In my boredom, I was thinking about why the simplest 3d object (i.e. the one with the least faces, sides, vertices) was the tetrahedron. After it made sense to me, I realized some cool stuff which was new to me. I also came up with the following goofy question:
Fill in the blank!
The simplest 4D object needs 5 cells, and each cell is the simplest 3D object. The simplest 3D object needs 4 faces, and each face is the simplest 2D object. The simplest 2D object needs 3 sides, and each side is the simplest 1D object. The simplest 1D object needs 2 points, and each point is the simplest (or should I say only?) 0D object. The simplest 0D object, or point, needs ______.
Waddya think?
A simplex can be modeled combinatorially as a set of vertices $\{v_1,v_2,\ldots,v_n\}$. Every subset of a simplex is also a simplex. The subsets with one element are vertices, the subsets with two elements are line segments, the subsets with three elements are triangles, the subsets with 4 elements are tetrahedra, etc.
The empty set is also a simplex. To fill in your blank, "the simplest 0D object, a vertex, requires one -1D object, and that is the empty simplex." That's as far as we can go. A simplex simply doesn't get any simpler than that.