A quick experiment in the 4-dimensional rotation of a hypercube.
A hypercube (or tesseract) is the 4-dimensional analogue of a cube. It has 16 corners, 36 edges, and 24 sides. All corners are right angles although they may seem like acute or obtuse angles when seem from a different viewpoint, just as the corners of a cube may seem sharper or wider depending on your viewpoint.
Rotation is achieved through a simple 4x4 transformation matrix which allows the hypercube to be rotated along a single plane at a time. In 3-dimensional rotation, rotation usually occurs around a linear axis but 4-dimensional rotation occurs around a planar axis.
You can check/uncheck the box to see the hypercube with solid sides or empty sides. Click on "Perspective" to select different methods of display.