[mci]

I invented a game that uses tiles in the shape of a regular hexagon plus a rhombus. IMHO, you can tile the plane aperiodically with them. See the first picture in [1].

[1] https://marcinciura.wordpress.com/2023/10/14/orinoko/

[gilleain]

Nice looking shape.

Maybe this was not your point, but the difference with the hat/spectre tile is that there is no periodic tiling (with a reflected hat).