I have a few related questions and I'd be happy to get some help with any one of them.
Is the stellation of a polyhedron generally a 'messy' affair that involves trimming away portions of the enlarged faces? (See below for my implicit assumption, $\text{stellation} \cong \text{dilation},$ that is probably wrong, I see now)
Are there any polyhedral stellations that come from simply dilating the faces, no trimming necessary?
Is there a good reference that explicitly defines stellation? I use truncation often but have gotten by with intuition, but this is not the case with stellation.
Context:
I am trying to create a very primitive animation/demonstration that shows the stellation of an octahedron to yield the stella octangula. Unfortunately, it seems that the mental image I have for stellation isn't living up to the real thing. I've always thought that one simply dilates each face, since this is what happens to the star polygons.
Quoting Coxeter (Regular Polytopes, section 6.2 on Polyhedra Stellation), it appears this is not necessarily the case:
In order to stellate a Polyhedron, we have to extend its faces symmetrically until they again form a polyhedron.
At any rate, I started with the stately octahedron, shown here using the software Grapher for OSX (I prefer the faces colored uniformly, but it defaults to checkerboard every time I scale).
Now I start to scale each face about its center; this image shows each face scaled by a factor of $2$. I'm noticing the triangular 'hole' starting to close up in the NorthEast region, for example.
Here it is scaled by a factor of $4$, where the three planes bounding the previous triangular 'hole' have finally met at a point.
And here's a closeup near the three planes meeting at that point, with the 'hole' finally closed.
In the last image I think I can see the stella octangula hiding underneath,
but the there are many portions of the enlarged faces that need to be thrown away.
I only have hands-on experience stellating regular polygons, by extending the edges, to produce star polygons. In that case, it's just a matter of finding the right scale factors for the edges with no trimming required.
My goal was for an expository lecture to non math-majors, but that animation is shaping up to be far too complicated.