Is there a known method to dissect Jessen's icosahedron and rearrange to form a cube?

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It can be shown that Jessen's icosahedron is scissors-congruent to a cube, meaning that it can be sliced into smaller polyhedral pieces that can be rearranged to form a solid cube. What is the simplest way to perform this dissection and reassembly? What cuts are required and how many pieces are necessary?