minerals with 5-fold and 10-fold symmetry that ought to have been mathematically impossible to exist. Turns out that the Crystallographic Restriction Theorem has an important caveat that people neglected up until the 1980s: it assumes that you have to have translational symmetry, which Penrose tilings do not.