Combinatorial maps

Okay kiddo, so let's pretend you have a big puzzle with a bunch of pieces, and you want to put them together to make a picture. But you don't just want to make any picture, you want to make a special picture where each piece is connected to exactly four other pieces, kind of like a grid.

Well, that's basically what a combinatorial map is! It's a way to represent a special kind of picture where each part (which we call a "face") is connected to exactly four other parts.

But to really understand it, we need to learn a few key words...

- Vertices: These are the points where the pieces meet.
- Edges: These are the lines that connect the vertices.
- Faces: These are the parts of the picture that are surrounded by edges.

So imagine you have a puzzle piece with a square shape. That's a face! And it has four edges, one on each side. Each edge connects to a vertex, and since there are four edges, there are also four vertices.

Now, if you take all the puzzle pieces and put them together in a certain way, you can make a combinatorial map. It's like a blueprint or a diagram of the puzzle. It shows how all the pieces fit together and how they're connected to each other.

The cool thing about combinatorial maps is that you can use them to study how different shapes and patterns are related to each other. You can even use them to create new puzzles and designs!

So that's it in a nutshell, kiddo. Combinatorial maps are a way to represent special kinds of pictures where everything fits together like a grid. It's like making a puzzle with a blueprint, and it helps us understand how different shapes are connected to each other.