Infinite stars

[guy]

Wenninger found that the standard duals (i.e. via a polar reciprocity about a concentric sphere) of uniform hemi polyhedra extend to infinity.
A uniform hemi polyhedron may be treated as a facetting of its convex hull.
If we define stellation and facetting as dual processes, then the convex core of any stellation is dual to that convex hull.
It follows that Wenninger duals are infinite stellations of their convex core.
But are they the only ones?

Each arm of a Wenninger dual is an infinite pyramid, whose vertex lies at infinity. But they are not the only infinite cells. There are also tetrahedral wedges with one whole edge lying at infinity, and which run between these pyramid arms. Just as the arms appear as prisms, so the tetrahedra appear as infinite pizza slices or wedges. The duals of all such infinite cells are finite (and overlapping) polyhedra within facettings of the dual convex hull.

I have been exploring all this and have put up an illustrated note at https://www.steelpillow.com/polyhedra/S ... stars.html.