I am working on a project that involves mapping the night sky's northern hemisphere onto the exterior surface of a small (16 cm radius) geodesic dome. The problem is, I don't know what map projection to convert to, or whether I need to create one. If so, I don't really know how.
I'm starting from a high-resolution image of the full night sky in an equirectangular projection in celestial coordinates.
I would like to map that onto the net of a geodesic dome, so that I can construct the dome with accurate star coordinates. I would like to use a computer program to convert the northern hemisphere of my equirectangular star map into the desired projection, if possible.