Editing 4-polytope (section)

==Definition==
A 4-polytope is a closed [[Four-dimensional space|four-dimension]]al figure. It comprises [[vertex (geometry)|vertices]] (corner points), [[edge (geometry)|edges]], [[face (geometry)|faces]] and [[cell (mathematics)|cells]]. A cell is the three-dimensional analogue of a face, and is therefore a [[polyhedron]]. Each face must join exactly two cells, analogous to the way in which each edge of a polyhedron joins just two faces. Like any polytope, the elements of a 4-polytope cannot be subdivided into two or more sets which are also 4-polytopes, i.e. it is not a compound.