This is a little different than other monotile uploads here. I've taken the extra step to produce multiple aspect ratios for the right-angle edges. So you can have a different monotile set than everybody else ;)

My favorite is the Phi ratio.

At some point I'll upload an OpenSCAD model that is configurable for an infinite number of ratios…

The gray “hat” polykite tile is an “einstein”, an aperiodic monotile. In other words, copies of this tile may be assembled into tilings of the plane (the tile “admits” tilings), yet copies of the tile cannot form periodic tilings, tilings that have translational symmetry. In fact, the tile admits uncountably many tilings. Credit: arXiv (2023). DOI: 10.48550/arxiv.2303.10798

• [https://arxiv.org/pdf/2303.10798.pdf](https://arxiv.org/pdf/2303.10798.pdf)
• [https://aperiodical.com/2023/03/an-aperiodic-monotile-exists/](https://aperiodical.com/2023/03/an-aperiodic-monotile-exists/)