I went back to basic optics 101 (searched the internet), and discovered that a plano-convex lens does basically the same thing if you flip it around, BUT the focal length will be different. The focal length will be longer if you present the flat surface to the light source. The difference in focal lengths increases as the thickness of the lens increases, and it increases as the power of the lens increases. As I think about it, I remember observing this effect before with plano convex lenses. If I had observed more closely, I would have noticed that the focal length had changed when I did my experiment, but it was not shifted by a lot.
That's interesting about the thickness of a lens effecting its focal length as once light is within a medium it shouldn't effect it at all. It is the change from one medium (air/glass) that bends light and allows lenses to operate in the first place. However, the fact the the Sun looks bigger at the horizon would support that because we are looking through more and more air.
I looked more closely at two different lenses from my star ball to see if I could see exactly how they were manufactured. A second magnitude lens system appears to be made from two lenses with the limiting star hole placed between them. These lens system appear to be pressed fit into a small metal tube with a flange about 1/4 inch in diameter for easy mounting in the star globe. It is extremely hard to tell but it appears that both surfaces facing outward appear to be flat. Thus I'm guessing that there are two plano convex lenses placed on either side of the limiting hole very much like a condenser set.
I was able to take apart the lens for Sirius as it is held together with a retaining ring very much like the lenses for the Milky Way and I found this one quite interesting. The size limiting hole is placed first facing the light source. The lens is then placed in the support. What is interesting is that this lens is a convex concave design. The convex side facing the light source, the concave facing out toward the screen. The amount of grind is very small on both sides and I wasn't sure until a put a straight edge across both sides to actually see the curvature. This curvature was less then that of the 18 inch star ball.
This led me to believe that the 2nd magnitude lens perhaps has a slight curve as well but it is so small that I couldn't say one way or another. It could be that there is just a small optical flat on one side of the star hole for support.
A few of the first magnitude star lenses have the star limiting hole on the outside facing the screen, but this could be because there metal and size could make them self supporting. They also hold a filter behind them for color if required.
In my mind it is obvious that the lenses are made by or for Spitz for this use only. Because of the very slight grind they are obviously a fairly long focal length. I'm concluding that the addition of a concave side to the lens that they no longer act as a focusing unit but more like a collimating one.
I don't think that any of these lenses will actually focus an image like a normal plano convex one will but I could be wrong.