Found it really helpful to get the spiraling right by labeling a dodecahedron (inspired by the explanations from the Evil Mad Scientists, which has great CAD illustrations you should check out) and marking the corresponding parts of the sculpture. You can download the pdf of the dodecahedron I used (with typed numbers) with some extra instructions below.

This is just taped like hinges on the inside (not hot glue gun-ed.)

I plan on re-designing and making another out of wood! As soon as I decide how to connect the parts cleanly together. Any suggestions?

Can also be made with an exacto knife (and changing the blade often!) instead of laser cutting the cardboard.

The design includes 40 pieces even though you only need 30 because I figured some would be messed up at the edges of the cardboard and by me pulling them out etc. If you do it with nicer/more expensive material you might want to delete down to 30 pieces.