I can see the equilateral/isosceles triangle thing making the flat spidron shape. And I can see how 4 of them could tile to make a square (and hence how you could map the 6 faces of a cube). And how 5 could make a pentagon, etc, and hence how you could map the faces of lots of polyhedra with those shapes. But I don't get how the edges of the original shape are then folded to get the wonderful rose-shaped solids.
Jim