With a single shape, it might be possible to fill all of space without ever finding a pattern that repeats.
Covering a floor with square tiles is easy: the same rows recur at regular intervals. But there are also shapes that fit together across a surface without leaving gaps or producing repetition. Mathematicians have long sought to achieve the same property in space, using three-dimensional blocks.
A researcher has just presented a shape called Chair44. It resembles a small chair built from seven cubes. But its faces are not smooth: tiny pyramid-shaped protrusions prevent certain arrangements.
These details make all the difference. When two pieces touch, they must follow precise positions. The constraints then extend to neighboring pieces. The result is astonishing: one could completely fill an infinite volume with this single block, but never in an arrangement that repeats regularly.
With ordinary bricks, it would be possible to build a repeating pattern. With Chair44, the shape would itself rule out that possibility.
The property would still hold if some copies were turned over as in a mirror. Mathematicians call this a “strongly aperiodic” tiling. Here, the word “tiling” refers to filling space.
To support his proposal, the researcher combines geometric reasoning with programs that check many possible arrangements. Part of the proof is also verified using software specialized in mathematical proofs.
However, caution is still needed. This research was submitted as a preprint, and its argument has not yet undergone a complete independent review. The result is therefore presented as a proposed proof, not as a definitively accepted theorem.
If confirmed, this block would provide an answer to a longstanding problem: finding a single shape that imposes a non-repeating arrangement in the three dimensions of our space, without needing to add other types of pieces.