A polytope is a generalization of polygon (2d) or polyhedron (3d) for any number of dimensions.
To put it another way, a polytope is an “n-dimensional” object. A polygon would then be a "2-dimensional" polytope and a polyhedron would be a "3-dimensional" one.
Like polygons and polyhedrons, a polytope must have “flat” countable sides.
Think pyramid, not perfect sphere.