A nice zome model of just its edges can be made. It is an approximation, because these "squares" are red on two sides and blue on the other two, so they are actually rectangles and not exactly square. The vertical supports at the bottom are critical, or the bottom pentagon would not be able to support all the weight. (Trust us, we know...)
Below is a view from the ceiling, which doesn't have the cluttered background, but the ceiling is not high enough to get the entire construction in the picture using my camera. The "vertical" edges of each prism are of size 2r3. The 10-gon edges alternate between b2+b1+b1+b2 and b1+b2+b2+b1.
If you take just the top two thirds of the sphere, you get a nice design for a dome. Below is a picture of it, with Victoria inside. We built the above by starting with this dome, then turning it over and adding the top.