Assembling spheres with magnets

I am circling back to the problem I described last October of tiling a sphere with identical puzzle pieces, because I’d like to be able to quickly put together things like portable planetarium domes and big acoustic focusing mirrors. Ideally I’d want to be able to carry something small and portable, and then put up or take down the resulting sphere very quickly.

If we go with the identical puzzle piece approach, then a sphere requires 60 slightly curved shapes (or 30 shapes for a hemisphere, if you want a planetarium dome). In its disassembled state, the sphere would consist of a stack of identically shaped pieces. I’m thinking that a nice way to make something both stackable and easy to assemble/disassemble would be to put tiny magnets along the edges.

You’d want to orient the magnets, as in the diagram below, so that the pieces stick together properly both when assembled and when disassembled / stacked. One way to do this would be to orient four magnets (shown as red dots) so that the north poles of two magnets point out of the sphere, and the south poles of the other two magnets point out of the sphere:

While this scheme works, it requires a lot of tiny magnets — four magnets per piece. That’s 120 magnets for a dome, and 240 for a full sphere. Fortunately we can replace half the magnets with small pieces of metal (shown as blue dots below), which are cheaper:

Now all that remains is to build the thing and see if it all works.