If you remove, from the middle of a tetrahedron, an octahedron of half the edge length, four small tetrahedra remain. Removing from these again the middle octahedra and iterating the procedure, one gets a fractal, namely the Sierpinski tetrahedron. The removed octahedra, too, form a fractal:

An inverse Sierpinski tetrahedron (Sketch)

I have built the surface of the octahedra removed during the first three iterations from cardboard and adhesive tape:

An inverse Sierpinski tetrahedron made from cardboard An inverse Sierpinski tetrahedron made from cardboard

Here is the net I had to cut out:

Net for the inverse Sierpinski tetrahedron
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