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I've noticed that the Solar System screen does not show the conquered worlds in PoP:TB v1.02_regfix_(31015) for some reason. The conquered (completed) levels would fill up the screen at the bottom, but for some reason all of the icons are blank. I've attached a screenshot from the manual that shows what's supposed to happen. I'm running Win7 64-bit.
I get exactly the same thing on Windows 10. Used to be fine - well, used to not work at all except running the non-3D version, but now it works from GOG Galaxy so that's one improvement!