Einstein Aperiodic Tiling tiles (Spectre)

The Spectre is an aperiodic monotile, also known as an einstein ('one stone' in German). You can use this shape to cover the plane out to infinity with no gaps.

If you used triangles, hexagons, or squares to tile the plane, you can easily do it in a repeating pattern like a checkerboard or a beehive. But if you tile the plane with the Spectre, the pattern never repeats.

Printing:

This version of the tile has a thin flat area and a raised rim for rigidity.  The rim can be printed in a different color for aesthetics and to make it easier to see which tiles are upside-down.  If you don't have a multi-color printer, you can manually change filaments after you have printed the flat area (0.6 mm thick).  If you do have a multi-color printer, there is a ‘painted’ version of the 3mf file with 35 clones (fitting on a Bambulab P1S build plate).

Links:

Classroom Activities

The original paper.

More information.