Icosahedron-Wrapping Monstrosity

Question

The following monstrosity of a shape:

... can be wrapped onto the surface of an icosahedron in a way that completely covers the entire icosahedron with no gaps and no overlaps.

How can it be done?

Answer 1

Here's a picture of the solution.

Once it was clear that the long hooks had to fold in on themselves rather than enclose something else, the rest followed.