3 ms·

Thanks for the link, this is very cool! Weird (to me) that five out of six images show the 3D case, which is way harder to understand than a tile on a 2D plane

by unwind 4y ago

Thanks for the link, this is very cool! Weird (to me) that five out of six images show the 3D case, which is way harder to understand than a tile on a 2D plane, at least in my view. It's also weird, for someone not at all familiar with the problem, that the concept of a "tile" includes non-connected shapes, i.e. there are outliers that are considered part of the tile but not connected to the main body. Apologies for absolutely no clue about terminology here.

thaumasiotes 4y ago
> It's also weird, for someone not at all familiar with the problem, that the concept of a "tile" includes non-connected shapes The base concept here isn't the idea of a "tile". It's the idea of "tiling the plane", where "tile" is a verb. You tile the plane with a shape by repeating the shape over it and covering the whole space without leaving any holes or causing any overlaps. Once you've defined the problem as "tiling", it's a natural step to call whatever shapes you happen to be using in your tiling scheme "tiles".
OscarCunningham 4y ago
I think the non-connected 'tile' was interesting simply because they hadn't yet found a connected one. When stuck solving a problem it's often helpful to look at what solutions would look like if some of the constraints were relaxed. But in fact, the connected solution ended up much simpler than the disconnected one!