Rendered from the file you download.
About this model
Could one shape cover an infinite plane without gaps while making every repeating pattern impossible? That was the long-standing ‘einstein’ problem—ein Stein means ‘one stone’ in German. Mathematicians had known aperiodic tile sets for decades, and Penrose reduced them to two shapes in the 1970s, but no single unmarked shape was known to force non-repetition through geometry alone.
In 2022, English tiling enthusiast David Smith discovered this hat-like polykite while experimenting with shapes. Joseph Samuel Myers, Craig S. Kaplan and Chaim Goodman-Strauss joined him to analyse it and proved in 2023 that copies of the Hat, including reflected copies, can tile the plane but can never form a periodic tiling.
The Hat became the first true aperiodic monotile under the standard mathematical definition, resolving a problem open for nearly 60 years. Print several copies to explore how simple local fits build an ordered, hierarchical pattern that never repeats.
Licence and attribution
The file remains available under its retained source licence. These permissions and obligations come from IteraMesh’s supported licence profile.
No attribution is required. You may still credit Christian Lawson-Perfect as the creator.
Notices retained with this model
- The source credits David Smith, Joseph Samuel Myers, Craig S. Kaplan and Chaim Goodman-Strauss with finding the aperiodic monotile.
A copyright licence covers the file. It does not grant rights to a trademark, design, patent, person’s likeness, or safety-critical use depicted by the model.
Source and provenance
Licensed import- Original creator
- Christian Lawson-Perfect · profile ↗
- Source page
- https://github.com/christianp/aperiodic-monotile
- Original download
- https://raw.githubusercontent.com/christianp/aperiodic-monotile/main/hat-monotile.stl
- Added to IteraMesh
- 21 October 2026
- Licence checked
- 19 October 2026, on the source page
- Changes
- None — the file is hosted as acquired
- File fingerprint
- sha256:46c89…ea01a2
IteraMesh hosts this copy under its licence. Christian Lawson-Perfect made it; IteraMesh did not.
Printing and safety
- File check
- Geometry validated before publication
- Units
- Not stated in stored evidence
- Printer and material
- Not verified by IteraMesh