Piecewise linear manifold

Imagine you have a shape made up of straight lines connected together, just like a LEGO toy you've built. Each of these straight lines has a different shape, and when you put them together, they make up a larger shape, kind of like a puzzle.

Now, let's say you want to understand this shape better, so you can study it and figure out how it works. But, because it's made up of all these different lines, it's hard to understand it as a whole.

So instead, you decide to break it down into smaller, simpler parts that are easy to understand. This is what we call a "piecewise linear manifold" - it's a way of breaking down a complicated shape into smaller, simpler shapes that are easier to study.

Each of these smaller shapes is called a "piece," just like each block of LEGO is a separate piece. And when you put them all together, you get a larger shape, just like how all the LEGO pieces come together to make a larger toy.

By breaking down the large shape into smaller pieces, you can understand how each piece is connected to the others, and how they work together to make up the larger shape. This can help you understand the shape better, and even use it for things like engineering or design.