A Hat Polykite, the first discovered Aperiodic Monotile,

You can infinitely combine these together, requiring no other shapes, to fill the plane. However, such a tiling will never repeat itself, so you cannot slide a copy of the tiling over itself and have it align,

Built in OpenSCAD so thingiverse customizer will allow you to change the size and thickness of the part, as well as the size of the chamfer. "size" refers to the horizontal dimension. the short dimension will always be about 72% of the long dimensions.

Chamfers are weird in OpenSCAD so I had to fake it a bit. "corner correction" changes the size of spheres put at the original vertices to remove remnants in the concave corners.