Start with a square.
A square has four vertices in two dimensions. A cube has eight in three dimensions. A tesseract extends the same construction into four dimensions, producing sixteen vertices and thirty-two edges.
Project a dimension down.
The lab rotates points in the XW and YZ planes, then perspective-projects each four-dimensional point into three dimensions. The familiar larger and smaller cubes are views of the same geometry. This is a mathematical visualization, not a physical four-dimensional display.
Experiment with time.
Select 4D in the lab and vary the time scale. Pause a rotation and inspect how edges line up. Different projections reveal different symmetries without changing the underlying object.