Sphinx tiling

Sphinx tiling is like a jigsaw puzzle, but instead of fitting different-shaped pieces together, we are fitting the same shape over and over again to cover a whole surface without any gaps or overlaps. Imagine you have a bunch of identical square tiles, just like the ones you might see on a bathroom floor. Now, say you have a big flat area, like a floor or a wall, and you want to cover it completely with these square tiles, leaving no space between them. That's where Sphinx tiling comes in!

To make sure the tiles line up perfectly, we use a special kind of symmetry called rotational symmetry. This means that we can turn the tile by some angle (like 90 degrees or 180 degrees) and it will still look the same. This is really useful because we can simply rotate the tile to fit it into different spots on the surface we're covering. By doing this, we can create all sorts of cool repeating patterns!

Sphinx tiling is named after the mythical creature, the Sphinx, because the arrangement of tiles can look like the head of a Sphinx. In fact, Sphinx tiling is a type of tessellation, which means that we are covering a surface with repeated shapes in a way that has no gaps or overlaps.

So, in simple terms, Sphinx tiling is like a game of fitting square tiles together in a way that makes a pattern without any gaps. We use rotational symmetry to make the tiles fit together perfectly, and the end result can look like the Sphinx's head!