In the mid-1800s, Schläfli figured out that in four dimensions, there are six regular solids, including one with 600 faces! Each of those 600 faces is itself a three-dimensional tetrahedron ...

In the three-dimensional world, there are five regular solids -- tetrahedron ... squares or pentagons. In four dimensions, there are six regular solids, which can be built based on the symmetries ...