So first let's get an example. A great dodecahedron.

{2

^{2}}doe

First off, 2 represents the number of times a process has been done. The superscript 2 represents what the process is exactly doing. Doe should be quite obvious, it's the base polytope being greatened.

1 - Stellating: Replacing the edges with larger edges on the same line.

2 - Greatening: Replacing the faces with larger faces on the same plane.

3 - Aggrandizing: Replacing the cells with larger cells on the same realm.

4 - Teroning: Replacing the terons with larger terons on the same flune.

...

n - n-stellation: Replacing the n elements with larger n-elements on the same hyperplane.

So yeah. An easy stellation notation that actually works for higher order versions of stellation.