This is still a work-in-progress, but as part of a Microsoft Research/schools project we are building a prototype planetarium out of cardboard and particleboard. The "dome" is a geodesic dome built out of triangles of cardboard and strong binder clips. The base of the dome forms a decagon (10-sided figure), but as the dome is titled 20 degrees, the dome support forms an elliptical decagon, and is made out of half inch particleboard to provide a solid base for the dome. The diagram shows the idea.
The reason for the 20 degree tilt is to provide a much better experience for the students when traveling through space - a vertical projection will give the impression that the planet or star is "falling" onto the viewers, whereas a view forward will give the impression of traveling to that planet or star. It is also simply more comfortable to look forward than to look up.
The projector and mirror are placed on a table to the right of the door in the image above.
Plans for building this planetarium (assuming of course it works!) will be posted shortly.