The hypercube
A hypercube is a 4 dimensional analogue of the cube. Details of the construction of this object are given, along with movies of a spinning hypercube.

An "inflated" hypercube
By inserting new vertices into the edges and faces of a hypercube, it may be "inflated'' to give an approximation to the hypersphere.

Hypertorus
Adding together three vectors, each rotating in 4-space with different frequencies and amplitudes, produces a trajectory along the surface of a hyper-torus.

How the models were produced
Details of the mathematics needed to model the structures, and how to turn the numbers into an animation.