Well, I just had a thought. Any polygon can be defined by a list of coordinates (x,y), based on their order.
But polyhedra can't be defined in this way - you would need a net* (2-d list) of coordinates (x,y,z) instead of just a list.
So, by analogy, to define polychora, you would need a 3-d list of coordinates (w,x,y,z).
Another way of defining polyhedra is to define them as a list of polygonal faces, and then define all the polygons required.
So, by analogy, the other way to define polychora is to define them as a list of polyhedral cells, and then define all the polyhedra required.
*A net can be defined by a list of data, one item for each item in the net, plus a list of connections, of which each item defines two items in the first list which are connected to each other.
... Hey, I've just got yet another idea for my office suite