When I first came to college, I had big plans to cover my room in glow-in-the-dark stars. It occurred to me upon arrival that my roommate might not be as crazy about the idea as I was.
During some research into low-cost cardboard construction methods, I stumbled across this picture of a press-fit geodesic dome, which was made at the MIT media lab, laser-cut from a sheet of cardboard. I realized that a smaller, simpler geometric shape could easily approximate the perfect sphere that a real planetarium could require.
I began by designing a sky map spread across twelve pentagons, to be folded into a dodecahedron shape. Using some simple geometry and Wolfram MathWorld, I found the dihedral angle necessary for the joining pieces. I got the star patterns off John Walker’s Fourmilab, and spread them by hand across the pentagons. (This should have been done geometrically via Mathematica, alas.)
I lasercut the patterns from a large piece of opaque blue acrylic, and cut the joiners from clear acrylic scrap. I discovered too late, as a planetarium, my project failed: I got too large of a lightbulb (I got a little excited at the Home Depot) and the focal length was totally wrong; the light shone out of the holes but would not project outwards onto the walls. With this in mind, I repurposed the planetarium into a hanging lamp.