Science & Tech · Science & Environment · 11 hrs ago
Chair44 is proposed as a strongly aperiodic 3D tile
Ioannis Tsiokos, director of the AI research lab Automorph, has announced a three-dimensional shape called Chair44.
The shape can be repeated to fill space without gaps or overlaps, while the resulting pattern never repeats.
This kind of shape is called an aperiodic monotile, meaning one shape can cover a space in a nonrepeating pattern.
A two-dimensional example, the hat, was proved to be an aperiodic monotile in 2023.
Mathematicians had known of a three-dimensional shape with a weaker form of aperiodicity, but Chair44 is presented as a stronger example that addresses a longstanding open problem.
Tsiokos says he used AI models to develop and check the work, which he published as a preprint.
The finding could renew interest in tiling mathematics, though the supplied information does not describe what further review or testing will happen next.
Researcher Ioannis Tsiokos has proposed Chair44, a three-dimensional shape that can tile space without gaps or overlaps in a nonrepeating pattern.
The shape is made by removing one small cube from a larger cube composed of eight cubes.
Tsiokos says he used artificial intelligence models to write the preprint and search for a 3D monotile.
Computer scientist Craig Kaplan says a 3D aperiodic monotile was already known, but described that earlier example as weakly aperiodic.
Kaplan said Chair44 addresses a longstanding open problem in tiling theory.
- Who
- Ioannis Tsiokos, director of Automorph, announced the proposed Chair44 monotile.
- What
- Chair44 is proposed as a 3D shape that tiles space without gaps or overlaps in a nonrepeating pattern.
- When
- The Scientific American article was published on October 12, 2026.
- Where
- Not stated.
- Why
- The discovery aims to provide a strong example of a three-dimensional aperiodic monotile, addressing a longstanding open problem in tiling theory.
This story does not have two clearly opposing sides.
David Smith discovered the hat-shaped tile, later proved to be a two-dimensional aperiodic monotile.
Scientific American published an article about Tsiokos’s proposed Chair44 monotile.
- Shape
- Chair44, a 3D monotile
- Construction
- A cube made of eight small cubes with one cube removed
- Proposed researcher
- Ioannis Tsiokos
- Earlier 3D example
- Schmitt-Conway-Danzer biprism
- Earlier discovery
- The hat-shaped tile was announced in 2023
What people are saying
For decades, we’ve known of an aperiodic monotile in 3D: a shape known as the Schmitt-Conway-Danzer biprism.
I’m pleased that we have the solution to what was, until recently, a nagging open problem in tiling theory.
I’m not a mathematician myself,
Now you have a seven-cube chair.
Sources
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