Modification of Nestra's Peter Ganine's Gothic Chess set. I repaired Nestra's STLs in meshmixer so the hat's could by created in OpenSCAD.
When you capture a promoted pawn, it's only worth one point, so it's important to remember that the piece is still a pawn, even though it has the power of a queen. These Chess Hats allow you to easily see that the pawn has simply taken on a new role, rather than transformed into a different piece.
I made this for playing four-player chess, as promotion is much more common in four-player chess. Often you won't have lost your original queen by the time you promote. (so it saves plastic compared to printing an extra queen piece).
Promoting to the queen is the most common choice, but there are situations in which other pieces may be chosen.
I've also used the gothic chess set to play checkers (just print four extra pawns), and for this, the King hat looks very nice on the promoted pieces.
The pawn hat is included for your amusement.
Printed with three outer walls, and very little infill. I did acetone vapor smoothing on some of the blue pieces seen in the photo.