Content-Type: text/shitpost

In !!n!! dimensions, in general, there are only three regular polyhedra. (For !!n=2,3,4!! there are more, but these are the only exceptions.) One of these is the !!n!!-simplex, which is the !!n!!-dimensional analogue of the triangle and the tetrahedron. It's natural to denote this as !!S_n!!.

And, happily, the symmetry group of !!S_n!! is !!S_n!!.