Cookie cutter in the shape of the einstein tile!

The einstein tile is a way to aperiodically tile the 2D plane. This means you can bake a set of cookies that perfectly tile the plane, but will never repeat! To make an infinite tiling, you'll need both the normal tile and its reflection.

Aperiodicity means that if you hypothetically tiled the entire 2D plane out to infinity, you couldn't take arbitrarily large regions of the tiling and shift them such that they look the same as another region. 

Aperiodic tilings have been known to exist since the 1960s, the first of which discovered was a set of 20,426 unique tiles discovered by Robert Burger. It took another 10 years for Roger Penrose to discover multiple 2 tile sets, but finding a single tile set, an einstein tile, proved extremely challenging. An einstein tile was proposed in 2010 by Joshua Socolar and Joan Taylor, however the tile was not connected (in the sense that the tile wasn't one single object, but had disconnected regions). But by 2023 a single connected tile, ‘the hat’, was discovered by David Smith. Its construction is very simple - as can be seen via the model pictures - just 8 kites glued together, but is just one of a family of aperiodic tiles known as ‘spectres’, which can be constructed by modifying the boundary edges of the hat. These spectres don't require the use of their mirror images to tile the plane too.

I highly recommend reading more about the einstein problem as well as aperiodic tilings as they're extremely interesting areas of maths.

I haven't been able to bake any cookies with these yet, though please do share your cookies, I'd love to see them! Pictures were printed on a FlashForge Creator Pro using eSUN Bone White PLA+.