All Questions

This is a question posed by Adam Chalcraft. I am posting it here because I think it deserves wider circulation, and because maybe someone already knows the answer. A polyomino is usually defined to ...

Question: how does one enumerate all star-convex $2n$-vertex sublattices of the plane that have the unique domino-tiling property? Definitions: A subset $S$ of the $xy$-plane is star-convex if there ...

It is known that a square can be partitioned into three similar rectangles, all mutually non-congruent. I don't think it's possible with four. With what numbers of rectangles can this be achieved? And ...

Can rotations and translations of this shape perfectly tile some equilateral triangle? I originally asked this on math.stackexchange where it was well received and we made some good progress. Here's ...

Suppose I tile $\mathbb{R}^3$ in a ($\mathbb{Z}^3$-)translation-invariant manner. If we insist on the tiling being regular, then we are left with only the cubic tiling. However, suppose that we ...