Is there a name for the shape that results from gluing a cube to each face a cube? I can't come with a natural description for it, and google doesn't seem to give any results (the closest being a depiction of a 7-point finite difference stencil). See figure:
Maybe you talking about a Tessaract.
The figure is Dali cross and it's a three-dimensional surface unfolding of a four-dimensional hypercube.
As a more familiar analogy you can take a three-dimensional cube and open its surface on the plane.