This is an interactive animation of a tesseract, aka hyperccube
-- the four-dimensional equivalent of a cube
XY If you only move this, it is as if you are rotating
a paper square on a table. This only rotates in the
first two dimensions
XZ,YZ Now we have added the third dimension, and rotating
these will be like rolling a dice in your fingers
XQ,YQ,ZQ These three rotations are between the previous three
dimensions, and the fourth. Notice that if all controls
are at zero (and perspective off) and you only rotate ZQ,
you will see nothing change, because this is a rotation
between the third and fourth dimension, and you cannot yet
see either (because you set the *Z rotations to 0)
You can turn perspective on or off, if it is on, you will see a more
realistic cube. The perspective projection is essentially an orthogonal
projection from 4d to 3d, and then a standard perspective projection
from 3d to 2d. So touching the *Q rotations doesn't really do anything
for the perspective.