constructing a pie with the topology of a sphere from 20 triangular sub-pie modules attached with amazing magnets.
Step 1: Layout and cut the pieces
we needed 20 equilateral triangles. choosing an altitude of 12 inches let us easily lay out two strips of them on a 24x48 inch sheet of 24 gauge steel. in order to get the dihedral angle at which the sides of the pans have to meet to form the whole icosahedron requires the sides to be sloped at darn near 120 degrees so if one just cuts out the diamond shaped tab in each corner, the results fit together quite nicely.
we decided to pick up a power-shear from harbor freight. cuts the sheet like butter and leaves a cleaner edge than the hand sheers. it wouldn't work for really detailed work but for reasonably smooth curves it's definitely worth it's weight and even for straight cuts it's significantly more affordable than a floor shear.
Step 2: Fold and rivet the sides
folding the pans was greatly simplified by a 18inch bending brake. when you have to repeat some step 3*20 times, it's definitely worth setting up the appropriate jig. here a piece of metal to clamp down the pan was cut to give the appropriate clearance and later re-used as a hold down for drilling. we used a pop rivet in each corner to hold things a bit more rigid.
remember that sheet metal is sharp. wear gloves, but don't be afraid to have fun.