Lee conformal world in a tetrahedron

Imagine you have a very special toy. It's a 3D shape called a tetrahedron. A tetrahedron is like a triangle but with 3 sides instead of 2. The toy is made of something that looks like paper, but it's very special. This paper can stretch and shrink, but it always stays the same shape.

Now, let's imagine that you live in this tetrahedron and you want to draw a map to show where everything is. But there's a problem. You can't just draw a flat map like you do for the world outside your toy. That's because your toy is not flat, and it's not a sphere like the Earth either. So how can you make a map that shows where everything is without making it all distorted and wonky?

Well, there's a clever math trick you can use called Lee Conformal World. What this means is that you can take your stretchy paper and wrap it all around the inside of the tetrahedron like a tight-fitting glove. When you do this, you'll notice that the corners of the tetrahedron become squished together. This is because the paper has to stretch to fit into the corners, just like when you try to wrap a present with too little paper.

Now that you have your stretchy paper wrapped around the tetrahedron, you can draw a map on it that shows where everything is. And because the paper can stretch and shrink, you can make sure that the map doesn't get all twisted up and distorted.

So there you have it, you've just created your very own Lee Conformal World inside a tetrahedron!