I am doing my math project on the properties of a spiked icosahedron. I already calculated the surface area and the volume through other methods, but the teacher asked me to find a generic formula for the properties through integration as well. The model is formed of $20$ identical pyramids, without a base, with the side length of $8.6$cm Each of the pyramids is made of three folded flaps, which have been folded of $15x15$ cm squares.
So I am stuck on the formula..