The primary kind of polytope that I tend to talk about and read about is 3 dimensional polytopes known as polyhedra, but there's also the familiar 2 dimensional polytopes aka polygons. Polytopes are always made up of polytopes of the dimension below. So 0 dimensional polytopes are just dots, 1 dimensional polytopes are lines which are bounded by points, 2 dimensional polytopes are called polygons(you have probably heard of these) and they're bounded by lines, and as mentioned before 3 dimensional polytopes are called polyhedra which are bounded by polygons.

Now I'm not as familiar with these but I can give an overview. From what I've read about I really only know about 4 dimensional polytopes which are called polychora and they're bounded by polyhedra. The term dimensions in things like science fiction or video games often refers to an alternate reality or something, but mathematically speaking it doesn't imply that at all; it just means that there's another axis. For example with 2d coordinates there's two axis, the x and y axis, and in 3d there's 3, x, y, and z. In 4 dimensions there's x, y, z, and w. Talking about 4 dimensional objects in this manner doesn't mean that a 4 dimensional space exists it's just exploring the properties of what 4 dimensional objects would have. There is no unique name for polytopes in 5 dimensions or above, they're just called 5-polytopes, 6-polytopes, etc. I also don't look much into polytopes above 4 dimensions or even 4 dimensional polytopes themselves but just so you know, that's how it extends to higher dimensions.