The Three-Symplex Is a Three-Cell

The three-symplex, if you can imagine it, that is four numbers, and there are four numbers that add up to one. The tetrahedron looks like a pyramid, but the base of the pyramid is also a triangle. And then, of course, if you have five corners, well, that's in four-dimensional space. We can't, so let's not try to visualize it, don't worry about it.