What is a polyhedron? The question is short, the answer is long. Although you may never have heard of the Polyhedron Kingdom before, it is nearly as vast and as varied as the animal, mineral, and vegetable kingdoms (and it overlaps all three of them). There are aristocrats and workers, families and individuals, old polyhedra with long and interesting histories and young polyhedra born yesterday or the day before. In this kingdom you can take a walking tour of polyhedral architecture, visit a nature preserve and an art gallery and an artisans’ polyhedra fair. As you stroll along you may even glimpse polyhedral ghosts from four-dimensional space.