You can represent a 3-dimensional cube on a 2-dimensional by letting the "depth" dimension be represented by a line at an angle. To represent a 4-dimensional cube on a 2-dimensional surface, simply pick two lines at angles. The edges of these hypercubes are specified by the vectors at the origin. The reason some of the cubes look distorted is a matter of perspective, just as the square faces of a regular cube look distorted when you draw a cube.
Move the vectors around to make the distorted cube faces of the hypercube less distorted.
How many cube faces can you find in a hypercube?