I am looking for the formula or sequence of values for the number of orientations of regular $n$-simplexes.
For orientation I mean a rotation such that the $n$-simplex is in the same previous position but with different facets/edges (for example, for the triangle, I can choose one of the 3 sides as base). Sorry for the not rigorous math language.
I have computed 1, 3, 12 for a 1-simplex, 2-simplex, 3-simplex respectively. I don't know if that is right, anyway I could not find anything suitable in OEIS or elsewhere.
Any hint?