Lepage test

Okay, so have you ever played with Legos? Remember how you can build different things with them by sticking different Legos together? Well, scientists also use Legos, but they call them "tessellations" which means a pattern made by repeating a shape over and over again without any gaps or overlaps.

Now, imagine you have a big piece of paper and you want to cover it completely with Legos without any gaps or overlaps. How do you know if it's possible or not? This is where the Lepage test comes in.

The Lepage test is a way to check if a tessellation can cover the whole paper without gaps or overlaps. It's like a rulebook that tells you if your tessellation is allowed or not. To use the Lepage test, you have to look at the angles of the shapes in your tessellation.

You see, each Lego has corners or angles, right? Some have more corners than others. The Lepage test says that if you add up the angles of all the shapes in your tessellation and the sum is 360 degrees, then your tessellation can cover the whole paper without gaps or overlaps! If the sum is not 360 degrees, then your tessellation won't work.

So, the Lepage test is a way to check if you can cover a big piece of paper with your Lego shapes without any gaps or overlaps. All you have to do is add up the angles of your shapes and see if they equal 360. Pretty cool, huh?