This is the tiling of a 3-D cube. It shows the starting point.
Wireframe of 4-D cube. This is what people normally do when
they show the hypercube. If you are unfamiliar with the hypercube,
this will help you see the simplest version.
Solid Model of tiled hypercube. All the surfaces are opaque, so
you see what's happening on the outside.
Consistently Transparent Model of tiled hypercube. The outer
surfaces are transparent, so you see what's happening on the inside.
A combination of 3) and 4). I think this is the most esthetically
appealing. It has a smooth transition between transparent and opaque.