Just so you don’t think that the Harry Potter game is the only place to find cool polygonal coins, here’s a question for you: what shape is the Susan B. Anthony dollar? Yes, it’s round, but if you look more closely you’ll see the outline of a regular hendecagon — an 11-sided polygon!
According to wikipedia, the coin was originally supposed to have this polygonal shape on the outside, but it was changed because vending machines could only handle round coins. As an interesting aside from the Susan B. Anthony House, the very first Susan B. Anthony dollar was released on July 2, 1979 in Rochester, New York! Go Rochester!
Several other countries have polygons coins as well. There are the heptagon-shaped 50 pence coins from Ireland and the United Kingdom (which may be why the Harry Potter tokens were shaped like heptagons)
There is the 2 francs coin from France with an octagon inside:
And don’t forget the dodecagon (12-sided) 20 centavos coin from Mexico!
Intrigued? Over at BezalelCoins there are examples of coins in almost every regular polygon shape through dodecagon, including a triangular 2-dollar coin from the Cook Islands in the South Pacific and a 9-sided 1-dollar coin from Tuvalu (a Polynesian island nation in the Pacific Ocean)! It’s enough to make me want to formalize my coin collection.