Abstract cell complex

An abstract cell complex is like a big puzzle made up of different pieces called cells. Each cell has a certain number of sides and can be a different shape, like a triangle or a square.

Think of it like building with Legos. You have a bunch of different types of Legos—some are long, some are short, some are rectangular, and some are irregularly shaped. You can combine them in different ways to make all types of cool structures.

In an abstract cell complex, you can combine the cells in different ways to make bigger structures. You can attach cells to each other along their sides, forming bigger shapes.

But here's the cool thing: you can also take the same cell and attach copies of it to itself in different ways. You can stack them on top of each other, or you can attach one side to another, forming a loop.

This flexibility in how you can combine the cells is what makes an abstract cell complex so powerful. And mathematicians have found all sorts of interesting ways to use this concept to study all types of things, from shapes and spaces to viruses and DNA molecules.