An aperiodic monotile, sometimes called an "einstein", is a shape that tiles the plane, but never periodically.

For more information about this shape, see:

• website dedicated to this shape
• video showing the space of related shapes
• paper preprint

About the 3D model and printing

The shape is chiral, and mirror images of the shape are used in tiling a plane. You can simply flip the physical printed tile over to get its mirror image. 

This model, therefore, has fillets on both the top and bottom edges for symmetry, but can still be printed without supports. 

Printing in two colors makes it easy to see the mirror image, and a gcode file has been provided with a color change. 

Photos (coming soon) show the tiles printed with the following parameters:

• Nozzle: 0.4 mm
• Layer height: 0.2 mm
• Infill: 20% grid (Prusaslicer “fast” mode)
• PLA