Einstein Tessellation (aperiodic tiling)

This model is a “from the ground up” recreation of the Einstein aperiodic tessellation. I built this using a series of construction lines to form a set of “allowed vertices” and then “walked” from point-to-point by specifying the angle rather than calculating the vertex positions manually. The full python source code is included in the file section!

An aperiodic monotile

David Smith, Joseph Samuel Myers, Craig S. Kaplan, Chaim Goodman-Strauss

A longstanding open problem asks for an aperiodic monotile, also known as an "einstein": a shape that admits tilings of the plane, but never periodic tilings. We answer this problem for topological disk tiles by exhibiting a continuum of combinatorially equivalent aperiodic polygons. 

I designed this in build123d which is a new CodeCAD package available here:

https://github.com/gumyr/build123d

The easiest way to customize this model is with a static build from my fork of CQ-editor which includes build123d – available here:

https://github.com/jdegenstein/jmwright-CQ-Editor/releases/

Build123d is under active development, so for the sake of preservation this model was built with build123d commit 03e105d from April 1st, 2023.

REVISION HISTORY:

230403: Initial Release