Here's a large cardboard construction I made with a group of teachers from Math for America.  It consists of sixty identical flat pieces that lock together with slots. The design is based on the twenty face planes of a regular icosahedron, so the result has 5-fold, 3-fold, and 2-fold axes of symmetry.

I pre-cut the parts on a band-saw and brought them with me.  Assembling them took over an hour and was trickier than I expected, but I learned a lot about how to organize it next time.

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