For questions on the $n$-simplex, an $n$-dimensional polytope with $n+1$ points.

A [simplex][1] is a higher dimensional analogue of a triangle or tetrahedron. The number of faces in a simplex can be determined using Pascal's triangle.

[1]: https://en.wikipedia.org/wiki/Simplex#:~:text=In%20geometry%2C%20a%20simplex%20(plural,0%2Dsimplex%20is%20a%20point%2C&text=a%204%2Dsimplex%20is%20a%205%2Dcell.