Convex Polytopes

Okay, so imagine you have a bunch of shapes. They can be any shape you want - triangles, squares, rectangles, even strange shapes that you've never seen before! Now, imagine you take a rubber band and stretch it around these shapes. The rubber band can't go through the shapes, it has to stay on the outside.

If you can stretch the rubber band and it stays on the outside of all the shapes without crossing over any of them, that group of shapes is called a "convex polytope."

But wait, there's more! Not only do the shapes have to be on the outside without crossing, but they also have to be connected. Think of it like a puzzle that you have to put together. The shapes fit perfectly, they don't overlap, and they make one continuous shape.

And when you look at a convex polytope, it will always have flat sides. If you put it on a table, it won't wobble around because the sides are flat and even.

So that's a convex polytope - a group of shapes that fit together perfectly with no overlaps and no wobbles.