In cubist artworks, objects are broken up, analyzed, and re-assembled in an abstracted form — instead of depicting objects from one viewpoint, the artist depicts the subject from a multitude of viewpoints to represent the subject in a greater context. Often the surfaces intersect at seemingly random angles, removing a coherent sense of depth. The background and object planes interpenetrate one another to create the shallow ambiguous space, one of cubism's distinct characteristics.
In contrast we might consider this summation of Hypercubism:
In hypercubist artworks, objects are particlized, analyzed and synthesized in a realistic form — instead of depicting all objects from one temporal perspective, the artist (or artists) depict the subject from a multitude of temporal perspectives to represent the subject in a greater temporality. Often the surfaces of intersect seamlessly, creating a coherent four-dimensional spacetime illusion. The background and object planes are always distinct to create deep concrete space, one of hypercubism's distinct characteristics
Besides being a bit of encyclopedic revisionism, these two definitions set up a useful theoretical dichotomy between Cubism and Hypercubism. Simply put:
Cubism shows multiple spaces in the same time while Hypercubism shows multiple times in the same space.