Individual assignment

Intro

Aperiodic Monotile: The “Einstein” of Tiling

An aperiodic monotile, also known as an einstein is a single geometric shape that can cover an infinite plane without gaps or overlaps in a pattern that never repeats.  The term comes from the German phrase ein Stein, meaning “one stone,” rather than referring to the physicist Albert Einstein. 

In 2022, retired printing engineer David Smith discovered the first true einstein, a 13-sided polygon he nicknamed “the Hat.” He collaborated with mathematicians and computer scientists to prove that this shape, along with an infinite family of related shapes (including “the Turtle” and “spectres”), creates aperiodic tilings.  This discovery solved a 50-year-old mathematical problem, proving that a single prototile can enforce non-periodicity, a feat previously thought impossible or requiring multiple tile shapes.

Design

Make a cut

Making the master mold

Making the negative

Hero shot