We took a bunch of bike wheels and zip-tied them together into a dome
Most bicycle shops, we found, throw away old and broken wheels. They still work fine for this project! You could buy them for a decent discount, though, if the shop keeps them.
After you have a good number (we used about 40), it's pretty simple. Just stand them up and use zip-ties or wire to attach them.
We had 12 26" wheels for the bottom layer and 12 24" wheels for the second. The size difference gave us an inward tilt. 8 24" ones for the third row, with 2 wheels for every 3 of the second row. The top was 1 24" wheel connected to 3 rims without spokes. The rims overlapped with the third row.
Thanks to Stevie's Happy Bikes, our local bike store that gave us all the wheels!