I am a mathematician (working mostly in three-dimensional geometry and topology) and mathematical artist (working mostly in 3D printing). I'll talk about some 3D prints I designed to help try to visualise four-dimensional objects. Just as a shadow of a three-dimensional object squishes it into the two-dimensional plane, we can squish a four-dimensional shape into three-dimensional space, where we can then make a sculpture of it. If the four-dimensional object isn't too complicated and we choose a good way to squish it, then we can get a very good sense of what it is like. I'll talk about the sphere in four-dimensional space, the four-dimensional polytopes (which are the four-dimensional versions of the three-dimensional polyhedra), and various sculptures, puzzles, and virtual reality experiences that have come from thinking about these things.
