S³

In mathematics, S³ (the 3-sphere) is the set of points that are equidistant from the origin in four-dimensional Euclidean space. It is a higher-dimensional analogue of a sphere. This artwork, S³, is a literal visualization of the 3-sphere in two different ways: one using hyperspherical coordinates, and the other using Hopf coordinates. The work reflects the contrast between conceptual simplicity in its mathematical definition and the difficulty of forming a visual intuition of it.