The Spectre Monotile

The Spectre is an aperiodic monotile discovered in 2023. It can tile the plane, but only non-periodically - no translation will map the tiling onto itself.

Interactive Shape Designer

Drag the red and blue control points to curve the edges. The same curve is applied to all 14 edges, alternating between the curve and its reflection.

Properties

• 14 equal-length edges
• All edge curves are congruent (same shape, some reflected)
• Can tile the plane without gaps or overlaps
• The tiling is necessarily aperiodic