We built rhombicosidodecahedrons.
It's not super mathematical and I probably need to do some kind of reflection or mathematical questioning but for now, we just enjoyed making something pretty.
I don't know how familiar you are with these but they are made out of 12 pentagons, 20 triangles, and 30 squares. Here are the templates.
The project starts with a lot of tracing and cutting. We used poster board but card stock works just as well. It's important to cut the little notches in each shape so that they can be folded. Fold up each edge to create a little tab. The tabs are then stapled to the tabs of another shape in a pattern.
Start with a pentagon and staple five squares on to each side of the pentagon. Then staple a triangle between each pair of squares. Now the pattern is that you only staple squares onto pentagons and triangles onto squares.
I don't have very good directions to give but this website helped a lot (scroll a lot), even though this guy did it differently and loves cats, it's still helpful to look at the pattern.
I should have taken pictures along the way to explain it better. But I didn't.