Earlier quoted context omitted.
Sorry to ruin your pun idea, but Stein doesn't mean geometric shape. The most common meaning is simply stone, but it can also mean board game piece. Words you might use for these shapes instead would be Form (meaning shape) or Kachel (meaning tile). Source: native speaker.
Simplified for concise comment above, but translation taken from the article: > (The term “einstein” comes from the German “ein stein,” or “one stone” — more loosely, “one tile” or “one shape.”) I'm mostly reacting to the use of "Einstein" as a label, which I always dislike. The article seemed to hint at a reason for the pun/reference (Smith found a "one shape") but there no was justification for bringing Albert into…
"Elusive 'einstein' solves long-standing math problem"
which is certainly true -- aperiodic monotiles have been _very_ elusive. Not sure if the author was trying for a double meaning... if so, it does seem like the incorrect secondary meaning has overtaken the primary meaning in a lot of people's minds.