Videos of a rotating 3-sphere.
Isoclinal rotation : https://youtu.be/jXs7Aosispk
Rotation with horatio of four : https://youtu.be/fOmeZkpU5js
The horatio is the between the rates of rotation of the two rotational planes. It's short for horological ratio. An isoclinal rotation has a horatio of one.
These are opaque spheres. One hemisphere is visible. I tried transparent spheres but it is too confusing.
These are projections in that the fourth dimension has no effect on the XY location in the image. The size of the dots depend on their distance from the observer. This distance includes all dimensions, so the fourth dimension is displayed indirectly.