Shadow of the Colossus

Shadow ( basically projection ) of higher dimensional objects in lower dimension is another method of 'seeing' these higher dimensional objects. The shadow of 3D cube on a 2D plane is a square inside a square with all the corners connected as shown in the figure.

Shadow of 3D cube

Extending this logic to 4D cube we can conclude that the shadow of a 4D cube on 3D space should be a cube inside another cube with all the edges connected as shown in figure.

Shadow of 4D cube