Eos but with a bunch of world building edits.

Someone used a high sided wish to make minting hereditary in their bloodline. Eventually there was a short war which killed most of those who were aware of minting, and sent the remaining mints (called djinn in this AU) into hiding. Some powerful families still have large stashes of coins, but they're dwindling.
Born Djinn preform the mental action to make coins unconsciously whenever they feel sufficient pain for it.
Coins are harder to make - by which I mean, in order to make a triangle in Astraeus, you need as much pain as it takes to make a square in Eos, and so on up the scale. Hexes are extremely rare, and there exists exactly one star in-setting which the makers of never attempted again.

Most common coin names:
Triangle: Trois
Square: Quatre
Pentagon: Cinq
Hexagon: Six
(Most aren't aware of a higher coin than hexagon, but the single "Star" is called the Sept)